Yes, it is possible to get non-significant results in post hoc test when we got the significant result in ANOVA. This can happen for several reasons, such as:
- The ANOVA is more sensitive to detect any differences among the groups, while the post hoc test is more conservative and adjusts for multiple comparisons. Therefore, the ANOVA may reject the null hypothesis of equal group means, but the post hoc test may fail to identify which specific pairs of groups are significantly different.
- The ANOVA is based on the assumption of normality and homogeneity of variance, while the post hoc test does not require these assumptions. Therefore, if the data violate these assumptions, the ANOVA may give a misleading result, while the post hoc test may be more robust and accurate.
- The ANOVA is affected by the sample size and the number of groups, while the post hoc test is not. Therefore, if the sample size is small or the number of groups is large, the ANOVA may have low power and high type II error rate, while the post hoc test may have higher power and lower type II error rate.
To interpret this situation, one can report that the ANOVA showed a significant effect of the factor on the outcome variable, but the post hoc test did not reveal any significant pairwise differences among the groups. This means that there is some evidence of heterogeneity among the group means, but it is not clear which groups are driving this effect. One can also discuss the possible reasons for this discrepancy and suggest further analysis or investigation to clarify the results.