Tag Archives: research

Academic vs Applied Research


Academic Research

Academic research falls into two categories. These two categories are

  • Research ON your field
  • Research FOR your field







Applied Research


  • research IN your field


  • Formative
  • Monitoring
  • Summative





In education, applied research is also known as action research.




Primary Tasks in Data Analysis



  1. Developing  your question(s)
  2. Data exploration
  3. Developing a statistical model
  4. Interpreting the results
  5. Sharing the results

Developing Your Question(s)



Data Exploration




Develop a Statistical Model



Interpreting the Results



Communication of Results


  • The audience or stakeholders
  • The actual answers to the questions
  • The benefits of knowing this




Generalized Models in R

Generalized linear models are another way to approach linear regression. The advantage of of GLM is that allows the error to follow many different distributions rather than only the normal distribution which is an assumption of traditional linear regression.

Often GLM is used for response or dependent variables that are binary or represent count data. THis post will provide a brief explanation of GLM as well as provide an example.

Key Information

There are three important components to a GLM and they are

  • Error structure
  • Linear predictor
  • Link function

The error structure is the type of distribution you will use in generating the model. There are many different distributions in statistical modeling such as binomial, gaussian, poission, etc. Each distribution comes with certain assumptions that govern their use.

The linear predictor is the sum of the effects of the independent variables. Lastly, the link function determines the relationship between the linear predictor and the mean of the dependent variable. There are many different link functions and the best link function is the one that reduces the residual deviances the most.

In our example, we will try to predict if a house will have air conditioning based on the interactioon between number of bedrooms and bathrooms, number of stories, and the price of the house. To do this, we will use the “Housing” dataset from the “Ecdat” package. Below is some initial code to get started.


The dependent variable “airco” in the “Housing” dataset is binary. This calls for us to use a GLM. To do this we will use the “glm” function in R. Furthermore, in our example, we want to determine if there is an interaction between number of bedrooms and bathrooms. Interaction means that the two independent variables (bathrooms and bedrooms) influence on the dependent variable (aircon) is not additive, which means that the combined effect of the independnet variables is different than if you just added them together. Below is the code for the model followed by a summary of the results

model<-glm(Housing$airco ~ Housing$bedrooms * Housing$bathrms + Housing$stories + Housing$price, family=binomial)
## Call:
## glm(formula = Housing$airco ~ Housing$bedrooms * Housing$bathrms + 
##     Housing$stories + Housing$price, family = binomial)
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.7069  -0.7540  -0.5321   0.8073   2.4217  
## Coefficients:
## (Intercept)                      -6.441e+00  1.391e+00  -4.632 3.63e-06
## Housing$bedrooms                  8.041e-01  4.353e-01   1.847   0.0647
## Housing$bathrms                   1.753e+00  1.040e+00   1.685   0.0919
## Housing$stories                   3.209e-01  1.344e-01   2.388   0.0170
## Housing$price                     4.268e-05  5.567e-06   7.667 1.76e-14
## Housing$bedrooms:Housing$bathrms -6.585e-01  3.031e-01  -2.173   0.0298
## ---
##     Null deviance: 681.92  on 545  degrees of freedom
## Residual deviance: 549.75  on 540  degrees of freedom
## AIC: 561.75
## Number of Fisher Scoring iterations: 4

To check how good are model is we need to check for overdispersion as well as compared this model to other potential models. Overdispersion is a measure to determine if there is too much variablity in the model. It is calcualted by dividing the residual deviance by the degrees of freedom. Below is the solution for this

## [1] 1.018056

Our answer is 1.01, which is pretty good because the cutoff point is 1, so we are really close.

Now we will make several models and we will compare the results of them

Model 2

#add recroom and garagepl
model2<-glm(Housing$airco ~ Housing$bedrooms * Housing$bathrms + Housing$stories + Housing$price + Housing$recroom + Housing$garagepl, family=binomial)
## Call:
##     Housing$stories + Housing$price + Housing$recroom + Housing$garagepl, 
##     family = binomial)
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.6733  -0.7522  -0.5287   0.8035   2.4239  
## Coefficients:
## (Intercept)                      -6.369e+00  1.401e+00  -4.545 5.51e-06
## Housing$bedrooms                  7.830e-01  4.391e-01   1.783   0.0745
## Housing$bathrms                   1.702e+00  1.047e+00   1.626   0.1039
## Housing$stories                   3.286e-01  1.378e-01   2.384   0.0171
## Housing$price                     4.204e-05  6.015e-06   6.989 2.77e-12
## Housing$recroomyes                1.229e-01  2.683e-01   0.458   0.6470
## Housing$garagepl                  2.555e-03  1.308e-01   0.020   0.9844
## Housing$bedrooms:Housing$bathrms -6.430e-01  3.054e-01  -2.106   0.0352
## ---
##     Null deviance: 681.92  on 545  degrees of freedom
## Residual deviance: 549.54  on 538  degrees of freedom
## AIC: 565.54
## Number of Fisher Scoring iterations: 4
#overdispersion calculation
## [1] 1.02145

Model 3

model3<-glm(Housing$airco ~ Housing$bedrooms * Housing$bathrms + Housing$stories + Housing$price + Housing$recroom + Housing$fullbase + Housing$garagepl, family=binomial)
## Call:
##     Housing$garagepl, family = binomial)
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.6629  -0.7436  -0.5295   0.8056   2.4477  
## Coefficients:
## (Intercept)                      -6.424e+00  1.409e+00  -4.559 5.14e-06
## Housing$bedrooms                  8.131e-01  4.462e-01   1.822   0.0684
## Housing$bathrms                   1.764e+00  1.061e+00   1.662   0.0965
## Housing$stories                   3.083e-01  1.481e-01   2.082   0.0374
## Housing$price                     4.241e-05  6.106e-06   6.945 3.78e-12
## Housing$recroomyes                1.592e-01  2.860e-01   0.557   0.5778
## Housing$fullbaseyes              -9.523e-02  2.545e-01  -0.374   0.7083
## Housing$garagepl                 -1.394e-03  1.313e-01  -0.011   0.9915
## Housing$bedrooms:Housing$bathrms -6.611e-01  3.095e-01  -2.136   0.0327
## ---
##     Null deviance: 681.92  on 545  degrees of freedom
## Residual deviance: 549.40  on 537  degrees of freedom
## AIC: 567.4
## Number of Fisher Scoring iterations: 4
#overdispersion calculation
## [1] 1.023091

Now we can assess the models by using the “anova” function with the “test” argument set to “Chi” for the chi-square test.

anova(model, model2, model3, test = "Chi")
## Analysis of Deviance Table
## Model 1: Housing$airco ~ Housing$bedrooms * Housing$bathrms + Housing$stories + 
##     Housing$price
## Model 2: Housing$airco ~ Housing$bedrooms * Housing$bathrms + Housing$stories + 
##     Housing$price + Housing$recroom + Housing$garagepl
## Model 3: Housing$airco ~ Housing$bedrooms * Housing$bathrms + Housing$stories + 
##     Housing$price + Housing$recroom + Housing$fullbase + Housing$garagepl
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1       540     549.75                     
## 2       538     549.54  2  0.20917   0.9007
## 3       537     549.40  1  0.14064   0.7076

The results of the anova indicate that the models are all essentially the same as there is no statistical difference. The only criteria on which to select a model is the measure of overdispersion. The first model has the lowest rate of overdispersion and so is the best when using this criteria. Therefore, determining if a hous has air conditioning depends on examining number of bedrooms and bathrooms simultenously as well as the number of stories and the price of the house.


The post explained how to use and interpret GLM in R. GLM can be used primarilyy for fitting data to disrtibutions that are not normal.

Proportion Test in R

Proportions are are a fraction or “portion” of a total amount. For example, if there are ten men and ten women in a room the proportion of men in the room is 50% (5 / 10). There are times when doing an analysis that you want to evaluate proportions in our data rather than individual measurements of mean, correlation, standard deviation etc.

In this post we will learn how to do a test of proportions using R. We will use the dataset “Default” which is found in the “ISLR” pacakage. We will compare the proportion of those who are students in the dataset to a theoretical value. We will calculate the results using the z-test and the binomial exact test. Below is some initial code to get started.


We first need to determine the actual number of students that are in the sample. This is calculated below using the “table” function.

##   No  Yes 
## 7056 2944

We have 2944 students in the sample and 7056 people who are not students. We now need to determine how many people are in the sample. If we sum the results from the table below is the code.

## [1] 10000

There are 10000 people in the sample. To determine the proprtion of students we take the number 2944 / 10000 which equals 29.44 or 29.44%. Below is the code to calculate this

table(Default$student) / sum(table(Default$student))
##     No    Yes 
## 0.7056 0.2944

The proportion test is used to compare a particular value with a theoretical value. For our example, the particular value we have is 29.44% of the people were students. We want to compare this value with a theoretical value of 50%. Before we do so it is better to state specificallt what are hypotheses are. NULL = The value of 29.44% of the sample being students is the same as 50% found in the population ALTERNATIVE = The value of 29.44% of the sample being students is NOT the same as 50% found in the population.

Below is the code to complete the z-test.

prop.test(2944,n = 10000, p = 0.5, alternative = "two.sided", correct = FALSE)
##  1-sample proportions test without continuity correction
## data:  2944 out of 10000, null probability 0.5
## X-squared = 1690.9, df = 1, p-value < 2.2e-16
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
##  0.2855473 0.3034106
## sample estimates:
##      p 
## 0.2944

Here is what the code means. 1. prop.test is the function used 2. The first value of 2944 is the total number of students in the sample 3. n = is the sample size 4. p= 0.5 is the theoretical proportion 5. alternative =“two.sided” means we want a two-tail test 6. correct = FALSE means we do not want a correction applied to the z-test. This is useful for small sample sizes but not for our sample of 10000

The p-value is essentially zero. This means that we reject the null hypothesis and conclude that the proprtion of students in our sample is different from a theortical proprition of 50% in the population.

Below is the same analysis using the binomial exact test.

binom.test(2944, n = 10000, p = 0.5)
##  Exact binomial test
## data:  2944 and 10000
## number of successes = 2944, number of trials = 10000, p-value <
## 2.2e-16
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
##  0.2854779 0.3034419
## sample estimates:
## probability of success 
##                 0.2944

The results are the same. Whether to use the “prop.test”” or “binom.test” is a major argument among statisticians. The purpose here was to provide an example of the use of both

Probability Distribution and Graphs in R

In this post, we will use probability distributions and ggplot2 in R to solve a hypothetical example. This provides a practical example of the use of R in everyday life through the integration of several statistical and coding skills. Below is the scenario.

At a busing company the average number of stops for a bus is 81 with a standard deviation of 7.9. The data is normally distributed. Knowing this complete the following.

  • Calculate the interval value to use using the 68-95-99.7 rule
  • Calculate the density curve
  • Graph the normal curve
  • Evaluate the probability of a bus having less then 65 stops
  • Evaluate the probability of a bus having more than 93 stops

Calculate the Interval Value

Our first step is to calculate the interval value. This is the range in which 99.7% of the values falls within. Doing this requires knowing the mean and the standard deviation and subtracting/adding the standard deviation as it is multiplied by three from the mean. Below is the code for this.

## [1] 104.7
## [1] 57.3

The values above mean that we can set are interval between 55 and 110 with 100 buses in the data. Below is the code to set the interval.

interval<-seq(55,110, length=100) #length here represents 
100 fictitious buses

Density Curve

The next step is to calculate the density curve. This is done with our knowledge of the interval, mean, and standard deviation. We also need to use the “dnorm” function. Below is the code for this.


We will now plot the normal curve of our data using ggplot. Before we need to put our “interval” and “densityCurve” variables in a dataframe. We will call the dataframe “normal” and then we will create the plot. Below is the code.

normal<-data.frame(interval, densityCurve)
ggplot(normal, aes(interval, densityCurve))+geom_line()+ggtitle("Number of Stops for Buses")


Probability Calculation

We now want to determine what is the provability of a bus having less than 65 stops. To do this we use the “pnorm” function in R and include the value 65, along with the mean, standard deviation, and tell R we want the lower tail only. Below is the code for completing this.

pnorm(65,mean = 81,sd=7.9,lower.tail = TRUE)
## [1] 0.02141744

As you can see, at 2% it would be unusually to. We can also plot this using ggplot. First, we need to set a different density curve using the “pnorm” function. Combine this with our “interval” variable in a dataframe and then use this information to make a plot in ggplot2. Below is the code.

CumulativeProb<-pnorm(interval, mean=81,sd=7.9,lower.tail = TRUE)
pnormal<-data.frame(interval, CumulativeProb)
ggplot(pnormal, aes(interval, CumulativeProb))+geom_line()+ggtitle("Cumulative Density of Stops for Buses")


Second Probability Problem

We will now calculate the probability of a bus have 93 or more stops. To make it more interesting we will create a plot that shades the area under the curve for 93 or more stops. The code is a little to complex to explain so just enjoy the visual.

pnorm(93,mean=81,sd=7.9,lower.tail = FALSE)
## [1] 0.06438284
p<-ggplot(MyDF,aes(x,y))+geom_line()+scale_x_continuous(limits = c(50, 110))
+ggtitle("Probabilty of 93 Stops or More is 6.4%")
shade <- rbind(c(93,0), subset(MyDF, x > 93), c(MyDF[nrow(MyDF), "X"], 0))

p + geom_segment(aes(x=93,y=0,xend=93,yend=ytop)) +
        geom_polygon(data = shade, aes(x, y))



A lot of work was done but all in a practical manner. Looking at realistic problem. We were able to calculate several different probabilities and graph them accordingly.

Types of Mixed Method Design


  • Embedded design
  • Transformative design
  • Multi-phase design

Embedded Design




Transformative Design




Multiphase Design






Mixed Methods

Mix Methods research involves the combination of qualitative and quantitative approaches in addressing a research problem. Generally, qualitative and quantitative methods have separate philosophical positions when it comes to how to uncover insights in addressing research questions.

For many, mixed methods have their own philosophical position, which is pragmatism. Pragmatist believe that if it works it’s good. Therefore, if mixed methods leads to a solution it’s an appropriate method to use.

This post will try to explain some of the mixed method designs. Before explaining it is important to understand that there are several common ways to approach mixed methods

  • Qualitative and Quantitative are equal (Convergent Parallel Design)
  • Quantitative is more important than qualitative (explanatory design)
  • Qualitative is more important than quantitative

Convergent Parallel Design 

This design involves the simultaneous collecting of qualitative and quantitative data. The results are then compared to provide insights into the problem. The advantage of this design is the quantitative data provides for generalizability while the qualitative data provides information about the context of the study.

However, the challenge is in trying to merge the two types of data. Qualitative and quantitative methods answer slightly different questions about a problem. As such it can be difficult to pain a picture of the results that are comprehensible.

Explanatory Design

This design puts emphasis on the quantitative data with qualitative data playing a secondary role. Normally, the results found in the quantitative data are followed up on in the qualitative part.

For example, if you collect surveys about what students think about college and the results indicate negative opinions, you might conduct interview with students to understand way they are negative towards college. A likert survey will not explain why students are negative. Interviews will help to capture why students have a particular position.

The advantage of this approach is the clear organization of the data. Quantitative data is more important. The drawback is deciding what about the quantitative data to explore when conducting the qualitative data collection.

Exploratory Design 

This design is the opposite of explanatory. Now the qualitative data is more important than the quantitative. This design is used when you want to understand a phenomenon in order to measure it.

It is common when developing an instrument to interview people in focus groups to understand the phenomenon. For example, if I want to understand what cellphone addiction is I might ask students to share what they think about this in interviews. From there, I could develop a survey instrument to measure cell phone addiction.

The drawback to this approach is the time consumption. It takes a lot of work to conduct interviews, develop an instrument, and assess the instrument.


Mixed methods are not that new. However, they are still a somewhat unusual approach to research in many fields. Despite this, the approaches of mixed methods can be beneficial depending on the context.

Types of Machine Learning



Predictive Models and Supervised Learning







Descriptive Models and Unsupervised Learning





Intro to Using Machine Learning

Machine learning is about using data to take action. This post will explain common steps that are taking when using machine learning in the analysis of data. In general, there are five steps when applying machine learning.

  1. Collecting data
  2. Preparing data
  3. Exploring data
  4. Training a model on the data
  5. Assessing the performance of the model
  6. Improving the model

We will go through each step briefly

Step One, Collecting Data

Data can come from almost anywhere. Data can come from a database in a structured format like mySQL. Data can also come unstructured such as tweets collected from twitter. However you get the data, you need to develop a way to clean and process it so that it is ready for analysis.

There are some distinct terms used in machine learning that some coming from traditional research my not be familiar.

  • example-An example is one set of data. In an excel spreadsheet, an example would be one row. In empirical social science research we would call an example a respondent or participant.
  • Unit of observation-This is how an example is measured. The units can be time, money, height, weight, etc.
  • feature-A feature is a characteristic of an example. In other forms of research we normally call a feature a variable. For example, ‘salary’ would be a feature in machine learning but a variable in traditional research.

Step Two, Preparing Data

This is actually the most difficult step in machine learning analysis. It can take up to 80% of the time. With data coming from multiple sources and in multiple formats it is a real challenge to get everything where it needs to be for an analysis.

Missing data needs to be addressed, duplicate records, and other issues are a part of this process. Once these challenges are dealt with it is time to explore the data.

Step Three, Explore the Data

Before analyzing the data, it is critical that the data is explored. This is often done visually in the form of plots and graphs but also with summary statistics. You are looking for some insights into the data and the characteristics of different features. You are also looking out for things that might be unusually such as outliers. There are also times when a variable needs to be transformed because there are issues with normality.

Step Four, Training a Model

After exploring the data, you should have an idea of what you want to know if you did not already know. Determining what you want to know helps you to decide which algorithm is most appropriate for developing a model.

To develop a model, we normally split the data into a training and testing set. This allows us to assess the model for its strengths and weaknesses.

Step Five, Assessing the Model

The strength of the model is deteremined. Every model has certain biases that limits its usefulness. How to assess a model depends on what type of model is developed and the purpose of the analysis. Whenever suitable, we want to try and improve the model.

Step Six, Improving the Model

Improve can happen in many ways. You might decide to normalize the variables in a different way. Or you may choose to add or remove features from the model. Perhaps you may switch to a different model.


Success in data analysis involves have a clear path for achieving your goals. The steps presented here provide one way of tackling machine learning.

Logistic Regression in R

Logistic regression is used when the dependent variable is categorical with two choices. For example, if we want to predict whether someone will default on their loan. The dependent variable is categorical with two choices yes they default and no they do not.

Interpreting the output of a logistic regression analysis can be tricky. Basically, you need to interpret the odds ratio. For example, if the results of a study say the odds of default are 40% higher when someone is unemployed it is an increase in the likelihood of something happening. This is different from the probability which is what we normally use. Odds can go from any value from negative infinity to positive infinity. Probability is constrained to be anywhere from 0-100%.

We will now take a look at a simple example of logistic regression in R. We want to calculate the odds of defaulting on a loan. The dependent variable is “default” which can be either yes or no. The independent variables are “student” which can be yes or no, “income” which how much the person made, and “balance” which is the amount remaining on their credit card.

Below is the coding for developing this model.

The first step is to load the “Default” dataseat. This dataseat is a part of the “ISLR” package. Below is the code to get started


It is always good to examine the data first before developing a model. We do this by using the ‘summary’ function as shown below.

##  default    student       balance           income     
##  No :9667   No :7056   Min.   :   0.0   Min.   :  772  
##  Yes: 333   Yes:2944   1st Qu.: 481.7   1st Qu.:21340  
##                        Median : 823.6   Median :34553  
##                        Mean   : 835.4   Mean   :33517  
##                        3rd Qu.:1166.3   3rd Qu.:43808  
##                        Max.   :2654.3   Max.   :73554

We now need to check our two continuous variables “balance” and “income” to see if they are normally distributed. Below is the code followed by the histograms.





The ‘income’ variable looks fine but there appear to be some problems with ‘balance’ to deal with this we will perform a square root transformation on the ‘balance’ variable and then examine it again by looking at a histogram. Below is the code.



As you can see this is much better looking.

We are now ready to make our model and examine the results. Below is the code.

Credit_Model<-glm(default~student+sqrt_balance+income, family=binomial, Default)
## Call:
## glm(formula = default ~ student + sqrt_balance + income, family = binomial, 
##     data = Default)
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2656  -0.1367  -0.0418  -0.0085   3.9730  
## Coefficients:
## (Intercept)  -1.938e+01  8.116e-01 -23.883  < 2e-16 ***
## studentYes   -6.045e-01  2.336e-01  -2.587  0.00967 ** 
## sqrt_balance  4.438e-01  1.883e-02  23.567  < 2e-16 ***
## income        3.412e-06  8.147e-06   0.419  0.67538    
## ---
##     Null deviance: 2920.6  on 9999  degrees of freedom
## Residual deviance: 1574.8  on 9996  degrees of freedom
## AIC: 1582.8
## Number of Fisher Scoring iterations: 9

The results indicate that the variable ‘student’ and ‘sqrt_balance’ are significant. However, ‘income’ is not significant. What all this means in simple terms is that being a student and having a balance on your credit card influence the odds of going into default while your income makes no difference. Unlike, multiple regression coefficients, the logistic coefficients require a transformation in order to interpret them The statistical reason for this is somewhat complicated. As such, below is the code to interpret the logistic regression coefficients.

##  (Intercept)   studentYes sqrt_balance       income 
## 3.814998e-09 5.463400e-01 1.558568e+00 1.000003e+00

To explain this as simply as possible. You subtract 1 from each coefficient to determine the actually odds. For example, if a person is a student the odds of them defaulting are 445% higher than when somebody is not a student when controlling for balance and income. Furthermore, for every 1 unit increase in the square root of the balance the odds of default go up by 55% when controlling for being a student and income. Naturally, speaking in terms of a 1 unit increase in the square root of anything is confusing. However, we had to transform the variable in order to improve normality.


Logistic regression is one approach for predicting and modeling that involves a categorical dependent variable. Although the details are little confusing this approach is valuable at times when doing an analysis.

Kruskal-Willis Test in R

Sometimes when the data that needs to be analyzed is not normally distributed. This makes it difficult to make any inferences based on the results because one of the main assumptions of parametric statistical test such as ANOVA, t-test, etc is normal distribution of the data.

Fortunately, for every parametric test there is a non-parametric test. Non-parametric test are test that make no assumptions about the normality of the data. This means that the non-normal data can still be analyzed with a certain measure of confidence in terms of the results.

This post will look at non-parametric test that are used to test the difference in means. For three or more groups we used the Kruskal-Wallis Test. The Kruskal-Wallis Test is the non-parametric version of ANOVA.



We are going to use the “ISLR” package available on R to demonstrate the use of the Kruskal-Wallis test. After downloading this package you need to load the “Auto” data. Below is the code to do all of this.


We now need to examine the structure of the data set. This is done with the “str” function below is code followed by the results

'data.frame':	392 obs. of  9 variables:
 $ mpg         : num  18 15 18 16 17 15 14 14 14 15 ...
 $ cylinders   : num  8 8 8 8 8 8 8 8 8 8 ...
 $ displacement: num  307 350 318 304 302 429 454 440 455 390 ...
 $ horsepower  : num  130 165 150 150 140 198 220 215 225 190 ...
 $ weight      : num  3504 3693 3436 3433 3449 ...
 $ acceleration: num  12 11.5 11 12 10.5 10 9 8.5 10 8.5 ...
 $ year        : num  70 70 70 70 70 70 70 70 70 70 ...
 $ origin      : num  1 1 1 1 1 1 1 1 1 1 ...
 $ name        : Factor w/ 304 levels "amc ambassador brougham",..: 49 36 231 14 161 141 54 223 241 2 ...

So we have 9 variables. We first need to find if any of the continuous variables are non-normal because this indicates that the Kruskal-Willis test is needed. We will look at the ‘displacement’ variable and look at the histogram to see if it is normally distributed. Below is the code followed by the histogram


This does not look normally distributed. We now need a factor variable with 3 or more groups. We are going to use the ‘origin’ variable. This variable indicates were the care was made 1 = America, 2 = Europe, and 3 = Japan. However, this variable is currently a numeric variable. We need to change it into a factor variable. Below is the code for this


The Test

We will now use the Kruskal-Wallis test. The question we have is “is there a difference in displacement based on the origin of the vehicle?” The code for the analysis is below followed by the results.

> kruskal.test(displacement ~ origin, data = Auto)

	Kruskal-Wallis rank sum test

data:  displacement by origin
Kruskal-Wallis chi-squared = 201.63, df = 2, p-value < 2.2e-16

Based on the results, we know there is a difference among the groups. However, just like ANOVA, we do not know were. We have to do a post-hoc test in order to determine where the difference in means is among the three groups.

To do this we need to install a new package and do a new analysis. We will download the “PCMR” package and run the code below

posthoc.kruskal.nemenyi.test(x=displacement, g=origin, dist='Tukey')

Here is what we did,

  1. Installed the PMCMR package and loaded it
  2. Loaded the “Auto” data and used the “attach” function to make it available
  3. Ran the function “posthoc.kruskal.nemenyi.test” and place the appropriate variables in their place and then indicated the type of posthoc test ‘Tukey’

Below are the results

Pairwise comparisons using Tukey and Kramer (Nemenyi) test	
                   with Tukey-Dist approximation for independent samples 

data:  displacement and origin 

  1       2   
2 3.4e-14 -   
3 < 2e-16 0.51

P value adjustment method: none 
Warning message:
In posthoc.kruskal.nemenyi.test.default(x = displacement, g = origin,  :
  Ties are present, p-values are not corrected.

The results are listed in a table. When a comparison was made between group 1 and 2 the results were significant (p < 0.0001). The same when group 1 and 3 are compared (p < 0.0001).  However, there was no difference between group 2 and 3 (p = 0.51).

Do not worry about the warning message this can be corrected if necessary

Perhaps you are wondering what the actually means for each group is. Below is the code with the results

> aggregate(Auto[, 3], list(Auto$origin), mean)
  Group.1        x
1       1 247.5122
2       2 109.6324
3       3 102.7089

Cares made in America have an average displacement of 247.51 while cars from Europe and Japan have a displacement of 109.63 and 102.70. Below is the code for the boxplot followed by the graph

boxplot(displacement~origin, data=Auto, ylab= 'Displacement', xlab='Origin')
title('Car Displacement')



This post provided an example of the Kruskal-Willis test. This test is useful when the data is not normally distributed. The main problem with this test is that it is less powerful than an ANOVA test. However, this is a problem with most non-parametric test when compared to parametric test.

Data Mining Process

Processes serve the purpose of providing people with a clear step-by-step procedures to accomplish a task. In many ways a process serves as a shortcut in solving a problem. As data mining is a complex situation with an endless number of problems there have been developed several processes for completing a data mining project. In this post we will look at the Cross-Industry Standard Process for Data Mining (CRISP-DM).



  1. Organizational understanding
  2. Data understanding
  3. Data preparation
  4. Modeling
  5. Evaluation
  6. Deployment

We will look at each step briefly

  1. Organizational Understanding


2. Data Understanding

Once a purpose and questions have been developed for data mining, it is necessary to determine what it will take to answer the questions. Specifically, the data scientist assess the data requirements, description, collection, and assesses data quality. In many ways, data understanding is similar to methodology of a standard research paper in which you assess how you will answer the research questions.

It is particularly common to go back and forth between steps one and two. Organizational understanding influences data understanding which influences data under standing.

3. Data Preparation


4. Modeling


5. Evaluation

Evaluation is about comparing the results of the study with the original questions. In many ways it is about determining the appropriateness of the answers to the research questions. This experience leads to ideas for additional research. As such, this step is similar to the discussion section of a research paper.

6. Deployment




Big Data & Data Mining

Dealing with large amounts of data has been a problem throughout most of human history. Ancient civilizations had to keep large amounts of clay tablets, papyrus, steles, parchments, scrolls etc. to keep track of all the details of an empire.

However, whenever it seemed as though there would be no way to hold any more information a new technology would be developed to alleviate the problem. When people could not handle keeping records on stone paper scrolls were invented. When scrolls were no longer practical books were developed. When hand-copying books were too much the printing press came along.

By the mid 20th century there were concerns that we would not be able to have libraries large enough to keep all of the books that were being developed. With this problem came the solution of the computer. One computer could hold the information of several dozen if not hundreds of libraries.

Now even a single computer can no longer cope with all of the information that is constantly being developed for just a single subject. This has lead to computers working together in networks to share the task of storing information. With data spread across several computers, it makes analyzing data much more challenging. It was now necessary to mine for useful information in a way that people used to mine for gold in the 19th century.

Big data is data that is too large to fit within the memory of a single computer. Analyzing data that is spread across a network of databases takes skills different from traditional statistical analysis. This post will explain some of the characteristics of big data as well as data mining.

Big Data Traits

The three main traits of big data are volume, velocity, and variety. Volume describes the size of big data, which means data to big to be on only one computer. Velocity is about how fast the data can be processed. Lastly, variety different types of data. common sources of big data includes the following

  • Metadata from visual sources such as cameras
  • Data from sensors such as in medical equipment
  • Social media data such as information from google, youtube or facebook

Data Mining

Data mining is the process of discovering a model in a big dataset. Through the development of an algorithm, we can find specific information that helps us to answer our questions. Generally, there are two ways to mine data and these are extraction and summarization.

Extraction is the process of pulling specific information from a big dataset. For example, if we want all the addresses of people who bought a specific book from Amazon the result would be an extraction from a big data set.

Summarization is reducing a dataset to describe it. We might do a cluster analysis in which similar data is combined on a characteristic. For example, if we analyze all the books people ordered through Amazon last year we might notice that one cluster of groups buys mostly religious books while another buys investment books.


Big data will only continue to get bigger. Currently, the response has been to just use more computers and servers. As such, there is now a need for finding information on many computers and servers. This is the purpose of data mining, which is to find pertinent information that answers stakeholders questions.

Decision Trees in R

Decision trees are useful for splitting data based into smaller distinct groups based on criteria you establish. This post will attempt to explain how to develop decision trees in R.

We are going to use the ‘College’ dataset found in the “ISLR” package. Once you load the package you need to split the data into a training and testing set as shown in the code below. We want to divide the data based on education level, age, and income

library(ISLR); library(ggplot2); library(caret)
 p=0.7, list=FALSE)
trainingset <- College[inTrain, ]
testingset <- College[-inTrain, ]

Visualize the Data

We will now make a plot of the data based on education as the groups and age and wage as the x and y variable. Below is the code followed by the plot. Please note that education is divided into 5 groups as indicated in the chart.

qplot(age, wage, colour=education, data=trainingset)
Create the Model

We are now going to develop the model for the decision tree. We will use age and wage to predict education as shown in the code below.

TreeModel<-train(education~age+income, method='rpart', data=trainingset)

Create Visual of the Model

We now need to create a visual of the model. This involves installing the package called ‘rattle’. You can install ‘rattle’ separately yourself. After doing this below is the code for the tree model followed by the diagram.



Here is what the chart means

  1. At the top is node 1 which is called ‘HS Grad” the decimals underneath is the percentage of the data that falls within the “HS Grad” category. As the highest node, everything is classified as “HS grad” until we begin to apply our criteria.
  2. Underneath nod 1 is a decision about wage. If a person makes less than 112 you go to the left if they make more you go to the right.
  3. Nod 2 indicates the percentage of the sample that was classified as HS grade regardless of education. 14% of those with less than a HS diploma were classified as a HS Grade based on wage. 43% of those with a HS diploma were classified as a HS grade based on income. The percentage underneath the decimals indicates the total amount of the sample placed in the HS grad category. Which was 57%.
  4. This process is repeated for each node until the data is divided as much as possible.


You can predict individual values in the dataset by using the ‘predict’ function with the test data as shown in the code below.

predict(TreeModel, newdata = testingset)


Prediction Trees are a unique feature in data analysis for determining how well data can be divided into subsets. It also provides a visual of how to move through data sequentially based on characteristics in the data.

Using Plots for Prediction in R

It is common in machine learning to look at the training set of your data visually. This helps you to decide what to do as you begin to build your model.  In this post, we will make several different visual representations of data using datasets available in several R packages.

We are going to explore data in the “College” dataset in the “ISLR” package. If you have not done so already, you need to download the “ISLR” package along with “ggplot2” and the “caret” package.

Once these packages are installed in R you want to look at a summary of the variables use the summary function as shown below.


You should get a printout of information about 18 different variables. Based on this printout, we want to explore the relationship between graduation rate “Grad.Rate” and student to faculty ratio “S.F.Ratio”. This is the objective of this post.

Next, we need to create a training and testing dataset below is the code to do this.

> library(ISLR);library(ggplot2);library(caret)
> data("College")
> PracticeSet<-createDataPartition(y=College$Enroll, p=0.7, +                                  list=FALSE) > trainingSet<-College[PracticeSet,] > testSet<-College[-PracticeSet,] > dim(trainingSet); dim(testSet)
[1] 545  18
[1] 232  18

The explanation behind this code was covered in predicting with caret so we will not explain it again. You just need to know that the dataset you will use for the rest of this post is called “trainingSet”.

Developing a Plot

We now want to explore the relationship between graduation rates and student to faculty ratio. We will be used the ‘ggpolt2’  package to do this. Below is the code for this followed by the plot.

qplot(S.F.Ratio, Grad.Rate, data=trainingSet)
As you can see, there appears to be a negative relationship between student faculty ratio and grad rate. In other words, as the ration of student to faculty increases there is a decrease in the graduation rate.

Next, we will color the plots on the graph based on whether they are a public or private university to get a better understanding of the data. Below is the code for this followed by the plot.

> qplot(S.F.Ratio, Grad.Rate, colour = Private, data=trainingSet)
It appears that private colleges usually have lower student to faculty ratios and also higher graduation rates than public colleges

Add Regression Line

We will now plot the same data but will add a regression line. This will provide us with a visual of the slope. Below is the code followed by the plot.

> collegeplot<-qplot(S.F.Ratio, Grad.Rate, colour = Private, data=trainingSet) > collegeplot+geom_smooth(method = ‘lm’,formula=y~x)
Most of this code should be familiar to you. We saved the plot as the variable ‘collegeplot’. In the second line of code, we add specific coding for ‘ggplot2’ to add the regression line. ‘lm’ means linear model and formula is for creating the regression.

Cutting the Data

We will now divide the data based on the student-faculty ratio into three equal size groups to look for additional trends. To do this you need the “Hmisc” packaged. Below is the code followed by the table

> library(Hmisc)
> divide_College<-cut2(trainingSet$S.F.Ratio, g=3)
> table(divide_College)
[ 2.9,12.3) [12.3,15.2) [15.2,39.8] 
        185         179         181

Our data is now divided into three equal sizes.

Box Plots

Lastly, we will make a box plot with our three equal size groups based on student-faculty ratio. Below is the code followed by the box plot

CollegeBP<-qplot(divide_College, Grad.Rate, data=trainingSet, fill=divide_College, geom=c(“boxplot”)) > CollegeBP
As you can see, the negative relationship continues even when student-faculty is divided into three equally size groups. However, our information about private and public college is missing. To fix this we need to make a table as shown in the code below.

> CollegeTable<-table(divide_College, trainingSet$Private)
> CollegeTable
divide_College  No Yes
   [ 2.9,12.3)  14 171
   [12.3,15.2)  27 152
   [15.2,39.8] 106  75

This table tells you how many public and private colleges there based on the division of the student-faculty ratio into three groups. We can also get proportions by using the following

> prop.table(CollegeTable, 1)
divide_College         No        Yes
   [ 2.9,12.3) 0.07567568 0.92432432
   [12.3,15.2) 0.15083799 0.84916201
   [15.2,39.8] 0.58563536 0.41436464

In this post, we found that there is a negative relationship between student-faculty ratio and graduation rate. We also found that private colleges have a lower student-faculty ratio and a higher graduation rate than public colleges. In other words, the status of a university as public or private moderates the relationship between student-faculty ratio and graduation rate.

You can probably tell by now that R can be a lot of fun with some basic knowledge of coding.

Simple Prediction

Prediction is one of the key concepts of machine learning. Machine learning is a field of study that is focused on the development of algorithms that can be used to make predictions.

Anyone who has shopped online at has experienced machine learning. When you make a purchase at an online store, the website will recommend additional purchases for you to make. Often these recommendations are based on whatever you have purchased or whatever you click on while at the site.

There are two common forms of machine learning, unsupervised and supervised learning. Unsupervised learning involves using data that is not cleaned and labeled and attempts are made to find patterns within the data. Since the data is not labeled, there is no indication into what is right or wrong

Supervised machine learning is using cleaned and properly labeled data. Since the data is labeled there is some form of indication whether the model that is developed is accurate or not. If the is incorrect then you need to make adjustments to it. In other words, the model learns based on its ability to accurately predict results. However, it is up to the human to make adjustments to the model in order to improve the accuracy of it.

In this post we will look at using R for supervised machine learning. The definition presented so far will make more sense with an example.

The Example

We are going to make a simple prediction about whether emails are spam or not using data from kern lab.

The first thing that you need to do is to install and load the “kernlab” package using the following code


If you use the “View” function to examine the data you will see that there are several columns. Each column tells you the frequency of a word that kernlab found in a collection of emails. We are going to use the word/variable “money” to predict whether an email is spam or not. First we need to plot the density of the use of the word “money” when the email was not coded as spam. Below is the code for this.

 col='blue',main="", xlab="Frequency of 'money'")

This is an advance R post so I am assuming you can read the code. The plot should look like the following.


As you can see, money is not used to frequently in emails  that are not spam in this dataset. However, you really cannot say this unless you compare the times ‘money’ is labeled nonspam to the times that it is labeled spam. To learn this we need to add a second line that explains to us when the word ‘money’ is used and classified as spam. The code for this is below with the prior code included.

lines(density(spam$money[spam$type=="spam"]), col="red")

Your new plot should look like the following


If you look closely at the plot doing a visual inspection, where there is a separation between the blue line for non spam and the red line for spam is the cutoff point for whether an email is spam or not. In other words, everything inside the arc is labeled correctly while the information outside the arc is not.

The next code and graph show that this cutoff point is around 0.1. This means that any email that has on average more than 0.1 frequency of the word ‘money’ is spam. Below is the code and the graph with the cutoff point indicated with a black line.

abline(v=0.1, col="black", lw= 3)

Rplot10.jpeg Now we need to calculate the accuracy of the use of the word ‘money’ to predict spam. For our current example we will simply use in “ifelse” function. If the frequency is greater than 0.1.

We then need to make a table to see the results. The code for the “ifelse” function and the table are below followed by the table.

predict<-ifelse(spam$money > 0.1, "spam","nonspam")
table(predict, spam$type)/length(spam$type)
predict       nonspam        spam
  nonspam 0.596392089 0.266898500
  spam    0.009563138 0.127146273

Based on the table that I am assuming you can read, our model accurately calculates that an email is spam about 71% (0.59 + 0.12) of the time based on the frequency of the word ‘money’ being greater than 0.1.

Off course, for this to be true machine learning we would repeat this process by trying to improve the accuracy of the prediction. However, this is an adequate introduction to this topic.

Survey Design

Survey design is used to describe the opinions, beliefs, behaviors, and or characteristics of a population based on the results of a sample. This design involves the use of surveys that include questions, statements, and or other ways of soliciting information from the sample. This design is used for descriptive purpose primarily but can be combined with other designs (correlational, experimental) at times as well. In this post we will look at the following.

  • Types of Survey Design
  • Characteristics of Survey Design

Types of Survey Design

There are two common forms of survey design which are cross-sectional and longitudinal.   A cross-sectional survey design is the collection of data at one specific point in time. Data is only collected once in a cross-sectional design.

A cross-sectional design can be used to measure opinions/beliefs, compare two or more groups, evaluate a program, and or measure the needs of a specific group. The main goal is to analyze the data from a sample at a given moment in time.

A longitudinal design is similar to a cross-sectional design with the difference being that longitudinal designs require collection over time.Longitudinal studies involve cohorts and panels in which data is collected over days, months, years, and even decades. Through doing this, a longitudinal study is able to expose trends over time in a sample.

Characteristics of Survey Design

There are certain traits that are associated with survey design. Questionnaires and interviews are a common component of survey design. The questionnaires can happen by mail, phone, internet, and in person. Interviews can happen by phone, in focus groups, or one-on-one.

The design of a survey instrument often includes personal, behavioral and attitudinal questions, and open/closed questions.

Another important characteristic of survey design is monitoring the response rate. The response rate is the percentage of participants in the study compared to the number of surveys that were distributed. The response rate varies depending on how the data was collected. Normally, personal interviews have the highest rate while email request have the lowest.

It is sometimes necessary to report the response rate when trying to publish. As such, you should at the very least be aware of what the rate is for a study you are conducting.


Surveys are used to collected data at one point in time or over time. The purpose of this approach is develop insights into the population in order to describe what is happening or to be used to make decisions and inform practice.


Intro to Making Plots in R

One of the strongest points of R in the opinion of many are the various features for creating graphs and other visualizations of data. In this post, we begin to look at using the various visualization features of R. Specifically, we are going to do the following

  • Using data in R to display graph
  • Add text to a graph
  • Manipulate the appearance of data in a graph

Using Plots

The ‘plot’ function is one of the basic options for graphing data. We are going to go through an example using the ‘islands’ data that comes with the R software. The ‘islands’ software includes lots of data, in particular, it contains data on the lass mass of different islands. We want to plot the land mass of the seven largest islands. Below is the code for doing this.

islandgraph<-head(sort(islands, decreasing=TRUE), 7)
plot(islandgraph, main = "Land Area", ylab = "Square Miles")
text(islandgraph, labels=names(islandgraph), adj=c(0.5,1))

Here is what we did

  1. We made the variable ‘islandgraph’
  2. In the variable ‘islandgraph’ We used the ‘head’ and the ‘sort’ function. The sort function told R to sort the ‘island’ data by decreasing value ( this is why we have the decreasing argument equaling TRUE). After sorting the data, the ‘head’ function tells R to only take the first 7 values of ‘island’ (see the 7 in the code) after they are sorted by decreasing order.
  3. Next, we use the plot function to plot are information in the ‘islandgraph’ variable. We also give the graph a title using the ‘main’ argument followed by the title. Following the title, we label the y-axis using the ‘ylab’ argument and putting in quotes “Square Miles”.
  4. The last step is to add text to the information inside the graph for clarity. Using the ‘text’ function, we tell R to add text to the ‘islandgraph’ variable using the names from the ‘islandgraph’ data which uses the code ‘label=names(islandgraph)’. Remember the ‘islandgraph’ data is the first 7 islands from the ‘islands’ dataset.
  5. After telling R to use the names from the islandgraph dataset we then tell it to place the label a little of center for readability reasons with the code ‘adj = c(0.5,1).

Below is what the graph should look like.


Changing Point Color and Shape in a Graph

For visual purposes, it may be beneficial to manipulate the color and appearance of several data points in a graph. To do this, we are going to use the ‘faithful’ dataset in R. The ‘faithful’ dataset indicates the length of eruption time and how long people had to wait for the eruption. The first thing we want to do is plot the data using the “plot” function.


As you see the data, there are two clear clusters. One contains data from 1.5-3 and the second cluster contains data from 3.5-5. To help people to see this distinction we are going to change the color and shape of the data points in the 1.5-3 range. Below is the code for this.

eruption_time<-with(faithful, faithful[eruptions < 3, ])
points(eruption_time, col = "blue", pch = 24)

Here is what we did

  1. We created a variable named ‘eruption_time’
  2. In this variable, we use the ‘with’ function. This allows us to access columns in the dataframe without having to use the $ sign constantly. We are telling R to look at the ‘faithful’ dataframe and only take the information from faithful that has eruptions that are less than 3. All of this is indicated in the first line of code above.
  3. Next, we plot ‘faithful’ again
  4. Last, we add the points from are ‘eruption_time’ variable and we tell R to color these points blue and to use a different point shape by using the ‘pch = 24’ argument
  5. The results are below



In this post, we learned the following

  • How to make a graph
  • How to add a title and label the y-axis
  • How to change the color and shape of the data points in a graph

Simple Regression in R

In this post, we will look at how to perform a simple regression using R. We will use a built-in dataset in R called ‘mtcars.’ There are several variables in this dataset but we will only use ‘wt’ which stands for the weight of the cars and ‘mpg’ which stands for miles per gallon.

Developing the Model

We want to know the association or relationship between the weight of a car and miles per gallon. We want to see how much of the variance of ‘mpg’ is explained by ‘wt’. Below is the code for this.

> Carmodel <- lm(mpg ~ wt, data = mtcars)


Here is what we did

  1. We created the variable ‘Carmodel’ to store are information
  2. Inside this variable, we used the ‘lm’ function to tell R to make a linear model.
  3. Inside the function, we put ‘mpg ~ wt’ the ‘~’ sign means ’tilda’ in English and is used to indicate that ‘mpg’ is a function of ‘wt’. This section is the actual notation for the regression model.
  4. After the comma, we see ‘data = mtcars’ this is telling R to use the ‘mtcar’ dataset.

Seeing the Results

Once you pressed enter you probably noticed nothing happens. The model ‘Carmodel’ was created but the results have not been displayed. Below is various information you can extract from your model.

The ‘summary’ function is useful for pulling most of the critical information. Below is the code for the output.

> summary(Carmodel)

lm(formula = mpg ~ wt, data = mtcars)

    Min      1Q  Median      3Q     Max 
-4.5432 -2.3647 -0.1252  1.4096  6.8727 

(Intercept)  37.2851     1.8776  19.858  < 2e-16 ***
wt           -5.3445     0.5591  -9.559 1.29e-10 ***

Residual standard error: 3.046 on 30 degrees of freedom
Multiple R-squared:  0.7528,	Adjusted R-squared:  0.7446 
F-statistic: 91.38 on 1 and 30 DF,  p-value: 1.294e-10


We are not going to explain the details of the output (please see simple regression). The results indicate a model that explains 75% of the variance or has an r-square of 0.75. The model is statistically significant and the equation of the model is -5.45x + 37.28 = y

Plotting the Model

We can also plot the model using the code below

> coef_Carmodel<-coef(Carmodel)
> plot(mpg ~ wt, data = mtcars)
> abline(a = coef_Carmodel[1], b = coef_Carmodel[2])


Here is what we did

  1. We made the variable ‘coef_Carmodel’ and stored the coefficients (intercept and slope) of the ‘Carmodel’ using the ‘coef’ function. We will need this information soon.
  2. Next, we plot the ‘mtcars’ dataset using ‘mpg’ and ‘wt’.
  3. To add the regression line we use the ‘abline’ function. To add the intercept and slope we use a = the intercept from our ‘coef_Carmodel’ variable which is subset [1] from this variable. For slope, we follow the same process but use a [2]. This will add the line and your graph should look like the following.


From the visual, you can see that as weight increases there is a decrease in miles per gallon.


R is capable of much more complex models than the simple regression used here. However, understanding the coding for simple modeling can help in preparing you for much more complex forms of statistical modeling.

Experimental Design: Within Groups

Within groups, experimental design is the use of only one group in an experiment. This is in contrast to a between-group design which involves two or more groups. Within-group design is useful when the number of is two low in order to split them into different groups.

There are two common forms of within-group experimental design, time-series, and repeated measures. Under time series there are interrupted times series and equivalent time series. Under repeated-measure, there is only repeated measure design. In this post, we will look at the following forms of within-group experimental design.

  • interrupted time series
  • equivalent time series
  • repeated measures design

Interrupted Time Series Design

Interrupted time series design involves several pre-tests followed by an intervention and then several post-test of one group. By measuring the several times, many threats to internal validity are reduced, such as regression, maturation, and selection. The pre-test results are also used as covariates when analyzing the post-tests.

Equivalent Time Series Design

Equivalent time series design involves the use of a measurement followed by intervention followed by measurement etc. In many ways, this design is a repeated post-test only design. The primary goal is to plot the results of the post-test and determine if there is a pattern that develops over time.

For example, if you are tracking the influence of blog writing on vocabulary acquisition, the intervention is blog writing and the dependent variable is vocabulary acquisition. As the students write a blog, you measure them several times over a certain period. If a plot indicates an upward trend you could infer that blog writing made a difference in vocabulary acquisition.

Repeated Measures

Repeated measures is the use of several different treatments over time. Before each treatment, the group is measured. Each post-test is compared to other post-test to determine which treatment was the best.

For example, let’s say that you still want to assess vocabulary acquisition but want to see how blog writing and public speaking affect it. First, you measure vocabulary acquisition. Next, you employ the first intervention followed by a second assessment of vocabulary acquisition. Third, you use the public speaking intervention followed by the third assessment of vocabulary acquisition. You now have three parts of data to compare

  1. The first assessment of vocabulary acquisition (a pre-test)
  2. The second assessment of vocabulary acquisition (post-test 1 after the blog writing)
  3. The third assessment of vocabulary acquisition (post-test 2 after the public speaking)


Within-group experimental designs are used when it is not possible to have several groups in an experiment. The benefits include needing fewer participants. However, one problem with this approach is the need to measure several times which can be labor intensive.

ANOVA with R

Analysis of variance (ANOVA) is used when you want to see if there is a difference in the means of three or more groups due to some form of treatment(s). In this post, we will look at conducting an ANOVA calculation using R.

We are going to use a dataset that is already built into R called ‘InsectSprays.’ This dataset contains information on different insecticides and their ability to kill insects. What we want to know is which insecticide was the best at killing insects.

In the dataset ‘InsectSprays’, there are two variables, ‘count’, which is the number of dead bugs, and ‘spray’ which is the spray that was used to kill the bug. For the ‘spray’ variable there are six types label A-F. There are 72 total observations for the six types of spray which comes to about 12 observations per spray.

Building the Model

The code for calculating the ANOVA is below

> BugModel<- aov(count ~ spray, data=InsectSprays)
> BugModel
   aov(formula = count ~ spray, data = InsectSprays)

                   spray Residuals
Sum of Squares  2668.833  1015.167
Deg. of Freedom        5        66

Residual standard error: 3.921902
Estimated effects may be unbalanced

Here is what we did

  1. We created the variable ‘BugModel’
  2. In this variable, we used the function ‘aov’ which is the ANOVA function.
  3. Within the ‘aov’ function we told are to determine the count by the difference sprays that is what the ‘~’ tilde operator does.
  4. After the comma, we told R what dataset to use which was “InsectSprays.”
  5. Next, we pressed ‘enter’ and nothing happens. This is because we have to make R print the results by typing the name of the variable “BugModel” and pressing ‘enter’.
  6. The results do not tell us anything too useful yet. However, now that we have the ‘BugModel’ saved we can use this information to find the what we want.

Now we need to see if there are any significant results. To do this we will use the ‘summary’ function as shown in the script below

> summary(BugModel)
            Df Sum Sq Mean Sq F value Pr(>F)    
spray        5   2669   533.8    34.7 <2e-16 ***
Residuals   66   1015    15.4                   

These results indicate that there are significant results in the model as shown by the p-value being essentially zero (Pr(>F)). In other words, there is at least one mean that is different from the other means statistically.

We need to see what the means are overall for all sprays and for each spray individually. This is done with the following script

> model.tables(BugModel, type = 'means')
Tables of means
Grand mean

     A      B      C      D      E      F 
14.500 15.333  2.083  4.917  3.500 16.667

The ‘model.tables’ function tells us the means overall and for each spray. As you can see, it appears spray F is the most efficient at killing bugs with a mean of 16.667.

However, this table does not indicate the statistically significance. For this we need to conduct a post-hoc Tukey test. This test will determine which mean is significantly different from the others. Below is the script

> BugSpraydiff<- TukeyHSD(BugModel)
> BugSpraydiff
  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = count ~ spray, data = InsectSprays)

           diff        lwr       upr     p adj
B-A   0.8333333  -3.866075  5.532742 0.9951810
C-A -12.4166667 -17.116075 -7.717258 0.0000000
D-A  -9.5833333 -14.282742 -4.883925 0.0000014
E-A -11.0000000 -15.699409 -6.300591 0.0000000
F-A   2.1666667  -2.532742  6.866075 0.7542147
C-B -13.2500000 -17.949409 -8.550591 0.0000000
D-B -10.4166667 -15.116075 -5.717258 0.0000002
E-B -11.8333333 -16.532742 -7.133925 0.0000000
F-B   1.3333333  -3.366075  6.032742 0.9603075
D-C   2.8333333  -1.866075  7.532742 0.4920707
E-C   1.4166667  -3.282742  6.116075 0.9488669
F-C  14.5833333   9.883925 19.282742 0.0000000
E-D  -1.4166667  -6.116075  3.282742 0.9488669
F-D  11.7500000   7.050591 16.449409 0.0000000
F-E  13.1666667   8.467258 17.866075 0.0000000

There is a lot of information here. To make things easy, wherever there is a p adj of less than 0.05 that means that there is a difference between those two means. For example, bug spray F and E have a difference of 13.16 that has a p adj of zero. So these two means are really different statistically.This chart also includes the lower and upper bounds of the confidence interval.

The results can also be plotted with the script below

> plot(BugSpraydiff, las=1)

Below is the plot



ANOVA is used to calculate if there is a difference of means among three or more groups. This analysis can be conducted in R using various scripts and codes.

Qualitative Research: Hermeneutics & Phenomenology

Key components of qualitative research include hermeneutics and phenomenology. This post will examine these two terms and their role in qualitative research.


Hermeneutics is essential a method of interpretation of a text. The word hermeneutics comes from Hermes, the Greek messenger God. As such, at least for the ancient Greeks, there was a connection with interpreting and serving as a messenger. Today, his term is most commonly associated with theology such as biblical hermeneutics.

In relation to biblical hermeneutics, Augustine (354-430) develop a process of hermeneutics that was iterative. Through studying the Bible and the meaning of one’s own interpretations of the Bible, a person can understand divine truth. There was no need to look at the context, history, or anything else. Simply the Word and your interpretation of it.

In the 17th century, the Dutch philosopher Spinoza expanded on Augustine’s view of hermeneutics by stating that the text, its historical context, and even the author of a text, should be studied to understand the text. In other words, text plus context leads to truth.

By combing Augustine’s view of the role of the individual in hermeneutics with Spinoza’s contribution to the context we arrive at how interpretation happens in qualitative research.

In qualitative research, data interpretation (aka hermeneutics) involves the individual’s interpretation combined with the context that the data comes from. Both the personal interpretation and the context of the data influence each other.


The develops in hermeneutics led to the development of the philosophy called phenomenology. Phenomenology states that a phenomenon can only be understood subjectively (from a certain viewpoint) and intuitively (through thinking and finding hidden meaning).

In phenomenology, interpretation happens through describing events, analyzing an event, and by connecting a current experience to another one or by finding similarities among distinct experiences.

For a phenomenologist, there is a constant work of reducing several experiences into abstract constructs through an inductive approach. This is a form of theory building that is connected with several forms of qualitative research, such as grounded theory.


Hermeneutics has played an important role in qualitative research by influencing the development of phenomenology. The study of a phenomenon is for the purpose of seeing how context will influence interpretation.

Experimental Designs: Between Groups

In experimental research, there are two common designs. They are between and within group design. The difference between these two groups of designs is that between group involves two or more groups in an experiment while within group involves only one group.

This post will focus on between group designs. We will look at the following forms of between group design…

  • True/quasi-experiment
  • Factorial Design

True/quasi Experiment

A true experiment is one in which the participants are randomly assigned to different groups. In a quasi-experiment, the researcher is not able to randomly assigned participants to different groups.

Random assignment is important in reducing many threats to internal validity. However, there are times when a researcher does not have control over this, such as when they conduct an experiment at a school where classes have already been established. In general, a true experiment is always considered superior methodological to a quasi-experiment.

Whether the experiment is a true experiment or a quasi-experiment. There are always two groups that are compared in the study. One group is the controlled group, which does not receive the treatment. The other group is called the experimental group, which receives the treatment of the study. It is possible to have more than two groups and several treatments but the minimum for between group designs is two groups.

Another characteristic that true and quasi-experiments have in common is the type of formats that the experiment can take. There are two common formats

  • Pre- and post test
  • Post test only

A pre- and post test involves measuring the groups of the study before the treatment and after the treatment. The desire normally is for the groups to be the same before the treatment and for them to be different statistically after the treatment. The reason for them being different is because of the treatment, at least hopefully.

For example, let’s say you have some bushes and you want to see if the fertilizer you bought makes any difference in the growth of the bushes.  You divide the bushes into two groups, one that receives the fertilizer (experimental group), and one that does not (controlled group). You measure the height of the bushes before the experiment to be sure they are the same. Then, you apply the fertilizer to the experimental group and after a period of time, you measure the heights of both groups again. If the fertilized bushes grow taller than the control group you can infer that it is because of the fertilizer.

Post-test only design is when the groups are measured only after the treatment. For example, let’s say you have some corn plants and you want to see if the fertilizer you bought makes any difference.in the amount of corn produced.  You divide the corn plants into two groups, one that receives the fertilizer (experimental group), and one that does not (controlled group). You apply the fertilizer to the control group and after a period of time, you measure the amount of corn produced. If the fertilized corn produces more you can infer that it is because of the fertilizer. You never measure the corn beforehand because they had not produced any corn yet.

Factorial design involves the use of more than one treatment. Returning to the corn example, let’s say you want to see not only how fertilizer affects corn production but also how the amount of water the corn receives affects production as well.

In this example, you are trying to see if there is an interaction effect between fertilizer and water.  When water and fertilizer are increased does production increase, is there no increase, or if one goes up and the other goes down does that have an effect?


Between group designs such as true and quasi-experiments provide a way for researchers to establish cause and effect. Pre- post test is employed as well as factorial designs to establish relationships between variables

Calculating Chi-Square in R

There are times when conducting research that you want to know if there is a difference in categorical data. For example, is there a difference in the number of men who have blue eyes and who have brown eyes. Or is there a relationship between gender and hair color. In other words, is there a difference in the count of a particular characteristic or is there a relationship between two or more categorical variables.

In statistics, the chi-square test is used to compare categorical data. In this post, we will look at how you can use the chi-square test in R.

For our example, we are going to use data that is already available in R called “HairEyeColor”. Below is the data

> HairEyeColor
, , Sex = Male

Hair    Brown Blue Hazel Green
  Black    32   11    10     3
  Brown    53   50    25    15
  Red      10   10     7     7
  Blond     3   30     5     8

, , Sex = Female

Hair    Brown Blue Hazel Green
  Black    36    9     5     2
  Brown    66   34    29    14
  Red      16    7     7     7
  Blond     4   64     5     8

As you can see, the data comes in the form of a list and shows hair and eye color for men and women in separate tables. The current data is unusable for us in terms of calculating differences. However, by using the ‘marign.table’ function we can make the data useable as shown in the example below.

> HairEyeNew<- margin.table(HairEyeColor, margin = c(1,2))
> HairEyeNew
Hair    Brown Blue Hazel Green
  Black    68   20    15     5
  Brown   119   84    54    29
  Red      26   17    14    14
  Blond     7   94    10    16

Here is what we did. We created the variable ‘HairEyeNew’ and we stored the information from ‘HairEyeColor’ into one table using the ‘margin.table’ function. The margin was set 1,2 for the table.

Now all are data from the list are combined into one table.

We now want to see if there is a particular relationship between hair and eye color that is more common. To do this, we calculate the chi-square statistic as in the example below.

> chisq.test(HairEyeNew)

	Pearson's Chi-squared test

data:  HairEyeNew
X-squared = 138.29, df = 9, p-value < 2.2e-16

The test tells us that one or more of the relationships are more common than others within the table. To determine which relationship between hair and eye color is more common than the rest we will calculate the proportions for the table as seen below.

> HairEyeNew/sum(HairEyeNew)
Hair          Brown        Blue       Hazel       Green
  Black 0.114864865 0.033783784 0.025337838 0.008445946
  Brown 0.201013514 0.141891892 0.091216216 0.048986486
  Red   0.043918919 0.028716216 0.023648649 0.023648649
  Blond 0.011824324 0.158783784 0.016891892 0.027027027

As you can see from the table, brown hair and brown eyes are the most common (0.20 or 20%) flowed by blond hair and blue eyes (0.15 or 15%).


The chi-square serves to determine differences among categorical data. This tool is useful for calculating the potential relationships among non-continuous variables

Philosophical Foundations of Research: Epistemology

Epistemology is the study of the nature of knowledge. It deals with questions as is there truth and or absolute truth, is there one way or many ways to see something. In research, epistemology manifest itself in several views. The two extremes are positivism and interpretivism.


Positivism asserts that all truth can be verified and proven scientifically and can be measured and or observed. This position discounts religious revelation as a source of knowledge as this cannot be verified scientifically. The position of positivist is also derived from realism in that there is an external world out there that needs to be studied.

For researchers, positivism is the foundation of quantitative research. Quantitative researchers try to be objective in their research, they try to avoid coming into contact with whatever they are studying as they do not want to disturb the environment. One of the primary goals is to make generalizations that are applicable in all instances.

For quantitative researchers, they normally have a desire to test a theory. In other words, the develop one example of what they believe is a truth about a phenomenon (a theory) and they test the accuracy of this theory with statistical data. The data determines the accuracy of the theory and the changes that need to be made.

By the late 19th and early 20th centuries, people were looking for alternative ways to approach research. One new approach was interpretivism.


Interpretivism is the complete opposite of positivism in many ways. Interpretivism asserts that there is no absolute truth but relative truth based on context. There is no single reality but multiple realities that need to be explored and understood.

For interpretist, There is a fluidity in their methods of data collection and analysis. These two steps are often iterative in the same design. Furthermore, intrepretist see themselves not as outside the reality but a player within it. Thus, they often will share not only what the data says but their own view and stance about it.

Qualitative researchers are interpretists. They spend time in the field getting close to their participants through interviews and observations. They then interpret the meaning of these communications to explain a local context specific reality.

While quantitative researchers test theories, qualitative researchers build theories. For qualitative researchers, they gather data and interpret the data by developing a theory that explains the local reality of the context. Since the sampling is normally small in qualitative studies, the theories do not often apply to many.


There is little purpose in debating which view is superior. Both positivism and interpretivism have their place in research. What matters more is to understand your position and preference and to be able to articulate in a reasonable manner. It is often not what a person does and believes that is important as why they believe or do what they do.

Internal Validity

In experimental research design, internal validity is the appropriateness of the inferences made about cause and effects relationships between the independent and dependent variables. If there are threats to internal validity it may mean that the cause and effect relationship you are trying to establish is not real. In general, there are three categories of external validity, which are..,

  • Participant threats
  • Treatment threats
  • Procedural threats

We will not discuss all three categories but will focus on participant threats

Participant Threats

There are several forms of threats to internal validity that relate to participants. Below is a list

  • History
  • Maturation
  • Regression
  • Selection
  • Mortality


A historical threat to internal validity is the problem of the passages of time from  the beginning to the end of the experiment. During this elapse of time, the groups involved in the study may have different experiences. These different experiences are history threats. One way to deal with this threat is to be sure that the conditions of the experiment are the same.


Maturation threat is the problem of how people change over time during an experiment. These changes make it hard to infer if the results of a study are because of the treatment or because of maturation. One way to deal with this threat is to select participants who develop in similar ways and speed.


Regression threat is the action of the researcher selecting extreme cases to include in their sample. Eventually, these cases regress to the mean, which impacts the results of the pretest or posttest. One option for overcoming this problem is to avoid outliers when selecting the sample.


Selection bias is the poor habit of picking people in a non-random why for an experiment Examples of this include choosing mostly ‘smart people for an experiment. Or working with petite women for a study on diet and exercise. Random selection is the strongest way to deal with this threat.


Mortality is the lost of participants in a study. It is common for participants in a study to dropout and quit for many reasons. This leads to a decrease in the sample size, which weakens the statistical interpretation. Dealing with this requires using larger sample sizes as well as comparing data of dropouts with those who completed the study.


Internal validity can ruin a paper that has not careful planned out how these threats work together to skew results. Researchers need to have an idea of what threats are out there as well as strategies that can alleviate them.

Comparing Samples in R

Comparing groups is a common goal in statistics. This is done to see if there is a difference between two groups. Understanding the difference can lead to insights based on statistical results. In this post, we will examine the following statistical test for comparing samples.

  • t-test/Wilcoxon test
  • Paired t-test

T-test & Wilcoxon Test

The T-test indicates if there is a significant statistical difference between two groups. This is useful if you know what the difference between the two groups are. For example, if you are measuring height of men and women, if you find that men are taller through a t-test, you can state that gender influences height because the only difference between men and women in this example is their gender.

Below is an example of conducting a t-test in R. In the example, we are looking at if there is a difference in body temperature between beavers who are active versus beavers who are not.

> t.test(temp ~ activ, data = beaver2)

	Welch Two Sample t-test

data:  temp by activ
t = -18.548, df = 80.852, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.8927106 -0.7197342
sample estimates:
mean in group 0 mean in group 1 
       37.09684        37.90306

Here is what happened

  1. We use the ‘t.test’ function
  2. Within the ‘t.test’ function we indicate that we want to if there is a difference in ‘temp’ when compared on the factor variable ‘activ’ in the data ‘beaver2’
  3. The output provides a lot of information. The t-stat is -18.58 any number at + 1.96 indicates statistical difference.
  4. Df stands for degrees of freeedom and is used to determine the t-stat and p-value.
  5. The p-value is basically zero. Anything less than 0.05 is considered statistically significant.
  6. Next, we have the 95% confidence interval, which is the range of the difference of the means of the two groups in the population.
  7. Lastly, we have the means of each group. Group 0, the inactive group. had a mean of 37.09684. Group 1. the active group, has a mean of  37.90306.

T-test assumes that the data is normally distributed. When normality is a problem, it is possible to use the Wilcoxon test instead. Below is the script for the Wilcoxon Test using the same example.

> wilcox.test(temp ~ activ, data = beaver2)

	Wilcoxon rank sum test with continuity correction

data:  temp by activ
W = 15, p-value < 2.2e-16
alternative hypothesis: true location shift is not equal to 0

A closer look at the output indicates the same results for the most part. Instead of the t-stat the W-stat is used but the p value is the same for both test.

Paired T-Test

A paired t-test is used when you want to compare how the same group of people respond to different interventions. For example, you might use this for a before and after experiment. We will use the ‘sleep’ data in R  to compare a group of people when they receive different types of sleep medication. The script is below

> t.test(extra ~ group, data = sleep, paired = TRUE)

	Paired t-test

data:  extra by group
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -2.4598858 -0.7001142
sample estimates:
mean of the differences 

Here is what happened

  1. We used the ‘t.test’ function and indicate we want to see if ‘extra’ (amount of sleep) is influenced by ‘group’ (two types of sleep medication.
  2. We add the new argument of ‘paired = TRUE’ this tells R that this is a paired test.
  3. The output is the same information as in the regular t.test. The only differences is at the bottom where R only tells you the difference between the two groups and not the means of each. For this example, the people slept about 1 hour and 30 minutes longer on the second sleep medication when compared to the first.


Comparing samples in R is a simple process of understanding what you want to do. With this knowledge, the script and output are not too challenge even for many beginners

Philosophical Foundations of Research: Ontology

Philosophy is a term that is commonly used but hard to define. To put it simply, philosophy explains an individuals or a groups worldview in general or in a specific context. Such questions as the nature of knowledge, reality, and existence are questions that philosophy tries to answer. There are different schools of thought on these questions and these are what we commonly call philosophies

In this post, we will try to look at ontology, which is the study of the nature of reality. In particular, we will define it as well as explain its influence on research.


Ontology is the study of the nature of being. It tries to understand the reality of existence. In this body of philosophy, there are two major camps, ontological realism, and ontological idealism.

Ontological realism believes that reality is objective. In other words, there is one objective reality that is external to each individual person. We are in a reality and we do not create it.

Ontological idealism is the opposite extreme. This philosophy states that there are multiple realities an each depends on the person. My reality is different from your reality and each of us builds our own reality.

Ontological realism is one of the philosophical foundations for quantitative research. Quantitative research is a search for an objective reality that accurately explains whatever is being studied.

For qualitative researchers, ontological idealism is one of their philosophical foundations. Qualitative researchers often support the idea of multiple realities. For them, since there is no objective reality it is necessary to come contact with people to explain their reality.

Something that has been alluded to but not stated specifically is the role of independence and dependence of individuals. Regardless of whether someone ascribes to ontological realism or idealis, there is the factor of whether people or independent of reality or dependent to reality. The level of independence and dependence contributes to other philosophies such as objectivism constructivism and pragmatism.

Objectivism, Constructivism and Pragmatism

Objectivism is the belief that there is a single reality that is independent of the individuals within it. Again this is the common assumption of quantitative research. At the opposite end we have constructivism which states that there are multiple realities and the are dependent on the individuals who make each respective reality.

Pragmatism supports the idea of a single reality with the caveat that it is true if it is useful and works. The application of the idea depends upon the individuals, which pushes pragmatism into the realm of dependence.


From this complex explanation of ontology and research comes the following implications

  • Quantitative and qualitative researchers differ in how they see reality. Quantitative researchers are searching for and attempting to explain a single reality while qualitative researchers are searching for and trying to explain multiple realities.
  • Quantitative and qualitative researchers also differ on the independence of reality. Quantitative researchers see reality as independent of people while qualitative researchers see reality as dependent on people
  • These factors of reality and its dependence shape the methodologies employed by quantitative and qualitative researchers.

Experimental Design: Treatment Conditions and Group Comparision

A key component of experimental design involves making decisions about the manipulation of the treatment conditions. In this post, we will look at the following traits of treatment conditions

  • Treatment Variables
  • Experimental treatment
  • Conditions
  • Interventions
  • Outcomes

Lastly, we will examine group comparison.

One of the most common independent variables in experimental design are treatment and measured variables. Treatment variables are manipulated by the researcher. For example, if you are looking at how sleep affects academic performance, you may manipulate the amount of sleep participants receive in order to determine the relationship between academic performance and sleep.

Measured variables are variables that are measured by are not manipulated by the researcher. Examples include age, gender, height, weight, etc.

An experimental treatment is the intervention of the researcher to alter the conditions of an experiment. This is done by keeping all other factors constant and only manipulating the experimental treatment, it allows for the potential establishment of a cause-effect relationship. In other words, the experimental treatment is a term for the use of a treatment variable.

Treatment variables usually have different conditions or levels in them. For example, if I am looking at sleep’s affect on academic performance. I may manipulate the treatment variable by creating several categories of the amount of sleep. Such as high, medium, and low amounts of sleep.

Intervention is a term that means the actual application of the treatment variables. In other words, I broke my sample into several groups and caused one group to get plenty of sleep the second group to lack a little bit of sleep and the last group got nothing. Experimental treatment and intervention mean the same thing.

The outcome measure is the experience of measuring the outcome variable. In our example, the outcome variable is academic performance.

Group Comparison

Experimental design often focuses on comparing groups. Groups can be compared between groups and within groups. Returning to the example of sleep and academic performance, a between group comparison would be to compare the different groups based on the amount of sleep they received. A within group comparison would be to compare the participants who received the same amount of sleep.

Often there are at least three groups in an experimental study, which are the controlled, comparison, and experimental group. The controlled group receives no intervention or treatment variable. This group often serves as a baseline for comparing the other groups.

The comparison group is exposed to everything but the actual treatment of the study. They are highly similar to the experimental group with the experience of the treatment. Lastly, the experimental group experiences the treatment of the study.


Experiments involve treatment conditions and groups. As such, researchers need to understand their options for treatment conditions as well as what types of groups they should include in a study.

Examining Distributions In R

Normal distribution is an important term in statistics. When we say normal distribution, we are speaking of the traditional bell curve concept. Normal distribution is important because it is often an assumption of inferential statistics that the distribution of data points is normal. Therefore, one of the first things you do when analyzing data is to check for normality.

In this post, we will look at the following ways to assess normality.

  • By graph
  • By plots
  • By test

Checking Normality by Graph

The easiest and crudest way to check for normality is visually through the use of histograms. You simply look at the histogram and determine how closely it resembles a bell.

To illustrate this we will use the ‘beaver2’ data that is already loaded into R. This dataset contains five variables “day”, “time”, “temp”, and “activ” for data about beavers. Day indicates what day it was, time indicates what time it was, temp is the temperature of the beavers, and activ is whether the beavers were active when their temperature was taking. We are going to examine the normality of the temperature of active and inactive. Below is the code

> library(lattice)
> histogram(~temp | factor(activ), data = beaver2)
  1. We loaded the ‘lattice’ package. (If you don’t have this package please download)>
  2. We used the histogram function and indicate the variable ‘temp’ then the union ( | ) followed by the factor variable ‘activ’ (0 = inactive, 1 = active)
  3. Next, we indicate the dataset we are using ‘beaver2’
  4. After pressing ‘enter’ you should see the following


As you look at the histograms, you can say that they are somewhat normal. The peaks of the data are a little high in both. Group 1 is more normal than Group 0. The problem with visual inspection is lack of accuracy in interpretation. This is partially solved by using QQ plots.

Checking Normality by Plots

QQplots are useful for comparing your data with a normally distributed theoretical dataset. The QQplot includes a line of a normal distribution and the data points for your data for comparison. The more closely your data follows the line the more normal it is. Below is the code for doing this with our beaver information.

> qqnorm(beaver2$temp[beaver2$activ==1], main = 'Active')
> qqline(beaver2$temp[beaver2$activ==1])

Here is what we did

  1. We used the ‘qqnorm’ function to make the plot
  2. Within the ‘qqnorm’ function we tell are to use ‘temp’ from the ‘beaver2’ dataset.
  3. From the ‘temp’ variable we subset the values that have a 1 in the ‘activ’ variable.
  4. We give the plot a title by adding ‘main = Active’
  5. Finally, we add the ‘qqline’ using most of the previous information.
  6. Below is how the plot should look


Going by sight again. The data still looks pretty good. However, one last test will determine conclusively if the dataset is normal or not.

Checking Normality by Test

The Shapiro-Wilks normality test determines the probability that the data is normally distributed. The lower the probability the less likely that the data is normally distributed. Below is the code and results for the Shapiro test.

> shapiro.test(beaver2$temp[beaver2$activ==1])

	Shapiro-Wilk normality test

data:  beaver2$temp[beaver2$activ == 1]
W = 0.98326, p-value = 0.5583

Here is what happened

  1. We use the ‘shapiro.test’ function for ‘temp’ of only the beavers who are active (activ = 1)
  2. R tells us the p-value is 0.55 or 55%
  3. This means that the probability of our data being normally distributed is 55% which means it is highly likely to be normal.


It is necessary to always test the normality of data before data analysis. The tips presented here provide some framework for accomplishing this.

Characteristics of Experimental Design

In a previous post, we began a discussion on experimental design. In this post, we will begin a discussion on the characteristics of experimental design. In particular, we will look at the following

  • Random assignment
  • Control over extraneous variables

Random Assignment

After developing an appropriate sampling method, a researcher needs to randomly assign individuals to the different groups of the study. One of the main reasons for doing this is to remove the bias of individual differences in all groups of the study.

For example, if you are doing a study on intelligence. You want to make sure that all groups have the same characteristics of intelligence. This helps for the groups to equate or to be the same. This prevents people from saying the reason there are differences between groups is because the groups are different and not because of the treatment.

Control Over Extraneous Variables

Random assignment directly leads to the concern of controlling extraneous variables. Extraneous variables are any factors that might influence the cause and effect relationship that you are trying to establish. These other factors confound or confuse the results of a study. There are several methods for dealing with this as shown below

  • Pretest-posttest
  • Homogeneous sampling
  • Covriate
  • Matching


A pre-test post-test allows a researcher to compare the measurement of something before the treatment and after the treatment. The assumption is that any difference in the scores of before and after is due to the treatment.Doing the tests takes into account the confounding of the different contexts of the setting and individual characteristics.

Homogeneous Sampling

This approach involves selecting people who are highly similar on the particular trait that is being measured. This removes the problem of individual differences when attempting to interpret the results. The more similar the subjects in the sample are the more controlled the traits of the people are controlled for.


Covariates is a statistical approach in which controls are placed on the dependent variable through statistical analysis. The influence of other variables are removed from the explained variance of the dependent variable. Covariates help to explain more about the relationship between the independent and dependent variables.

This is a difficult concept to understand. However, the point is that you use covariates to explain in greater detail the relationship between the independent and dependent variable by removing other variables that might explain the relationship.


Matching is deliberate, rather than randomly, assigning subject to various groups. For example, if you are looking at intelligence. You might match high achievers in both groups of the study. By placing he achievers in both groups you cancel out there difference.


Experimental design involves the cooperation in random assignment of inclusive differences in a sample. The goal of experimental design is to be sure that the sample groups are mostly the same in a study. This allows for concluding that what happened was due to the treatment.

Two-Way Tables in R

A two-way table is used to explain two or more categorical variables at the same time. The difference between a two-way table and a frequency table is that a two-table tells you the number of subjects that share two or more variables in common while a frequency table tells you the number of subjects that share one variable.

For example, a frequency table would be gender. In such a table, you only know how many subjects are male or female. The only variable involved is gender. In a frequency table, you would learn some of the following

  • Total number of men
  • Total number of women
  • Total number of subjects in the study

In a two-way table, you might look at gender and marital status. In such a table you would be able to learn several things

  • Total number of men are married
  • Total number of men are single
  • Total number of women are married
  • Total number of women are single
  • Total number of men
  • Total number of women
  • Total number of married subjects
  • Total number of single subjects
  • Total number of subjects in the study

As such, there is a lot of information in a two-way table. In this post, we will look at the following

  • How to create a table
  • How to add margins to a table
  • How to calculate proportions in a table

Creating a Table

In the example, we are going to look at two categorical variables. One variable is gender and the other is marital status. For gender, the choices are “Male” and Female”. For marital status, the choicest are ‘Married” and “Single”. Below is the code for developing the table.

Marriage_Study<-matrix(c(34,20,19,42), ncol = 2)
colnames(Marriage_Study) <- c('Male', 'Female')
rownames(Marriage_Study) <- c('Married', 'Single')
Marriage_table <- as.table(Marriage_Study)

There has already been a discussion on creating matrices in R. Therefore, the details of this script will not be explained here.

If you type this correctly and run the script you should see the following

        Male Female
Married   34     19
Single    20     42

This table tells you about married and single people broken down by their gender. For example, 34 males are married.

Adding Margins and Calculating Proportions

A useful addition to a table is to add the margins. The margins tell you the total number of subjects in each row and column of a table. To do this in R use the ‘addmargins’ function as indicated below.

> addmargins(Marriage_table)
        Male Female Sum
Married   34     19  53
Single    20     42  62
Sum       54     61 115

We now know the total number of Married people, Singles, Males, and Females. In addition to the information we already knew.

One more useful piece of information is to calculate the proportions. This will allow us to know what percentage of each two-way possibility makes up the table. To do this we will use the “prop.table” function. Below is the script

> prop.table(Marriage_table)
             Male    Female
Married 0.2956522 0.1652174
Single  0.1739130 0.3652174

As you can see, we now know the proportions of each category in the table.


This post provided information on how to construct and manipulate data that is in a two-way table. Two-way tables are a useful way of describing categorical variables.

Experimental Design: A Background

Experimental design is now considered a standard methodology in research. However, this now classic design has not always been a standard approach. In this post, we will the following

  • The definition of experiment
  • The history of experiments
  • When to conduct experiments


The word experiment is derived from the word experience. When conducting an experiment, the researcher assigns people to have different experiences. He then determines if the experience he assigned people to had some effect on some sort of outcome. For example, if I want to know if the experience of sunlight affects the growth of plants I may develop two different experiences

  • Experience 1: Some plants receive sunlight
  • Experience 2: Some plants receive no sunlight

The outcome is the growth of the plants.By giving the plants different experiences of sunlight I can determine if sunlight influences the growth of plants.

History of Experiments

Experiments have been around informally since the 10th century with work done in the field of medicine. The use of experiments as known today began in the early 20th century in the field of psychology. By the 1920’s group comparison became an establish characteristics of experiments. By the 1930’s, random assignment was introduced. By the 1960’s various experimental designs were codified and documented. By the 1980’s there was literature coming out that addressed threats to validity.

Since the 1980’s experiments have become much more complicated with the development of more advanced statistical software problems. Despite all of the new complexity, normally simple experimental designs are easier to understand

When to Conduct Experiments

Experiments are conducted to attempt to establish a cause and effect relationship between independent and dependent variables. You try to create a controlled environment in which you provide the experience or independent variable(s) and then measure how they affect the outcome or dependent variable.

Since the setting of the experiment is controlled. You can say withou a doubt that only the experience influence the outcome. Off course, in reality, it is difficult to control all the factors in a study. The real goal is to try and limit the effect that these other factors have on the outcomes of a study.


Despite their long history, experiments are relatively new in research. This design has grown and matured over the years to become a powerful method for determining cause and effect. Therefore, researchers should e aware of this approach for use in their studies.

Plotting Correlations in R

A correlation indicates the strength of the relationship between two or more variables.  Plotting correlations allows you to see if there is a potential relationship between two variables. In this post, we will look at how to plot correlations with multiple variables.

In R, there is a built-in dataset called ‘iris’. This dataset includes information about different types of flowers. Specifically, the ‘iris’ dataset contains the following variables

  • Sepal.Length
  • Sepal.Width
  • Petal.Length
  • Petal.Width
  • Species

You can confirm this by inputting the following script

> names(iris)
[1] "Sepal.Length" "Sepal.Width"  "Petal.Length" "Petal.Width"  "Species"

We now want to examine the relationship that each of these variables has with each other. In other words, we want to see the relationship of

  • Sepal.Length and Sepal.Width
  • Sepal.Length and Petal.Length
  • Sepal.Length and Petal.Width
  • Sepal.Width and Petal.Length
  • Sepal.Width and Petal.Width
  • Petal.Length and Petal.Width

The ‘Species’ variable will not be a part of our analysis since it is a categorical variable and not a continuous one. The type of correlation we are analyzing is for continuous variables.

We are now going to plot all of these variables above at the same time by using the ‘plot’ function. We also need to tell R not to include the “Species” variable. This is done by adding a subset code to the script. Below is the code to complete this task.

> plot(iris[-5])

Here is what we did

  1. We use the ‘plot’ function and told R to use the “iris” dataset
  2. In brackets, we told R to remove ( – ) the 5th variable, which was species
  3. After pressing enter you should have seen the following


The variable names are placed diagonally from left to right. The x-axis of a plot is determined by variable name in that column. For example,

  • The variable of the x-axis of the first column is ‘Sepal.Length”
  • The variable of the x-axis of the second column is ‘Sepal.Width”
  • The variable of the x-axis of the third column is ‘Petal.Length”
  • The variable of the x-axis of the fourth column is ‘Petal.Width”

The y-axis is determined by the variable that is in the same row as the plot. For example,

  • The variable of the y-axis of the first column is ‘Sepal.Length”
  • The variable of the y-axis of the second column is ‘Sepal.Width”
  • The variable of the y-axis of the third column is ‘Petal.Length”
  • The variable of the y-axis of the fourth column is ‘Petal.Width”

AS you can see, this is the same information. We will now look at a few examples of plots

  • The plot in the first column second row plots “Sepal.Length” as the x-axis and “Sepal.Width” as the y-axis
  • The plot in the first column third row plots “Sepal.Length” as the x-axis and “Petal.Length” as the y-axis
  • The plot in the first column fourth row plots “Sepal.Length” as the x-axis and “Petal.Width” as the y-axis

Hopefully, you can see the pattern. The plots above the diagonal are mirrors of the ones below. If you are familiar with correlational matrices this should not be surprising.

After a visual inspection, you can calculate the actual statistical value of the correlations. To do so use the script below and you will see the table below after it.

> cor(iris[-5])
             Sepal.Length Sepal.Width Petal.Length Petal.Width
Sepal.Length    1.0000000  -0.1175698    0.8717538   0.8179411
Sepal.Width    -0.1175698   1.0000000   -0.4284401  -0.3661259
Petal.Length    0.8717538  -0.4284401    1.0000000   0.9628654
Petal.Width     0.8179411  -0.3661259    0.9628654   1.0000000

As you can see, there are many strong relationships between the variables. For example “Petal.Width” and “Petal.Length” has a correlation of .96, which is almost perfect. This means that when “Petal.Width” grows by one unit “Petal.Length” grows by .96 units.


Plots help you to see the relationship between two variables. After visual inspection, it is beneficial to calculate the actual correlation.

Analyzing Qualitative Data

Analyzing qualitative data is not an easy task. Instead of punching script into a statistical programming and receiving results, you become the computer who needs to analyze the data. For this reason alone, the analysis of qualitative data is difficult as different people will have vastly different interpretations of data.

This post will look at the following

  • The basic characteristics of qualitative data analysis
  • Exploring and coding data

Basic Characteristics

Qualitative data analysis has the following traits

  • Inductive form
  • Analyzing data while still collecting data
  • Interpretative

Qualitative analysis is inductive by nature. This indicates that a researcher goes from specific examples to the generation of broad concepts or themes. In many ways, the researcher is trying to organize and summarize what they found in their research coherently in nice neat categories and themes.

Qualitative analysis also involves analyzing while still collecting data.You begin to process the data while still accumulating data. This is an iterative process that involves moving back and forth between analysis and collection of data. This is a strong contrast to quantitative research which is usually linear in nature.

Lastly, qualitative analysis is highly subjective. Everyone who views the data will have a different perspective on the results of a study. This means that people will all see different ideas and concepts that are important in qualitative research.

Exploring and Coding

Coding data in qualitative research can be done with text, images, and or observations. In coding, a researcher determines which information to share through the development of segments, codes, categories, themes. Below is the process for developing codes and categories

1. Read the text

Reading the text means to get familiar with it and now what is discussed.

2. Pick segments of quotes to include in the article

After reading the text, you begin to pick quotes from the interview that will be used for further inductive processing

3, Develop codes from segments

After picking many different segments, you need to organize them into codes. All segments in one code have something in common that unites them as a code.

4. Develop categories from codes

The next level of abstract is developing categories from codes. The same process in step 3 is performed here.

5. Develop themes from categories

This final step involves further summarizing the results of the categories development into themes. The process is the same as steps 3 and 4.

Please keep in mind that as you move from step 1 to 5 the number of concepts decreases. For example, you may start with 50 segments that are reduced to 10 codes then reduce to 5 categories and finally 3 themes.


Qualitative data analysis is not agreed upon. There are many different ways to approach this. In general, the best approach possible is one that is consistent in terms of its treatment of the data. The example provided here is just one approach to organizing data in qualitative research.

Basics of Histograms and Plots in R

R has many fascinating features for creating histograms and plots. In this post, we will only cover some of the most basic concepts of make histograms and plots in R. The code for the data we are using is available in a previous post.

Making a Histogram

We are going to make a histogram of the ‘mpg’ variable in our ‘cars’ dataset. Below is the code for doing this followed by the actual histogram.

Histogram of mpg variable

Histogram of mpg variable

Here is what we did

  1. We used the ‘hist’ function to create the histogram
  2. Within the hist function we told r to make a histogram of ‘mpg’ variable found in the ‘cars’ dataset.
  3. An additional argument that we added was ‘col’. This argument is used to determine the color of the bars in the histogram. For our example, the color was set to gray.

Plotting Multiple Variables

Before we look at plotting multiple variables you need to make an adjustment to the ‘cyl’ variable in our cars variable. THis variable needs t be changed from a numeric to a factor variable as shown below

cars$cyl<- as.factor(cars$cyl)

Boxplots are an excellent way of comparing groups visually. In this example, we will compare the ‘mpg’ or miles per gallon variable by the ‘cyl’ or number of cylinders in the engine variable in the ‘cars’ dataset. Below is the code and diagram followed by an explanation.

boxplot(mpg ~ cyl, data = cars)


Here is what happened.

  1. We use the ‘boxplot’ function
  2. Within this function we tell are to plot mpg and cyl using the tilda  ” ~ ” to tell R to compare ‘mpg’ by the number of cylinders

The box of the boxplot tells you several things

  1. The bottom of the box tells you the 25th percentile
  2. The line in the middle of the box tells you the median
  3. The top of the box tells you the 75th percentile
  4. The bottom line tells you the minimum or lowest value excluding outliers
  5. The top line tells you the maximum or highest value excluding outliers

In order boxplot above, there are three types of cylinders 4, 6, and 8. For 4 cylinders the 25th percentile is about 23 mpg, the 50th percentile is about 26 mpg, while the 75th percentile is about 31 mpg. The minimum value was about 22 and the maximum value was about 35 mpg. A close look at the different blots indicates that four cylinder cars have the best mpg followed by six and finally eight cylinders.


Histograms and boxplots serve the purpose of describing numerical data in a visual manner. Nothing like a picture helps to explain abstract concepts such mean and median.

Content Analysis In Qualitative Research

Content analysis serves the purpose in qualitative research to enable you to study human behavior indirectly through how people choose to communicate. The type of data collected can vary tremendously in this form of research. However, common examples of data include images, documents, and media.

In this post, we will look at the following in relation to content analysis

  • The purpose of content analysis
  • Coding in content analysis
  • Analysis in content analysis
  • Pros and cons in content analysis


The purpose of content analysis is to study the central phenomenon through the analysis of examples of the communication of people connected with the central phenomenon. This information is coded into categories and themes. Categories and themes are just different levels of summarizing the results of the analysis. Themes are a summary of categories and categories are a direct summary of the data that was analyzed.


Coding the data is the process of organizing the results in a comprehensible way. In terms of coding, there are two choices.

  • Establish categories before beginning the analysis
  • Allow the categories to emerge during analysis

Which is best depends on the research questions and context of the study.

There are two forms of content manifest content and latent content. Manifest content is evidence that is directly seen such as the words in an interview. Latent content refers to the underlying meaning of content such as the interpretation of an interview.

The difference between these two forms of content is the objective or subjective nature of them. Many studies include both forms as this provides a fuller picture of the central phenomenon.


There are several steps to consider when conducting a content analysis such as…

  • Define your terms-This helps readers to know what you are talking about
  • Explain what you are analyzing-This can be words, phrases, interviews, pictures, etc.
  • Explain your coding approach-Explained above
  • Present results

This list is far from complete but provides some basis for content analysis

Pros and Cons

Pros of content analysis include

  • Unobtrusive-Content analysis does not disturb the field or a people group normally
  • Replication-Since the documents are permanent, it is possible to replicate a study
  • Simplicity-Compared to other forms of research, content analysis is highly practical to complete

Cons include

  • Validity-It is hard to assess the validity of the analysis. The results of an analysis is the subjective opinion of an individual(s)
  • Limited data-Content analysis is limited to recorded content. This leaves out other forms of information


Content analysis provides another way for the qualitative research to analyze the world. There are strengths and weaknesses to this approach as there are such for forms of analysis. The point is to understand that there are times when the content analysis is appropriate

Describing Categorical Data in R

This post will explain how to create tables, calculate proportions, find the mode, and make plots for categorical variables in R. Before providing examples below is the script needed to setup the data that we are using

cars <- mtcars[c(1,2,9,10)]
cars$gear <- ordered(cars$gear)


Frequency tables are useful for summarizing data that has a limited number of values. It represents how often a particular value appears in a dataset. For example, in our cars dataset, we may want to know how many different kinds of transmission we have. To determine this, use the code below.

> transmission_table <- table(cars$am)
> transmission_table

  auto manual 
    19     13

Here is what we did.

  1. We created the variable ‘transmission_table’
  2. In this variable, we used the ‘table’ function which took information from the ‘am’ variable from the ‘cars’ dataset.
  3. Final we displayed the information by typing ‘transmission_table’ and pressing enter


Proportions can also be calculated. A proportion will tell you what percentage of the data belongs to a particular category. Below are the proportions of automatic and manual transmissions in the ‘cats’ dataset.

> transmission_table/sum(transmission_table)

   auto  manual 
0.59375 0.40625

The table above indicates that about 59% of the sample consists of automatic transmissions while about 40% are manual transmissions


When dealing with categorical variables there is not mean or median. However, it is still possible to calculate the mode, which is the most common value found. Below is the code.

> mode_transmission <-transmission_table ==max(transmission_table)
> names(transmission_table) [mode_transmission]
[1] "auto"

Here is what we did.

  1. We created the variable ‘mode_transmission’ and use the ‘max’ function to calculate the max number of counts in the transmission_table.
  2. Next we calculated the names found in the ‘transmission_table’ but we subsetted the ‘modes_transmission variable
  3. The most common value was ‘auto’ or automatic tradition,


Plots are one of the funniest capabilities in R. For now, we will only show you how to plot the data that we have been using. What is seen here is only the simplest and basic use of plots in R and there is a much more to it than this. Below is the code for plotting the number of transmission by type in R.

> plot(cars$am)

If you did this correctly you should see the following.


All we did was have R create a visual of the number of auto and manual transmissions.Naturally, you can make plots with continuous variables as well.


This post provided some basic information on various task can be accomplished in R for assessing categorical data. These skills will help researchers to take a sea of data and find simple ways to summarize all of the information.

Interviews in Qualitative Research

Interviews provide another way to collect data when conducting qualitative research. In this post, we will look at the following,

  • Characteristics of the interviewees
  • Types of interviews
  • Types of questions
  • Tips for conducting interviews

Characteristics of the Interviewees

Qualitative research involves two types of interviewees. If you are interviewing only one person this is a one-on-one interview. If you are interviewing a group this is often called a focus group.

One-on-One interviewing allows for in-depth data collection but takes a great deal of time. Focus groups, on the other hand, allows a researcher to gather a more varied opinion while saving time. Care also must be taken to make sure everyone participates in a focus group.

Types of Interviews

There are three common types of interview structured, semi-structured and informal. Structured interviews consist of a strict set of questions that are read in order word for word to interviewees. The goal is for the interviewee to answer all questions.

At the opposite extreme are informal interviews which are conversations that can flow in any direction. There is no set script of questions and the interviewee can go anywhere they want in the conversation

The middle ground between formal and informal interviewing is semi-structured interviews. In this approach, the researcher has questions they want to ask but they can vary the order, reword, ask follow-up questions, and or omit questions As such, there is a negotiable format in semi-structured interviews.

Types of Questions

There are several types of questions that are used in qualitative research. The types are self-explanatory and are listed below with an example

  • Knowledge question-“How does email work?”
  • Experience question-“What was it like growing up in the 1990’s?”
  • Opinion question-“What is your view of the tax cuts?”
  • Feeling question-“How do the change in curfew make you feel?”
  • Sensory question-“What does the kitchen smell like?”

Keep in mind that open ended questions are more common the closed-ended questions in qualitative research. This allows the interviewee to share their perspective rather than reply yes and no.

Tips for Conducting Interviews

Below are some tips for conducting interviews

  • Establish rapport-Establishing some form of relationship helps the interviewee to feel comfortable.
  • Location matters-Pick a quiet place to conduct the interview(s) if possible.
  • Record the interview-This is standard practice and is necessary in order to develop a transcript.
  • Take notes-Even with a recording, taking notes helps you to recall what happened during the interview.
  • Use wisdom with questions-Avoid leading questions which are unfair and make sure to ask one question at a time.
  • Show respect and courtesy during the interview-Be polite and considerate of the interviewee who has given you some of their time.

This not meant to be an exhaustive list but rather to provide some basic guidelines.


Along with observations, interviews is one of the most common forms of data collection in qualitative research. When you are in the field doing interviews it is important to consider what kind of interview you are doing, what questions you are going to ask, as well as the guidelines for conducting interviews presented in this post.

Observation in Qualitative Research

Observation is one of several forms of data collection in qualitative research. It involves watching and recording, through the use of notes, the behavior of people at the research site. In this post, we will cover the following

  • Different observational roles
  • The guidelines for observation
  • Problems with observation

Observational Roles

The role you play as an observer can vary between two extremes which are

nonparticipant to participant observer. A nonparticipant observer does not participate in any of the activities of the people being studied. For example, you are doing teaching observations, as you sit in the classroom you only watch what happens and never participate.

The other extreme is a participant observer. In this role, a researcher takes part in the activities of the group. For example, if you are serving as a teacher in a lower income community and are observing the students while you teach and interact with them this is participant observer.

Between these two extremes of non-participation and participation are several other forms of observation.  For example, a a non-participant observer can be an observer-as-participant or a complete observer. Furthermore, a participant observer can be a participant-as-observer or complete participant. The difference between these is whether or not the the group being studied knows the identity of the researcher.

Guidelines for Observation

  • Decide your role-What type of observer are you
  • Determine what you are observing-The observation must support what you are trying to learn about the central phenomenon 
  • Observe the subject multiple times-This provides a deeper understanding of the subjects
  • Take notes-An observer should of some way of taking notes. These notes are called fieldnotes and provide a summary of what was seen during the observation.

Problems with Observation

Common problems that are somewhat related when doing observations are observer effect, observer bias, observer expectations. The observer effect is how the people being observed change their behavior because of the presence of an outsider. For example, it is common for students to behave differently when the principal comes to observe the teacher. They modify their behavior because of the presence of the principal. In addition, if the students are aware of the principal’s purpose, they may act extra obedient for the sake of their teacher.

Observer bias is the potential that a researchers viewpoint may influence what they see. For example, if a principal is authoritarian he may view a democratic classroom with a laid back teacher as chaotic when the students may actually be learning a great deal.

Observer expectation is the observer assuming beforehand what they are going to see. For example, if a researcher is going to observe students in a lower income school, he will expect to see low performing unruly students. This becomes a self-fulfilling prophecy as the researcher sees what they expected to see.


Observation is one of the forms of data collection in qualitative research. Keeping in mind the types of observation, guidelines, and problems can help a researcher to succeed.