Return to Answer

First, whether you focus on the results of the overall ANOVA or the multiple comparisons depends on your research question. The null hypothesis in the overall ANOVA is that all data were sampled from one population with one mean. Multiple comparison tests are pairwise tests of the means of the groups. They are valid to perform even when the overall ANOVA is not significant. So ask yourself: is your research question "Do the data provide evidence that the means are not all identical"? If yes, focus on the result of the overall ANOVA which in your case provides evidence that not all groups have equal means.

Second, in your case, the failure of detecting any statistically significant post-hoc comparisons might also be due to statistical power (or lack thereof). In this post, whuber wrote:

[...] in some cases the data can reveal that the true means likely differ but it cannot identify with sufficient confidence which pairs of means differ. [whuber]

This might well be the case in your example. It might be that you have only enough data to answer the question that there is evidence that not all group means are the same but not which group means differ from each other.

First, whether you focus on the results of the overall ANOVA or the multiple comparisons depends on your research question. The null hypothesis in the ANOVA is that all groups are sampled from the same population with the same mean. Multiple comparison tests are pairwise tests of the means of the groups. They are valid to perform even when the overall ANOVA is not significant. So ask yourself: is your research question "Do the data provide evidence that the means are not all identical"? If yes, focus on the result of the overall ANOVA which in your case provides evidence that not all groups have equal means.

Second, in your case, the failure of detecting any statistically significant post-hoc comparisons might also be due to statistical power (or lack thereof). In this post, whuber wrote:

[...] in some cases the data can reveal that the true means likely differ but it cannot identify with sufficient confidence which pairs of means differ. [whuber]

This might well be the case in your example. It might be that you have only enough data to answer the question that there is evidence that not all group means are the same but not which group means differ from each other.

First, whether you focus on the results of the overall ANOVA or the multiple comparisons depends on your research question. The null hypothesis in the overall ANOVA is that all data were sampled from one population with one mean. Multiple comparison tests are pairwise tests of the means of the groups. They are valid to perform even when the overall ANOVA is not significant. So ask yourself: is your research question "Do the data provide evidence that the means are not all identical"? If yes, focus on the result of the overall ANOVA which in your case provides evidence that not all groups have equal means.

Second, in your case, the failure of detecting any statistically significant post-hoc comparisons might also be due to statistical power (or lack thereof). In this post, whuber wrote:

[...] in some cases the data can reveal that the true means likely differ but it cannot identify with sufficient confidence which pairs of means differ. [whuber]

This might well be the case in your example. It might be that you have only enough data to answer the question that there is evidence that not all group means are the same but not which group means differ from each other.

First, whether you focus on the results of the overall ANOVA or the multiple comparisons depends on your research question. The null hypothesis in the overall ANOVA is that all data were sampled from one population with one mean. Multiple comparison tests are pairwise tests of the means of the groups. They are valid to perform even when the overall ANOVA is not significant. So ask yourself: is your research question "Do the data provide evidence that the means are not all identical"? If yes, focus on the result of the overall ANOVA which in your case provides evidence that not all groups have equal means.

Second, in your case, the failure of detecting any statistically significant post-hoc comparisons might also be due to statistical power (or lack thereof). In this post, whuber wrote:

[...] in some cases the data can reveal that the true means likely differ but it cannot identify with sufficient confidence which pairs of means differ. [whuber]

This might well be the case in your example. It might be that you have only enough data to answer the question that there is evidence that not all group means are the same but not which group means differ from each other.

First, whether you focus on the results of the overall ANOVA or the multiple comparisons depends on your research question. The null hypothesis in the overall ANOVA is that all data were sampled from one population with one mean. Multiple comparison tests are pairwise tests of the means of the groups. They are valid to perform even when the overall ANOVA is not significant. So ask yourself: is your research question "Do the data provide evidence that the means are not all identical"? If yes, focus on the result of the overall ANOVA which in your case provides evidence that not all groups have equal means.

Second, in your case, the failure of detecting any statistically significant post-hoc comparisons might also be due to statistical power (or lack thereof). In this post, whuber wrote:

[...] in some cases the data can reveal that the true means likely differ but it cannot identify with sufficient confidence which pairs of means differ. [whuber]

This might well be the case in your example. It might be that you have only enough data to answer the question that there is evidence that not all group means are the same but not which group means differ from each other.

First, whether you focus on the results of the overall ANOVA or the multiple comparisons depends on your research question. The null hypothesis in the overall ANOVA is that all data were sampled from one population with one mean. Multiple comparison tests are pairwise tests of the means of the groups. They are valid to perform even when the overall ANOVA is not significant. So ask yourself: is your research question "Do the data provide evidence that the means are not all identical"? If yes, focus on the result of the overall ANOVA which in your case provides evidence that not all groups have equal means.

Second, in your case, the failure of detecting any statistically significant post-hoc comparisons might also be due to statistical power (or lack thereof). In this post, whuber wrote:

[...] in some cases the data can reveal that the true means likely differ but it cannot identify with sufficient confidence which pairs of means differ. [whuber]

This might well be the case in your example. It might be that you have only enough data to answer the question that there is evidence that not all group means are the same but not which group means differ from each other.