Representing Two Categorical Variables - AP Statistics

The proportion of the total count for a specific category. Frequency expressed as a fraction of the total.

Use separate bars for each category. Overlapping bars make data unreadable and misleading.

The frequency distribution of variables. Cross-tabulation of two categorical variables.

Sum of $\frac{(O_i - E_i)^2}{E_i}$ for each cell. Compares observed frequencies to expected frequencies.

The two categorical variables are independent. Assumes no relationship exists between the variables.

A strong association between two categorical variables. Higher values suggest variables are not independent.

Check for data entry errors or missing data. Mismatched totals indicate calculation or data entry errors.

To display the relationship between two categorical variables. Rectangle areas represent frequencies proportionally.

The count for a specific category combination in a two-way table. Shows the intersection frequency of two specific categories.

Context provides meaning to the statistical findings. Situational understanding is essential for meaningful conclusions.

Ensure axes are labeled with the correct variables. Correct labels prevent misinterpretation of the data.

The threshold for rejecting the null hypothesis, often 0.05. Cutoff point for determining statistical significance.

The probability of observing the data if the null hypothesis is true. Lower p-values provide stronger evidence against independence.

Check calculations for each percentage. Percentages within rows/columns should sum to 100%.

The frequency of a cell divided by the overall total, multiplied by 100. Shows each cell as percentage of grand total.

The frequency of a cell divided by the column total, multiplied by 100. Shows distribution within each column as percentages.

The frequency of a cell divided by the row total, multiplied by 100. Shows distribution within each row as percentages.

$(r-1)(c-1)$ where $r$ is rows and $c$ is columns. Accounts for table dimensions in hypothesis testing.

One variable does not affect the distribution of the other. Knowledge of one variable doesn't change the other's distribution.

Confusing association with causation. Association doesn't prove one variable causes the other.

Frequencies cannot be negative; check data entry. Frequencies must be counts, never negative values.

Expected frequencies should be at least 5 for each cell. Low expected frequencies make the test unreliable.

To test the association between two categorical variables. Determines if categorical variables are independent.

The proportion of the total for a subcategory. Height shows conditional frequency within that category.

The proportion of the total for a category. Width corresponds to marginal frequency of that category.

To visually represent the conditional distributions of a categorical variable. Shows how one variable is distributed within levels of another.

A frequency divided by the total for a row or column. Frequency relative to a specific row or column total.

The total frequency for a row or column in a two-way table. Totals along the edges showing single variable frequencies.

To display the relationship between two categorical variables. Rectangle areas represent frequencies proportionally.