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Let's say we have a database of 160 participants, but only 60 participants are selected for the next phase of the study. Let's say that all participants (N = 160) filled in the test (eg. a depression score). Now we want to compare the results of the depression test between the selected groups of interest (say, students, workers and pensioners) - in the first group of N=160 and subgroup of N=60. N = 60 have equal sample sizes of each group (students, workers and pensioners; N = 20), and N = 160 have unequal sample sizes (e.g. students N = 100, workers N = 40 and retire persons N = 20). The ANOVA test is significant for N = 60 group, but not significant of N = 150 group. Is there a way to perform some other test (only one) to test the depression scores differences in both samples (N=60 subgroup and N = 160 group)? How to evaluate which test shows a "true" effect?

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    $\begingroup$ How, precisely, were the 60 participants selected for the second phase? The issue is whether they are a representative sample of all 160. What is the "effect" to which you are referring? Differences in scores between the two study phases or changes in the between-group differences or perhaps something else? $\endgroup$
    – whuber
    Jun 28, 2023 at 22:20

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