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I'm trying to compare several sets of experiment data, by comparing means. I read there are several different tests such as Each Pair, Student’s t and All Pairs, Tukey HSD, which give different circles of different radius, an example shown below

enter image description here

How are the circles defined? How do I calculate the radius? And is there a rule what test one should use for what kind of data?

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    $\begingroup$ What kind of software is that? $\endgroup$ – user88 Feb 10 '13 at 12:17
  • $\begingroup$ @mbq, This is JMP. But is this comparison circle a general concept, not specific to the software? $\endgroup$ – LWZ Feb 10 '13 at 17:13
  • $\begingroup$ This is a first time I see such plot, so I think it is native to JMP. BTW I bet SAS would sue for even thinking to implement this in other applications (-; $\endgroup$ – user88 Feb 10 '13 at 19:53
  • $\begingroup$ @mbq, I'm sure they'll do. But what applications are these plots for? Or what other criteria I can use to compare data? Basically I want to compare several data sets and find out which set is significantly different from others, so I can exclude them in my future development. $\endgroup$ – LWZ Feb 10 '13 at 20:41
  • $\begingroup$ I suspect the red ones are outliers due to various methods and radii somewhat correspond to confidence intervals; but honestly I have no idea what this mean. However the question is now properly tagged so I hope some JMP expert will give you a satisfying answer soon. $\endgroup$ – user88 Feb 10 '13 at 21:18
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There is a discussion of the circle construction in the JMP help/manuals. See Statistical Details for Comparison Circles.

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those are post-hoc tests which should be performed after a ANOVA in JMP. I don't think you should take into account the circle, which are here I think for visual comparison.

If you have issue for statistical test: Clic on mean/ANOVA to obtain the result of the ANOVA, it will indicate if you have a statistical difference among your conditions/treatments. If the result provided below the graph is significant (in Analysis of Variance: Prob>F is <0.05 or lower), you can perform one of the posthoc test: choose one, not all of them. Choice may depend on your dataset or statistical reasons but I am not expert enough to provide you good explanation of all post hoc tests. Usually, in Biology, each pair student t test or Tukey HSD are used. Tukey HSD may provide less Type I error. Tukey HSD results are detailed below the figure and give you groups such as A, B, AB, C, D, etc... Different letter will indicate conditions/groups that are significantly different. Results also give the detailed P statistic. This is the result you want.

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