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I have three individuals with 50 measurements of walking movement. The measurements have been transformed to be normally distributed. I applied a one way ANOVA, and it showed that the three groups are different from each other, namely the third group from the second and first group. However, the difference is of 7 cm, which is negligible in clinical terms.

How do I address this? The pvalue is <0.0001, but the difference is not clinically significant.

I have also tried Kruskal Wallis nonparametric test ANOVA, and it remained significant.

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  • $\begingroup$ Just to add briefly to the answer provided by @Dave, you can also always look at the effect size, which I would guess is very small here. I like also looking at effect sizes in these cases since it's a kind of sanity check on the model: if the effect size suggests that this is a non-trivial difference, then maybe the model is misspecified or there is an error somewhere in the data $\endgroup$
    – Billy
    Commented Dec 21, 2020 at 21:53

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The hypothesis test is doing exactly what it claims to be able to do: it is flagging to the investigator that there is an unusually high F-stat, too high for the null hypothesis to be believable.

Armed with that information, the investigator is allowed to conclude, "That is not enough of a difference to be interesting. There is no clinical significance."

"Practical significance" of the “effect size” is a good general term for this that you will find in the literature and here on Cross Validated. In your field of medicine, clinical significance would be a fine specific term.

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