Multiple Comparisons

In statistical analysis, what is the primary purpose of conducting post hoc comparisons after an initial test rejects the null hypothesis?

When comparing three or more group means, researchers must follow a logical sequence of statistical decisions. Match each statistical outcome or procedure with its specific role in this process.

A clinical psychologist is investigating the effectiveness of three different treatments for social anxiety: Cognitive Behavioral Therapy (CBT), Mindfulness-Based Stress Reduction (MBSR), and a Control group. After collecting anxiety scores from all participants, the researcher wants to identify which specific treatments are significantly more effective than the others. Arrange the following steps in the correct statistical sequence to reach this conclusion.

In a psychological experiment comparing three or more groups, a significant result from the initial overall statistical test is sufficient on its own to identify exactly which specific pairs of group means are significantly different from one another.

When a one-way ANOVA results in rejecting the null hypothesis, researchers conduct post hoc comparisons to determine exactly which pairs of group means are significantly different from each other.

A researcher compares mean anxiety scores across four therapy groups using an overall statistical test and finds a significant result. Because this overall test only indicates that not all group means are equal — without revealing which specific groups differ — the researcher must conduct _____ to identify exactly which pairs of group means are significantly different from one another.

In a psychological experiment comparing the effectiveness of three different mnemonic strategies on memory recall, a researcher obtains a significant result in a one-way ANOVA ($F(2, 87) = 5.12, p = .008$). If the researcher concludes that 'Strategy 1 is significantly superior to Strategy 3' based solely on this result, this specific conclusion is statistically _____ because the omnibus test does not pinpoint which group means are significantly different from one another.