I am confused by my results. I tested significance of means for 5 groups of my data and ANOVA confirmed there was a significant result - so there is a mean that is statistically significantly different from other means. Then I use Tukey HSD to determine which pair of groups is causing the significant difference. I've only ever worked with simple data where it was very obvious which means clustered, but the following results are confusing me:
From a tutorial online the results from a Tukey HSD test showed:
## Site alpha groups
## Sil 72.99945 a
## Mah 62.03473 a
## Jam 32.62941 b
Clearly this means that group Jam clusters alone (it is labeled as b) so its mean is significantly different from the means of the other two groups.
Now here are my results:
Group alpha groups
1 1.5712 a
2 0.9868 ab
3 0.7421 ab
4 0.6506 b
5 0.4565 b
My questions/confusions are:
So this means that group 1 clusters alone in a, but then it is not significantly different from any of the other groups because 'a' also appears for groups 2 and 3? Or perhaps it is significantly different because it is the only one clustering to 'a' by itself?
Or perhaps the interpretation is that when comparing group 1 and 4 or group 1 and 5, it is significantly different because their lettering is different. But when comparing groups 2 and 3 to any other group, those pair are not sig diff because letters are shared?
Since my ANOVA on this dataset detected significance, does this automatically mean there is at least one group's mean that has to be significantly different from all other groups?
Finally, I've run into a scenario where my ANOVA shows significance but after running Tukey HSD, all groups have the same significance letter - how is this possible?