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
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.
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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.