Paired t-test with multiple measurements per pair

Question

I'm measuring a property of tissue using two different tools A and B. I've made 10 measurements with A and 10 measurements with B, on the same tissue. I've performed these measurements on 8 different pieces of tissue.

• Independent variables: Tool used (A or B) and tissue (1-8)
• Dependent variable: The property measured 10 times for {A,1}, 10 times for {A,2}, etc.

What would be an appropriate tool for testing whether tools A and B give the same mean? If I had just performed one measurement on each tissue, I would have used the paired t-test with 8 pairs.

Please apologise my imprecise wording, it was a while since I worked with statistics and I'd be happy to clarify anything.

Answer 1

If your design is fully balanced (as it looks like from your description, and there is no missing data), you can just replace the replicate measurements with their means and then continue with the paired comparison (at least if you have approximately normal(ish) additive errors ...). Otherwise, this is repeated measures data, and can be measured as such.

If you are using R, with package lme4 it could look like (with your data in long form):

library(lme4)
mod0 <- lmer(Y ~ tool + (1 | tissue), data=your_data_frame)
summary(mod0)