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I have a behavioral measure obtained from N participants over 5 levels of a condition C -- 10, 30, 50, 70, an, 90 degrees. With a one-way repeated measures ANOVA, I find a significant effect of C. Now qualitatively it appears that the behavioral measure increases from 10 to 30, and slightly from 30 to 50, but then saturates at 50 degrees.

Is there a way to show statistically that I'm finding an effect that increases at first and then saturates? Would it be sufficient to say that 10 & 30, and 30 & 50 are statistically different (through paired t-tests), but 50 & 70, and 70 & 90 are not (and that the resulting p-values for these two are very large)?

Thanks!

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    $\begingroup$ What does saturates mean? Does it mean that the slope of increase is going to zero? $\endgroup$ Sep 6, 2012 at 22:07
  • $\begingroup$ Yes, that is what I meant. $\endgroup$
    – Vanya
    Sep 7, 2012 at 12:45

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If saturation means that the slope of increase is going to 0, then I think you could show this by testing the paired differences and showing that the are not significant different from 0 for 50-70 and 70 -90 but perhaps are statistically signficantly greater than 0 for 0-30 and 30-50. However, statistical significance depends on sample size. If N is large then small increases at the higher levels would be declared significant. If N is small even large difference might not be statistically significant at the low levels.

I think it would probably be better to define a small slope A that you would consider to be small enough to indicate saturation and you test the null hypothesis that the difference is less than A versus the alternative that it is bigger than A. Hopefully you would then be able to say that at the lower temperatures the increase is statistically significantly greater than A and for the high temperatures the increase is not statistically significantly greater than A.

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  • $\begingroup$ Thank you so much for the suggestions. I will conduct and report both tests to be on the safe side. $\endgroup$
    – Vanya
    Sep 7, 2012 at 12:47

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