8.2. Classifying by One Variable

Data scientists often need to classify individuals into groups according to shared features, and then identify some characteristics of the groups. For example, in the example using Galton’s data on heights, we saw that it was useful to classify families according to the parents’ midparent heights, and then find the average height of the children in each group.

This section is about classifying individuals into categories that are not numerical. We begin by recalling the basic use of group.

8.2.1. Counting the Number in Each Category

The group method with a single argument counts the number of rows for each category in a column. The result contains one row per unique value in the grouped column.

Here is a small table of data on ice cream cones. The group method can be used to list the distinct flavors and provide the counts of each flavor.

cones = Table().with_columns(
    'Flavor', make_array('strawberry', 'chocolate', 'chocolate', 'strawberry', 'chocolate'),
    'Price', make_array(3.55, 4.75, 6.55, 5.25, 5.25)
Flavor Price
strawberry 3.55
chocolate 4.75
chocolate 6.55
strawberry 5.25
chocolate 5.25
Flavor count
chocolate 3
strawberry 2

There are two distinct categories, chocolate and strawberry. The call to group creates a table of counts in each category. The column is called count by default, and contains the number of rows in each category.

Notice that this can all be worked out from just the Flavor column. The Price column has not been used.

But what if we wanted the total price of the cones of each different flavor? That’s where the second argument of group comes in.

8.2.2. Finding a Characteristic of Each Category

The optional second argument of group names the function that will be used to aggregate values in other columns for all of those rows. For instance, sum will sum up the prices in all rows that match each category. This result also contains one row per unique value in the grouped column, but it has the same number of columns as the original table.

To find the total price of each flavor, we call group again, with Flavor as its first argument as before. But this time there is a second argument: the function name sum.

cones.group('Flavor', sum)
Flavor Price sum
chocolate 16.55
strawberry 8.8

To create this new table, group has calculated the sum of the Price entries in all the rows corresponding to each distinct flavor. The prices in the three chocolate rows add up to \(\$16.55\) (you can assume that price is being measured in dollars). The prices in the two strawberry rows have a total of \(\$8.80\).

The label of the newly created “sum” column is Price sum, which is created by taking the label of the column being summed, and appending the word sum.

Because group finds the sum of all columns other than the one with the categories, there is no need to specify that it has to sum the prices.

To see in more detail what group is doing, notice that you could have figured out the total prices yourself, not only by mental arithmetic but also using code. For example, to find the total price of all the chocolate cones, you could start by creating a new table consisting of only the chocolate cones, and then accessing the column of prices:

cones.where('Flavor', are.equal_to('chocolate')).column('Price')
array([4.75, 6.55, 5.25])
sum(cones.where('Flavor', are.equal_to('chocolate')).column('Price'))

This is what group is doing for each distinct value in Flavor.

# For each distinct value in `Flavor, access all the rows
# and create an array of `Price`

cones_choc = cones.where('Flavor', are.equal_to('chocolate')).column('Price')
cones_strawb = cones.where('Flavor', are.equal_to('strawberry')).column('Price')

# Display the arrays in a table

grouped_cones = Table().with_columns(
    'Flavor', make_array('chocolate', 'strawberry'),
    'Array of All the Prices', make_array(cones_choc, cones_strawb)

# Append a column with the sum of the `Price` values in each array

price_totals = grouped_cones.with_column(
    'Sum of the Array', make_array(sum(cones_choc), sum(cones_strawb))
Flavor Array of All the Prices Sum of the Array
chocolate [4.75 6.55 5.25] 16.55
strawberry [3.55 5.25] 8.8

You can replace sum by any other functions that work on arrays. For example, you could use max to find the largest price in each category:

cones.group('Flavor', max)
Flavor Price max
chocolate 6.55
strawberry 5.25

Once again, group creates arrays of the prices in each Flavor category. But now it finds the max of each array:

price_maxes = grouped_cones.with_column(
    'Max of the Array', make_array(max(cones_choc), max(cones_strawb))
Flavor Array of All the Prices Max of the Array
chocolate [4.75 6.55 5.25] 6.55
strawberry [3.55 5.25] 5.25

Indeed, the original call to group with just one argument has the same effect as using len as the function and then cleaning up the table.

lengths = grouped_cones.with_column(
    'Length of the Array', make_array(len(cones_choc), len(cones_strawb))
Flavor Array of All the Prices Length of the Array
chocolate [4.75 6.55 5.25] 3
strawberry [3.55 5.25] 2

8.2.3. Example: NBA Salaries

The table nba contains data on the 2015-2016 players in the National Basketball Association. We have examined these data earlier. Recall that salaries are measured in millions of dollars.

nba1 = Table.read_table(path_data + 'nba_salaries.csv')
nba = nba1.relabeled("'15-'16 SALARY", 'SALARY')
Paul Millsap PF Atlanta Hawks 18.6717
Al Horford C Atlanta Hawks 12
Tiago Splitter C Atlanta Hawks 9.75625
Jeff Teague PG Atlanta Hawks 8
Kyle Korver SG Atlanta Hawks 5.74648
Thabo Sefolosha SF Atlanta Hawks 4
Mike Scott PF Atlanta Hawks 3.33333
Kent Bazemore SF Atlanta Hawks 2
Dennis Schroder PG Atlanta Hawks 1.7634
Tim Hardaway Jr. SG Atlanta Hawks 1.30452

... (407 rows omitted)

1. How much money did each team pay for its players’ salaries?

The only columns involved are TEAM and SALARY. We have to group the rows by TEAM and then sum the salaries of the groups.

teams_and_money = nba.select('TEAM', 'SALARY')
teams_and_money.group('TEAM', sum)
Atlanta Hawks 69.5731
Boston Celtics 50.2855
Brooklyn Nets 57.307
Charlotte Hornets 84.1024
Chicago Bulls 78.8209
Cleveland Cavaliers 102.312
Dallas Mavericks 65.7626
Denver Nuggets 62.4294
Detroit Pistons 42.2118
Golden State Warriors 94.0851

... (20 rows omitted)

2. How many NBA players were there in each of the five positions?

We have to classify by POSITION, and count. This can be done with just one argument to group:

C 69
PF 85
PG 85
SF 82
SG 96

3. What was the average salary of the players at each of the five positions?

This time, we have to group by POSITION and take the mean of the salaries. For clarity, we will work with a table of just the positions and the salaries.

positions_and_money = nba.select('POSITION', 'SALARY')
positions_and_money.group('POSITION', np.mean)
C 6.08291
PF 4.95134
PG 5.16549
SF 5.53267
SG 3.9882

Center was the most highly paid position, at an average of over 6 million dollars.

If we had not selected the two columns as our first step, group would not attempt to “average” the categorical columns in nba. (It is impossible to average two strings like “Atlanta Hawks” and “Boston Celtics”.) It performs arithmetic only on numerical columns and leaves the rest blank.

nba.group('POSITION', np.mean)
C 6.08291
PF 4.95134
PG 5.16549
SF 5.53267
SG 3.9882