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Z score interpretation for Dunn's test

anzac21

I just performed a Kruskal-Wallis Test to compare movements between 4 groups of frogs and now I am going through the pairwise Dunn's comparisons. I'm trying to report my results in a paper. How do I interpret the z-scores that JMP gives for Dunn's Test?

For example, for one of the comparisons the first level (let's call Group A) is compared to the second level (let's call Group . JMP gives me a Z score of -3.64. My interpretation of this is that Group A is 3.64 units less than Group B. So I'm wondering, when I go to report my results in the text, would it be incorrect for me to make a statement like "Group B frogs moved greater distances (mean: 42 meters +/- 0.5; Z = -3.64, P = <0.0001) than Group A (mean: 2 meters +/- 0.2)? Would I need to remove the negative symbol before the Z score because JMP was using Group A as the reference rather than Group B? Or would the Z score be something different altogether if Group B were the reference?

I know I could just state that Group B frogs moved shorter distances than Group A frogs and not have to worry about it, but I'm trying to be concise and Group C and Group D also moved greater distances than Group A so instead of using a lot of text going back and forth, I'd like to list the stats consecutively like this:

"Pairwise comparisons indicated that Group B, Group C, and Group D frogs exhibited significantly greater daily distances (Group B: mean = 43.38 ± 13.07 m/day, z = -5.52, P = <0.0001; Group C: mean = 11.30 ± 2.17 m/day; z = -4.46, P = <0.0001; Group mean = 10.20 ± 2.11 m/day, z = -4.34, P = <0.0001) than Group A frogs (mean = 0.24 ± 0.13 m/day; Fig. 5b)."

Accepted answers

MRB3855

Hi @anzac21 . If you provide screenshots of the output we’d be better positioned to respond fully. That said, your interpretation of the z score is incorrect. The z-score is the statistic that the p-value is calculated from. Briefly, it can be thought of as a signal to noise ratio. It it is large enough, the signal (difference between groups) is said to be “statistically significant”. “Large enough”, in this context, is often said to be when the p-value is less than 0.05. So, the z-score and the p-value are telling you the same thing, just in different ways. To avoid confusion, you may choose to just report the p-value. For me, however, p-values can be misleading; I prefer confidence intervals…but that is for another discussion.

All comments

MRB3855

anzac21

Hi @MRB3855, thank you for the response.

I see, so the z-score is more about magnitude than the sign (+ or -)? The signs were what was confusing me in my situation because I wasn't sure if they were critical to the interpretation of my results. Here is a screenshot of what I'm getting: Screenshot 2024-02-23 at 8.23.40 AM.png

So on the last row, if WebbSoftRelease was in the second column level and SRSHardRelease was in the first column level, would the Z-score be unchanged?

MRB3855

Hi @anzac21 No, the sign would change (but the magnitude would be the same). It will always be the same sign as the score mean difference. It is calculated as (score mean difference)/(std err diff).