Tukey HSD test and p value

[#1]

I have two groups of data that I want to compare via the Tukey test. Graphical representation of the groups shows pairs as overlapping circles while ordered differences report p value is <0.05.  how can this difference explained? 

[#2 · Accepted solution]

Hi @JMPBeginer , and welcome. This phenomena can happen if the degree of overlap is not "enough": See link below.

Comparison Circles (jmp.com)

[#3]

This was something I discovered several years ago - I also thought the overlapping circles would have meant p>.05.  The correct explanation using the tangent lines and angles I find to be the rare JMP display that is not helpful.  The Tukey HSD analysis provides plenty of ways to explore which differences are significant and the circles are the least useful (in my opinion).

[#4]

The initial presentation of the comparison circles is not the end. You are supposed to interact with them. The center of each circle is plotted at the group mean. Click on a circle. This action is the same as asking, " Which means differ from this?" The selected group is plotted with a thick red line. The groups that are not significantly different are plotted in a thin red line. The groups which are significantly different are plotted with a thin gray line. Note that the font used to label the groups in the main plot is updated to synchronize with the circles.

[#5]

Thank you all for the answers ! That really helped with understanding the evaluation and being able to describe the results in my report