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I have a series of experiments that are done in a series of blocks(groups). When comparing the means of group 1 and group 2 that arent statistically significant p=0.84. However looking at the group 1 mean and group 2 mean, group 1 is always lower. Can I take the mean of group1a, group1b, group1c, group1d and the mean of group2a, group2b, group2c, group2d and do a t test with that?

in R: example data

group1<-c(0.7142857, 0.7042857, 0.7160, 0.7142857)
group2<-c(0.7380952, 0.7480952, 0.7280952, 0.734)
t.test(group1, group2)

Welch Two Sample t-test

data: group1 and group2 t = -4.9851, df = 5.082, p-value = 0.003974 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -0.03761274 -0.01210151 sample estimates: mean of x mean of y 0.7122143 0.7370714

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Are a, b, c, and d different experiments conducted on the same individuals (so that each individual takes tests a, b, c and d)? In that case, I don't think you should pool the results like you did.

Provided that the dependent variable is continuous, you could try a linear mixed model approach with group as a fixed effect and subject id as a random effect. This is needed to take into account that scores on the different tests might be correlated within each subject:

library(lme4)
lmer (score ~ group + (1|id))

If the experiments are scored differently, you should center and scale the scores (so that means and standard deviations are the same for all tests) before you enter them into the model.

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  • $\begingroup$ Hi Jonas, a,b,c,d are different experiments (same experiment different days) on the same individuals. The difference between Group1 and Group2 is I know something different about them and want to see if that difference is important. However, when I pool a,b,c,d group1 and do the same for group 2 and do a t test, I get nonsign data, but as mentioned group 1 mean is always lower than group 2 mean for each block comparison. $\endgroup$
    – Chad
    Sep 2, 2015 at 20:16
  • $\begingroup$ You can't pool the results because you need to take into account the correlation within each subject, so you need to do the mixed models approach as I describe above. You can't pool the means either, because you will ignore the variance in the results from the different individuals, and you will also ignore the correlation within each subject. So if you don't get significant results when pooling the results in all groups, I think your study is underpowered to detect the difference between the groups. $\endgroup$
    – JonB
    Sep 2, 2015 at 20:25

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