Which of the following is not a goodness-of-fit measure used in the context of the $\chi ²$ goodness-of-fit test?

• A. Pearson correlation coefficient
• B. Likelihood ratio statistic
• C. $\chi ²$ statistic
• D. $p$-value

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the context of the chi-square goodness-of-fit test, which is used to determine how well observed categorical data fit an expected distribution.
2. Step 2: Identify common goodness-of-fit measures used in this test, such as the Chi-square statistic, which measures the discrepancy between observed and expected frequencies.
3. Step 3: Recognize the Likelihood ratio statistic as another measure related to goodness-of-fit, often used as an alternative to the Chi-square statistic.
4. Step 4: Know that the p-value is used to assess the statistical significance of the test statistic, helping decide whether to reject the null hypothesis.
5. Step 5: Understand that the Pearson correlation coefficient measures the linear relationship between two continuous variables and is not a goodness-of-fit measure in the context of the chi-square test.