Best way to analyse my data: 2-way repeated measures anova?

#1
:wave::wave: Hi TalkStats :wave::wave:

I have a data set which is outlined in the table below:

\(
\begin{tabular}{|l|cr|}
\hline
ID & baseline & response \\
\hline
1 & $x_1$ & $y_1$ \\
1 & $x_2$ & $y_2$ \\
1 & $x_3$ & $y_3$ \\
1 & $x_4$ & $y_4$ \\
2 & $x_5$ & $y_5$ \\
2 & $x_6$ & $y_6$ \\
2 & $x_7$ & $y_7$ \\
3 & $\cdots$ & $\cdots$ \\
\hline
\end{tabular}
\)

The data consists of 4 different ID's (4 different humans), and each human has had a baseline recording (\( x \)) and a response recording (\( y \)) taken about 3 times (this varies from human to human). I want to compare the means \( \bar{x} \) and \( \bar{y} \), whilst controlling for the fact that I have a repeated measures, and 3-4 recordings for each human.

I have tried comparing weight means, but this doesnt account for the fact that I have 4 different people. How would I analyse this data, given the low number of recordings (approximately \( n=14 \) in total).

I think the best idea would be to do a 2-way repeated measures ANOVA, with one of the independent variables being the human ID, taking values 1-4. What do you guys think?

:tup::yup::tup: Thanks for your help!!! :tup::yup::tup:
 
#2
Hi and welcome aboard :)

Your chosen test seems the best (of course if its assumptions are met). However, in your discussion, if your findings were nonsignificant (which is not unlikely) you should state that you had a low test power (as a limitation) and should afterward state that "this study was a pilot study and can be used as a guide for directing future studies in the right way". (because nonsignificant results of such a small sample cannot be so reliable).

Note: it is possible that the assumptions of repeated-measures two-way ANOVA are not met in your rather small sample. In that case, you should use a Freidman test (its nonparametric alternative) instead.