11.4: Chapter 11 - Key Terms and Symbols

Key Terms

\(\chi^2\) Distribution: a right-skewed probability distribution used primarily in tests of categorical data, such as the goodness-of-fit test and the test for independence. It is defined by degrees of freedom and becomes more symmetric as the degrees of freedom increase.

Degrees of Freedom: the number of independent values that can vary in an analysis. For a goodness-of-fit test, it is calculated as the number of categories minus 1. For a test of independence, it is calculated as (number of rows − 1) × (number of columns − 1).

Expected Frequency: the theoretical count of observations in each category or cell, assuming the null hypothesis is true. It is used to compare with the observed frequency.

Goodness-of-Fit Test: a \(\chi^2\) test determines if a sample distribution matches an expected or theoretical distribution.

Independence (Test of): a \(\chi^2\)test used to determine whether two categorical variables are independent or related based on data collected in a contingency table.

Observed Frequency: The actual count of observations collected in each category or cell from the sample data.

Test Statistic: A value computed from sample data that is used in hypothesis testing. Chi-square tests measure the discrepancy between observed and expected frequencies.

Key Symbols

\( \chi^2 \) – chi-square test statistic.

\( O \) – observed frequency.

\( E \) – expected frequency.

\( df \) – degrees of freedom.

\( p \) – p-value.

\( \alpha \) – significance level.

\( k \) – number of categories (for goodness-of-fit).

\( r \) – number of rows (in a contingency table).

\( c \) – number of columns (in a contingency table).

\( n \) – total sample size.