Next, Flaye decides to run post-hoc tests with Holm correction. The results are shown below.

data: attendance and day

fri sat
sat 0.61283 -
sun 5.6e-05 0.00019

Which of the following is the best interpretation of these results?

Question

Next, Flaye decides to run post-hoc tests with Holm correction. The results are shown below.

data:  attendance and day

fri     sat    
sat 0.61283 -      
sun 5.6e-05 0.00019

Which of the following is the best interpretation of these results?

BlackTom AI · Accepted Answer

Holm-corrected pairwise p-values from the table are: Fri vs Sat = 0.61283, Fri vs Sun = 5.6e-05, Sat vs Sun = 0.00019. These are adjusted p-values from the post-hoc tests and are interpreted against a significance level (typically α = 0.05). 1) Relevant concepts - Pairwise post-hoc p-values: show whether the mean attendance differs between two days. - Holm correction: a stepwise multiple-comparison adjustment; the reported p-values are already adjusted, so compare them directly to α. - Statistical significance: p < 0.05 indicates a significant difference. 2) Step-by-step reasoning - Compare Fri vs Sat: p = 0.61283. Since 0.61283 > 0.05, there is no significant difference between Friday and Saturday attendance. - Compare Fri vs Sun: p = 5.6e-05 = 0.000056. Since 0.000056 < 0.05, Friday and Sunday differ significantly. - Compare Sat vs Sun: p = 0.00019. Since 0.00019 < 0.05, Saturday and Sunday differ significantly. 3) Intermediate calculations (for comparison with a stricter correction) - Bonferroni-adjusted p would be p * number_of_comparisons (3): - Fri vs Sun: 0.000056 * 3 = 0.000168 < 0.05 → still significant - Sat vs Sun: 0.00019 * 3 = 0.00057 < 0.05 → still significant - Fri vs Sat: 0.61283 * 3 = 1.83849 > 0.05 → not significant 4) Why the correct answer is correct Because both comparisons involving Sunday produce p-values far below 0.05 (after Holm adjustment), Sunday’s attendance is significantly different from both Friday and Saturday. The Fri–Sat comparison is not significant. 5) Why the other options are incorrect - "61.3%..." is a misreading of a p-value, not a proportion of attendance. - "Friday has significantly higher attendance than Sunday..." is wrong direction and contradicts the p-values (Fri vs Sun is significant, but it doesn’t state which is higher; the table reports only significance). - "Friday and Saturday have the highest correlation..." conflates correlation with pairwise mean-difference tests; the table gives p-values for differences, not correlations. - "None would have been significant if Bonferroni..." is false because the very small p-values remain significant even after Bonferroni adjustment. Conclusion: Attendance on Sunday is significantly different than both other days. This matches the correct interpretation.

Next, Flaye decides to run post-hoc tests with Holm correction. The results are shown below. data: attendance and day fri sat sat 0.61283 - sun 5.6e-05 0.00019 Which of the following is the best interpretation of these results?Single choice

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