Statistics/Different Types of Data/Quantitative and Qualitative Data

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  1. Introduction
    1. What Is Statistics?
    2. Subjects in Modern Statistics
    3. Why Should I Learn Statistics? 0% developed
    4. What Do I Need to Know to Learn Statistics?
  2. Different Types of Data
    1. Primary and Secondary Data
    2. Quantitative and Qualitative Data
  3. Methods of Data Collection
    1. Experiments
    2. Sample Surveys
    3. Observational Studies
  4. Data Analysis
    1. Data Cleaning
    2. Moving Average
  5. Summary Statistics
    1. Measures of center
      1. Mean, Median, and Mode
      2. Geometric Mean
      3. Harmonic Mean
      4. Relationships among Arithmetic, Geometric, and Harmonic Mean
      5. Geometric Median
    2. Measures of dispersion
      1. Range of the Data
      2. Variance and Standard Deviation
      3. Quartiles and Quartile Range
      4. Quantiles
  6. Displaying Data
    1. Bar Charts
    2. Comparative Bar Charts
    3. Histograms
    4. Scatter Plots
    5. Box Plots
    6. Pie Charts
    7. Comparative Pie Charts
    8. Pictograms
    9. Line Graphs
    10. Frequency Polygon
  7. Probability
    1. Combinatorics
    2. Bernoulli Trials
    3. Introductory Bayesian Analysis
  8. Distributions
    1. Discrete Distributions
      1. Uniform Distribution
      2. Bernoulli Distribution
      3. Binomial Distribution
      4. Poisson Distribution
      5. Geometric Distribution
      6. Negative Binomial Distribution
      7. Hypergeometric Distribution
    2. Continuous Distributions
      1. Uniform Distribution
      2. Exponential Distribution
      3. Gamma Distribution
      4. Normal Distribution
      5. Chi-Square Distribution
      6. Student-t Distribution
      7. F Distribution
      8. Beta Distribution
      9. Weibull Distribution
  9. Testing Statistical Hypothesis
    1. Purpose of Statistical Tests
    2. Formalism Used
    3. Different Types of Tests
    4. z Test for a Single Mean
    5. z Test for Two Means
    6. t Test for a single mean
    7. t Test for Two Means
    8. paired t Test for comparing Means
    9. One-Way ANOVA F Test
    10. z Test for a Single Proportion
    11. z Test for Two Proportions
    13. Spearman's Rank Coefficient
    14. Pearson's Product Moment Correlation Coefficient
    15. Chi-Squared Tests
      1. Chi-Squared Test for Multiple Proportions
      2. Chi-Squared Test for Contingency
    16. Approximations of distributions
    1. Unbiasedness
    2. Measures of goodness
    3. UMVUE
    4. Completeness
    5. Sufficiency and Minimal Sufficiency
    6. Ancillarity
  11. Practice Problems
    1. Summary Statistics Problems
    2. Data-Display Problems
    3. Distributions Problems
    4. Data-Testing Problems
  12. Numerical Methods
    1. Basic Linear Algebra and Gram-Schmidt Orthogonalization
    2. Unconstrained Optimization
    3. Quantile Regression
    4. Numerical Comparison of Statistical Software
    5. Numerics in Excel
    6. Statistics/Numerical_Methods/Random Number Generation
  13. Multivariate Data Analysis
    1. Principal Component Analysis
    2. Factor Analysis for metrical data
    3. Factor Analysis for ordinal data
    4. Canonical Correlation Analysis
    5. Discriminant Analysis
  14. Analysis of Specific Datasets
    1. Analysis of Tuberculosis
  15. Appendix
    1. Authors
    2. Glossary
    3. Index
    4. Links

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Qualitative data[edit]

Qualitative data is a categorical measurement expressed not in terms of numbers, but rather by means of a natural language description. In statistics, it is often used interchangeably with "categorical" data.

  For example: favorite color = "blue"
               height = "tall"

Although we may have categories, the categories may have a structure to them. When there is not a natural ordering of the categories, we call these nominal categories. Examples might be gender, race, religion, or sport.

When the categories may be ordered, these are called ordinal variables. Categorical variables that judge size (small, medium, large, etc.) are ordinal variables. Attitudes (strongly disagree, disagree, neutral, agree, strongly agree) are also ordinal variables, however we may not know which value is the best or worst of these issues. Note that the distance between these categories is not something we can measure.

Quantitative data[edit]

Quantitative data is a numerical measurement expressed not by means of a natural language description, but rather in terms of numbers. However, not all numbers are continuous and measurable. For example, the social security number is a number, but not something that one can add or subtract.

  For example: molecule length = "450 nm" 
               height = "1.8 m"

Quantitative data always are associated with a scale measure.

Probably the most common scale type is the ratio-scale. Observations of this type are on a scale that has a meaningful zero value but also have an equidistant measure (i.e., the difference between 10 and 20 is the same as the difference between 100 and 110). For example, a 10 year-old girl is twice as old as a 5 year-old girl. Since you can measure zero years, time is a ratio-scale variable. Money is another common ratio-scale quantitative measure. Observations that you count are usually ratio-scale (e.g., number of widgets).