# Repeated measures ANOVA with replicated measurements.

I have performed an experiment testing 3 different modes of operation on 16 participants. Each mode of operation was tested twice per user.

User    Mode    Trial1Time  Trial2Time
1       1       20          30
1       2       5           7
1       3       40          25
2       1       10          20
2       2       15          17
2       3       30          35
3       1       13          26
3       2       11          11
3       3       35          38


I have run repeated measures ANOVA on my data using only the Trial1Times. I would like to use both Trial1 and Trial2 in the analysis however as I have such a small number of participants.

1. Is this possible with repeated measures?
2. If so, does this add statistical power to the results?
3. (Bonus) How would I go about doing this in SPSS?

Appendix: The data formatted in a different way (The actual numbers are different too, but I just made it up as an example)

User    Mode1   Mode1   Mode2   Mode2   Mode3   Mode3
Test1   Test2   Test1   Test2   Test1   Test2
1       10      15      20      25      30      35
2       12      12      23      21      31      33
3       14      16      27      26      35      39


1. Yes, this is very possible
2. Yes, this will add power

3. You'll need to format the data according to your second example to use SPSS repeated measures. Then you need to select Analyze -> General Linear Model -> Repeated Measures. In the Within-Subject Factor Name box, first type Mode and select 3 for number of levels, then click add. Then enter Time into the Factor Name box, select 2 for number of levels, and click add. Then click 'Define'. You should be able to select the six variables you've created and they'll slot into the right within-subjects boxes. Then just adjust any settings you want, click OK, and you'll have the analysis you want. Here's the syntax, though for slightly different variable names:

DATASET ACTIVATE DataSet0.
GLM Mode1.Trial1Time Mode1.Trial2Time Mode2.Trial1Time Mode2.Trial2Time Mode3.Trial1Time Mode3.Trial2Time
/WSFACTOR=Mode 3 Polynomial Time 2 Polynomial
/METHOD=SSTYPE(3)
/CRITERIA=ALPHA(.05)
/WSDESIGN=Mode Time Mode*Time.


Generally, one would have thought that you take mean of 2 trial times and apply repeated measures ANOVA test. This will be most understandable to the reviewers of your data. How to do this is trivial. This will add to the credibility of the study but I am not sure of the power calculations for this.

Sorry this is coming late. I suppose my response will be for others with similar challenges. The method described by Sean is correct. It is called a two way repeated measures design such that your experiment has two factors namely 1) mode: 3 levels and 2) time: 2 levels. For better understanding, there are YouTube videos on two way repeated measures design.