Two-Way Tables & relative frequency

Analyze categorical associations between two variables. Calculate joint, marginal, and conditional relative frequencies, and visualize proportional overlaps.

Frequency Grid & Conditional Proportions

Modify counts in the cells directly using the + and adjusters. Toggle display modes on the right to instantly convert values into relative percentages, and examine the stacked proportional distribution of grade preferences.

Grade Level Math Science English Row Totals
7th Grade
12
12
6
30
8th Grade
16
16
8
40
Col Totals 28 28 14 70

1. Display Mode

2. Relationship Preset

3. Association Diagnostics

Independent (No Association)

If the subject preferences are significantly different between 7th and 8th graders, there is a statistical association. If the conditional ratios are identical, the preferences are independent of grade level.

Proportions & Frequency Walkthrough

Trace how relative and conditional proportions are compiled and evaluated to check for statistical associations.

Trace Calculations Steps

Two-Way Table Quiz

Evaluate your understanding of joint, marginal, and conditional probabilities, and how to verify variables association.

Question 1 of 5 Score: 0/0

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Correct Answer!

Explanation text...

Two-Way Table Definitions


  • Joint Frequency: The entries inside the cells of the table that represent counts of subjects matching both row and column categories (e.g. 7th Graders who like Math).
  • Marginal Frequency: The totals along the bottom row or rightmost column representing totals of single categories.
  • Joint Relative Frequency: Cell count divided by grand total.
  • Conditional Relative Frequency: Cell count divided by its row total (or column total). Critical for verifying dependency.
  • Checking Association: If the conditional relative frequencies of column options differ significantly between rows, the variables are associated.