ANOVA with some paired and some unpaired subjects

Question

I am a biologist rather than statistician so I might lack some insight.

I have measurements on two paired groups (baseline and follow-up) along with a separate group of healthy controls. In addition the design of the study is unbalanced (n = 12 for B and F and n = 5 for HC).

Question

• Is there an ANOVA technique that would allow me to carry out a fair ANOVA taking the inherent pairing into account for groups Baseline and follow-up?

I've done some analysis already with paired t-tests for baseline versus follow-up and then unpaired tests for each group versus the healthy controls but I wondered whether I was missing a more elegant technique.

Answer 1

An ANOVA is used in designed experiments, this experiment doesn't sound like it was planned. I am not trying to be a purist here, but with unplanned experiments it frequently happens that statistically significant results come from extraneous influences.

Even in experiments that result in using a paired statistic, procedure is important. Suppose that you want to determine the effect of two medications, call them A and B, on mice. Also, suppose that you will give each mouse both medications after a suitable time has passed between the first medication. If you subject each mouse in the experiment first to medication A and then to medication B, and you run a paired t-test on the measured response with a statistically significant result; you will not known if the sigficance is from the difference in medications A and B or if it is a response to receiving any type of medication. Here, medications A and B are counfounded with just being medicated.

If you followed some correct procedure in this experiment, you could also set up a regression model to analyze your data. ANOVA's are a special case of fitting data using a linear model.