Understanding Chi-Square Test for Frequency Data Analysis

Jan 04, 2026

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The Chi-square test is a statistical method used to analyze frequencies or proportions among two or more groups. It involves calculating the Chi-square statistic by summing the squared difference between observed and expected frequencies, divided by the expected frequencies. This test helps determine if there's a significant association between categorical variables, such as class and survival on the Titanic. By employing the bootstrap method, researchers can estimate proportions and test hypotheses about independence across groups.

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Understanding Chi-Square Test for Frequency Data Analysis

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Ch. 28 Chi-square test • Used when the data are frequencies (counts) or proportions for 2 or more groups. • Example 1

5. Calculate ((observed-expected)^2) expected 6. Calculate Chi-square = sum of the values from step 5. The degrees of freedom = (# rows - 1)x(# columns – 1). Find the p-value using the Chi-square table. Activity: Titanic survival data
Example 2: Titanic survival data grouped by class.
Null hypothesis: Class and survival are independent. In other words, everyone had the same chance of survival. Use the bootstrap method to estimate the proportions in the box based on the observed data. Null hypothesis: The proportion of “yes” in every class is the same as the overall proportion = 38%.