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I have run a mixed effect model using GraphPad Prism 9 software on mouse blood pressure data. I have 8 subjects (3 in one genotype group, 5 in the other), and I have blood pressure data across time for most of these subjects (hence the mixed model, not 2-way ANOVA). I would like to know whether the blood pressure of these mice significantly differ at any time point between the genotypes.

There certainly seems to be significant differences starting at day 7 (the SEM bars do not overlap)...

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And to further support this idea, the Time x Genotype term is significant when I inspect the full model...

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However, none of the multiple comparisons at each time point between genotype are significant. How could this be?

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Can someone please help me understand how the multiple comparisons are not significant? Can I "reject the null hypothesis" that there are no differences between these genotypes over time?

The only thought that I've been able to come up with to explain this result already (but I feel are unsatisfactory) is that my sample size is too low and there are just too many multiple comparisons, reducing my power. I have not been able to find any satisfactory explanations online elsewhere or this site (however, if someone knows of one - please point me to it!)

I appreciate your input and advice in advance

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It is interesting to see such a strong effect of the Genotype x Time interaction in the model, that does not carry forward to a specific Day on the post-hoc testing.

As for why this mismatch might occur, I'm not super familiar with the Prism interface for estimating LMMs, but my best guesses would be that the effect of multiple days (7,8,9) together is driving the effect on ANOVA, but that the effect size on individual days is too small, in the context of small and unbalanced sample sizes (N=3, 5).

The choice of multiple comparison procedures may also affect this -- the Sidak procedure is generally considered more conservative when tests are positively dependent (yours would appear to be, since the different days are not independent tests). You could consider the Tukey honest significant differences test (aka Tukey-Kramer when group sizes are unequal) instead but it shares some of the same assumptions regarding test independence.

Opinions might differ on whether true multiple comparison controls are needed on such a small number of planned contrasts (9 days, 2 groups), or whether separate t-tests would not be unreasonable (assuming normality). The so-called "Fisher's protected LSD" refers to the procedure of using unadjusted p-values from the LSD test when F-tests from ANOVA show significance, which could be applied in this case.

Ultimately small effect/sample size may be your main issue, so more data is always helpful.

The textbook Biostatistical Analysis - Jerrold H. Zar has a very accessible discussion of ANOVA, and MCPs that you might find enlightening.

Ref: Sidak correction, https://en.wikipedia.org/wiki/%C5%A0id%C3%A1k_correction

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