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I am conducting an experimental study. I have 2 groups: The first group contains 3 healthy persons and the other one contains 3 patients (sick people). For each person of the sudy, we collect several cells, from which we extract 3 features. The goal is to show significant differences between the 2 groups. In other way, we have:

enter image description here

x are numerical values

Which test is the more suitable to show significant difference between the patient and the healthy group?

I saw several tests like Hotelling, ANOVA..., but in those tests the mean of each group is computed on all cells of all the people of a group without making a difference between the person within the group. Is it possible to include person variablity in such test? Is 2-way ANOVA a solution to take into consideration the people in the comparison? The two independant variables (factors) are thus the identity of the person and its situation (Healthy or patient)?

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  • $\begingroup$ A test is not enough in this case. A linear model is the natural progression, to include the variability of the patients you can include a random effect. $\endgroup$ Commented Feb 6, 2020 at 9:03

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You could include patient as a random effect in your model to account for correlation between cells from the same patient. Something like:

lmer(group ~ feature1 + (1 | patient), data=data)

or

aov(group ~ feature1 + Error(patient/feature1), data=data)

Syntax not tested, taken from this blog.

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