Final answer:
The Bonferroni-Holm test increases the test power over the Bonferroni test by using a step-down procedure to adjust the alpha levels for multiple comparisons.
Step-by-step explanation:
The Bonferroni-Holm test improves on the Bonferroni test by adjusting the alpha level in a step-down procedure. This test controls the family-wise error rate like the original Bonferroni but is less conservative. The procedure starts by ordering the p-values from smallest to largest and then comparing each to a different alpha level. For the first test, alpha is divided by the number of tests (n), for the second test, alpha is divided by n-1, and so on. If a p-value is smaller than its corresponding alpha level, the null hypothesis for that test is rejected, and the procedure continues to the next smallest p-value, testing against a new alpha level. Otherwise, the procedure stops, which means that subsequent hypotheses are not rejected.
Essentially, the Bonferroni-Holm test adjusts the alpha level based on the number of comparisons that remain, which offers a slight increase in power over the traditional Bonferroni test. For instance, if a null hypothesis is not rejected at significant level alpha = 0.01, this implies one does not have sufficient evidence to reject it, aligning with scenario d, Do not reject the null hypothesis. The claim in scenario f suggests that when results are not statistically significant, the academic group's claim is considered correct.