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Section 6.11 Key Takeaways
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The Chi-Square test helps us determine whether two categorical variables are related.
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It compares the observed frequencies (what we saw) to the expected frequencies (what we’d expect by chance).
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A large Chi-Square statistic and a p-value < .05 suggest that the relationship is statistically significant.
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Degrees of freedom (df) are based on the number of categories: (rows - 1) * (columns - 1).
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Cramer’s V measures the
strength of the relationship, similar to a correlation coefficient:
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Residuals show which specific groups contribute most to the Chi-Square result.
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Visualizations (like bar charts or heatmaps) make it easier to interpret where the differences lie.
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Statistical significance ≠ practical significance — even weak relationships can be significant with large samples.
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Example takeaway: Cranberry treatment showed fewer infections than expected — a weak but meaningful effect!
