In Your Comment State: When Should You Run A Post

In Your Comment State The Followingwhen Should You Run Post Hoc Tests

When should you run post hoc tests? Why would you conduct a post hoc test? Explain why not just run three different t-tests, one comparing groups 1 and 2, one comparing groups 1 and 3, and one comparing groups 2 and 3? Provide an example in which you would need to run a post-hoc test. Part 2: State whether the example provided justifies the need to conduct a post-hoc test. In your reply explain your agreement or disagreement. - Imagine looking for the Ace of Clubs in a deck of cards: if you pull one card from the deck, the odds are pretty low but if you keep trying eventually you will pull the Ace.

Paper For Above instruction

Post hoc tests are statistical procedures conducted after an ANOVA (Analysis of Variance) has indicated that there are significant differences among group means. The primary purpose of these tests is to identify specifically which groups differ from each other, as ANOVA alone does not specify the nature of these differences. Conducting post hoc tests is essential when the initial analysis suggests overall significance, but pinpointing the particular pairs of groups that differ requires further examination.

One might ask why not just run multiple independent t-tests to compare each pair of groups instead of employing post hoc procedures. While at first glance, this approach seems straightforward, it is statistically flawed because it inflates the Type I error rate, which is the probability of falsely rejecting the null hypothesis when it is true. Performing multiple t-tests without adjustment increases the likelihood that at least one test will produce a significant result purely by chance. For example, if three t-tests are conducted at an alpha level of 0.05, the probability of at least one false positive exceeds 10%, undermining the reliability of the results. As a solution, post hoc tests incorporate adjustments—such as the Bonferroni correction or Tukey's Honestly Significant Difference (HSD)—that control the familywise error rate, ensuring that the overall probability of false positives remains within an acceptable threshold.

An example where post hoc testing is needed involves a study examining the effects of three different teaching methods (A, B, and C) on student performance. Suppose an ANOVA reveals a significant overall difference among the groups. To determine which specific methods differ, researchers would conduct post hoc tests. Comparing only pairs directly, such as method A vs. B, A vs. C, and B vs. C, necessitates adjustments to maintain the integrity of statistical inference. These adjustments guard against the increased risk of Type I errors that come with multiple comparisons. If, for instance, the ANOVA shows that students taught with method A perform significantly better overall, the subsequent post hoc tests might reveal that A differs significantly from C but not from B. This detailed comparison informs educators about which teaching method is most effective without increasing the chance of false positives.

Regarding the analogy of searching for the Ace of Clubs in a deck of cards: if you pull just one card, your odds of selecting the Ace are quite low, roughly 1 in 52. However, if you repeatedly draw cards—akin to conducting multiple comparisons or tests—the probability of eventually drawing the Ace increases. This illustrates why multiple testing without proper correction inflates the Type I error. Without appropriate adjustments, pursuing multiple t-tests (or multiple comparisons) is like repeatedly trying to find the Ace: the chance of a false positive (incorrectly declaring a difference or an effect) accumulates, leading to potentially misleading conclusions. Therefore, in research, it is essential to use post hoc tests that control for this increased risk, much like understanding that repeatedly shuffling the deck and drawing many cards raises the chance of finding that elusive Ace, but with a need for proper correction to avoid false confidence.

References

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