What effect size measure should they calculate for this dataset?

Question

BlackTom AI · Accepted Answer

Cramer's V is appropriate because it quantifies association strength for two categorical (nominal) variables analyzed with a chi-square test.

1) Relevant concepts:
- Categorical association: when both variables are nominal (e.g., gender and preference), effect size for a contingency table is required.
- Cramer's V: standardized measure (0 to 1) for chi-square tests, adjusts for table size.
- Other measures: Cohen's d (mean difference for continuous outcome between groups); eta-squared and partial eta-squared (ANOVA/variance explained for continuous outcomes); R2 (variance explained in regression).

2) Step-by-step reasoning:
- Determine variable types: if both variables in the dataset are categorical and you performed (or will perform) a chi-square test of independence, use Cramer's V.
- Compute chi-square statistic (χ2) from the contingency table.
- Obtain total sample size n and table dimensions r (rows) and c (columns).

3) Calculation (intermediate steps/formula):
- Let r = number of rows, c = number of columns.
- Degrees for adjustment = min(r - 1, c - 1).
- Cramer's V = sqrt( χ2 / (n * min(r - 1, c - 1)) ).
- Example workflow: calculate χ2 from observed/expected counts → compute denom = n * min(r - 1, c - 1) → divide χ2 by denom → take square root → result between 0 and 1.

4) Why this is correct:
- Cramer's V standardizes the chi-square statistic so effect size is comparable across table sizes; it is the conventional effect-size measure paired with chi-square tests of independence for categorical data.

5) Why other options are incorrect:
- Cohen's d: for standardized mean differences between two groups on a continuous outcome, not for contingency tables.
- η2 (eta squared): measures variance explained in ANOVA (continuous dependent variable).
- Partial η2: used when controlling for other factors in ANOVA/ANCOVA designs.
- R2: proportion of variance explained in regression models (continuous outcome), not for nominal-by-nominal association.

6) Conclusion:
Because the dataset involves an association between categorical variables assessed via chi-square, the correct effect size to calculate is Cramer's V, which matches the provided answer.

What effect size measure should they calculate for this dataset?单项选择题

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