A researcher conducts a study and finds a statistically significant difference between two groups. Which of the following statements is NOT necessarily true?

Question

A researcher conducts a study and finds a statistically significant difference between two groups.  Which of the following statements is NOT necessarily true?

BlackTom AI · Accepted Answer

When interpreting a statistically significant difference between two groups, several statements are often considered, but not all are guaranteed by significance alone.
Option 1: 'The results are unlikely to have occurred due to random chance.' This is the essence of statistical significance: a low probability that the observed difference is due to random variation alone, assuming the null is true. It is a core implication of finding significance, though it does not quantify practical importance.
Option 2: 'The null hypothesis can be rejected.' A statistically significant result typically leads to rejecting the null hypothesis, because the observed difference is unlikely under the null model, given the chosen alpha level. This follows from standard hypothesis testing logic.
Option 3: 'The difference between the groups is practically meaningful.' Here lies the subtlety: statistical significance does not automatically imply practical or clinical significance. A result can be statistically significant yet have a trivial effect size or be irrelevant in real-world terms, especially with large sample sizes where small differences become statistically detectable. This is the statement we must mark as NOT necessarily true.
Option 4: 'The p-value is less than the significance level (alpha).' By definition of statistical significance, a p-value below alpha supports rejecting the null; this is a direct consequence of achieving significance, and thus is typically true when a difference is statistically significant.
Altogether, only option 3 is not guaranteed by the finding of statistical significance, because significance does not automatically translate to practical importance, whereas the other statements reflect standard interpretations of significance testing.

A researcher conducts a study and finds a statistically significant difference between two groups. Which of the following statements is NOT necessarily true? Single choice

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