ANOVA result indicated that there were sig. differences while Tukey post-hoc test revealed that there were no statistically sig. differences [duplicate]

Question

I was conducted one-way ANOVA analysis to examone the level of knowledge shaorng among the employees based on there age differences. One-way ANOVA indicated that there were significant differences in the level on KS while Tukey post-hoc test revealed that there were no statistically significant differences on the level of knowledge sharing between the groups based on the respondent's age differences.

So, what is the conclusion of this result and why the result shows a different result? AND, how do i interpret this result? Table: Mean Scores on Level of Knowledge Sharing among Employees - Based on Age.

Age No. Mean    SD
20-29   34  3.82    1.13
30-39   54  3.87    0.92
40-49   56  3.41    1.06
over 50 45  3.32    1.24
Total   189 3.59    1.10


Table: ANOVA

    Sum of Squares  df  Mean Square F   Sig.
Between Groups  11.029  3   3.676   3.120   .027
Within Groups   218.021 185 1.178       
Total   229.050 188         


Table: Multiple Comparisons

(I) Age (J) Age Mean Difference (I-J)   Std. Error  Sig.    95% CI Lower Bound  Upper Bound
20-29   30-39   -.047-  .238    .997    -.66-   .57
        40-49   .408    .236    .311    -.20-   1.02
        over 50 .501    .247    .180    -.14-   1.14
30-39   20-29   .047    .238    .997    -.57-   .66
        40-49   .455    .207    .127    -.08-   .99
        over 50 .548    .219    .063    -.02-   1.12
40-49   20-29   -.408-  .236    .311    -1.02-  .20
        30-39   -.455-  .207    .127    -.99-   .08
        over 50 .093    .217    .974    -.47-   .66
over 50 20-29   -.501-  .247    .180    -1.14-  .14
        30-39   -.548-  .219    .063    -1.12-  .02
        40-49   -.093-  .217    .974    -.66-   .47

Many thanks for helping me to find the answer of my question.

Answer 1

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.