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I have a dataset where I need to test whether there are significant differences between GroupA and GroupB.

GroupA and GroupB contain values obtained from an experiment that was repeated over 3 days (Day = 1, 2, 3). Measurements are obtained over 6 hours for each of the 3 days starting at 0 (Hour = 0, 1, 2, 3, 4, 5, 6). Since the data for the experiment are obtained hourly, the data within each group are not independent of each other.

I am not sure how to test for a significant difference if the values within a group are not independent. Any guidance will be greatly appreciated.

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    $\begingroup$ Given that you have gone to the bother of making timed measurements I would suppose that you are at least interested in some sort of time-dependence. Do not think that a 'significance test' is the full extent of a proper analysis of your data and do not take advice from anyone who does not first ask for plots of the data. $\endgroup$ Commented Oct 28, 2022 at 20:40

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Assuming the measurements are continuous and reasonably normal, one way to address your question is by means of a linear mixed model. This will include a dummy for the group, a random intercept for the statistical unit and a random intercept for day within each unit.

In R this can be done by the following command

library(nlme) mod_lme <- lme(resp ~ group, random = ~ 1 | unit_id/day, data = mydata) summary(mod_lme)

To assess the difference between the two groups, just look at the confidence interval of the parameter associated with the variable group.

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