8.3_Cross-Classifying_by_More_than_One_Variable.ipynb - Colab

Cross-Classifying by More than One Variable

Cross-classification is a useful method when individuals possess multiple features that can be categorized in various ways. For instance, in a population of college students, each student can be classified based on attributes such as their major and the number of years they have been in college. This allows for insightful analysis through a combination of categorical variables, enhancing the ability to draw conclusions about the groups being studied.

Two Variables: Counting the Number in Each Paired Category

To demonstrate cross-classification, consider the dataset more_cones, which consists of the flavor, color, and price of six different ice cream cones:

• Flavor: strawberry, chocolate, bubblegum

• Color: pink, light brown, dark brown

• Price: Various prices are associated with the different combinations of flavor and color.

Using the group method, you can count the ice cream cones by flavor alone. To classify the cones by both flavor and color, you can pass a list of labels as an argument to the group method:

more_cones.group(['Flavor', 'Color'])

In the result, there will be one row for each unique combination of flavor and color. For example, two cones might be categorized as dark brown chocolate and two as pink strawberry, although the total number of cones is six. This demonstrates how individual attributes can be effectively grouped and analyzed simultaneously.

Exploring Columns Beyond Counts

When aggregating data with a second argument in the group method, you can display results in a more organized format, such as a pivot table, which is particularly effective for analyzing relationships between two variables.

Pivot Tables: Rearranging the Output of Group

The pivot method offers a powerful alternative to group, providing a grid format that visually represents relationships between categories, like flavor and color, in a table. For example:

more_cones.pivot('Flavor', 'Color')

This command produces a table that displays counts of all possible flavor and color pairs, including non-existent pairings across the dataset. Moreover, pivot places values into adjacent columns, enhancing readability and comparative analysis when studying various variable traits.

Grouping by Three or More Variables

The versatility of group and pivot extends to three or more categorical variables, allowing for complex analyses that can underscore intricate relationships between different attributes. However, it's crucial to note that as the number of variables increases, the combinations of categories also expand significantly, which can complicate data interpretation.

Example: Education and Income among Californians

A practical application of these concepts can be seen in analyzing the educational attainment and personal income of Californian adults from a dataset that includes various demographic nuances. The entire dataset contains as many as 127 combinations of age, gender, and education level.

When focusing merely on educational attainment and its correlation to personal income, one effective approach is to use the functions such as group to find the population count based on educational levels and income levels. This can be achieved through filtering and selecting columns from the dataset.

Percent Distribution of Educational Levels

Analyzing educational attainment can reveal important insights: for example, more than 30% of adults may have a Bachelor's degree or higher, while a significant portion is without a high school diploma. By converting raw counts to percentages, comparative relationships across educational categories can become clearer and allow for meaningful analysis in terms of income levels.

def percents(array_x):
    return np.round((array_x/sum(array_x))*100, 2)

The above function aids in calculating the distribution percentages effectively.

Visualizing the Data

The resulting distribution of personal income across educational categories can then be visualized through various graphical representations, such as bar charts, which exhibit noticeable trends—for example, demonstrating that individuals with a Bachelor's degree are significantly more likely to have higher incomes compared to those without a high school diploma.

This comprehensive study elucidates the power of cross-classifying data when integrating multiple categorical variables, yielding valuable insights into the societal trends and economic behaviors of distinct demographic groups.