# Beauchamp:ANOVAs in MATLAB

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While all of your data may be in Excel, unfortunately, the Excel for Mac doesn't do ANOVAs.

So, let's use MATLAB! In this example, I'm doing a 2x2 ANOVA on the BOLD amplitudes of response in the right STS (dependent measure).

The two factors are perceiver group (strong McGurk perceivers are '1' and non-perceivers are '2') and stimulus condition (McGurk is '1', non-McGurk incongruent is '2', and congruent is '3').

I'd like to know if there is a significant difference in the right STS response between the subjects who did and did not perceive the McGurk effect, between the responses to the 3 different stimuli, and if there is an interaction between perceiver group and stimulus type.

The data for the dependent measure and each factor are put into columns in Excel.

R_STS PerceiverGroup StimulusType 0.1662 1 1 0.0467 1 1 0.1364 1 1 -0.0025 1 1 0.0185 1 1 0.1162 1 1 0.1935 1 1 0.2685 2 1 0.0704 2 1 0.3541 2 1 0.1392 2 1 0.2367 2 1 0.0507 2 1 -0.0558 2 1 0.0738 2 1 0.0473 2 1 0.0119 2 1 0.1375 1 2 0.1354 1 2 0.1931 1 2 -0.26 1 2 0.0425 1 2 0.2904 1 2 0.3069 1 2 0.4702 2 2 -0.0295 2 2 0.391 2 2 0.2323 2 2 0.6401 2 2 0.0562 2 2 0.0488 2 2 0.0567 2 2 0.0635 2 2 -0.0592 2 2 0.1264 1 3 0.1002 1 3 0.1368 1 3 -0.0933 1 3 0.0391 1 3 0.2585 1 3 0.1405 1 3 -0.002 2 3 0.0307 2 3 0.1367 2 3 0.2007 2 3 0.438 2 3 0.0782 2 3 0.0595 2 3 0.0279 2 3 -0.0203 2 3 -0.0746 2 3

Then, I copied the data from each into a array in MATLAB with the same name.
(Copy only numerical data in "Excel", then type v=[ (paste) ] (enter).

Then, run the function 'anovan.m' in MATLAB:

anovan(R_STS,{PerceiverGroup StimulusType},'model',2,'varnames',strvcat('Group','Stim'))

The output is a chart-- copy it back into your Excel spreadsheet to have the numbers handy.

Source Sum Sq. d.f. Mean Sq. F Prob>F -------------------------------------------------------- Group 0.00787 1 0.00787 0.3 0.5848 Stim 0.03208 2 0.01604 0.62 0.544 Group*Stim 0.01316 2 0.00658 0.25 0.7775 Error 1.1696 45 0.02599 Total 1.2314 50

In this example, there was not a significant main effect of perceiver group or stimulus type (both p > 0.5) on the right STS response. There was also no interaction between the two factors (p > 0.7).

Degrees of freedom:

For the numerator, it's the number of categories in that factor minus one (a-1). Or, for the interaction, multiply (a-1)*(b-1). In this case, the numerator df is 1 (from 2-1) for the Perceiver Group factor and 2 (from 3-1) for the Stimulus Condition Factor. For the interaction, the numerator df is 2 (from 1*2). For the denominator, it's the total number of data points (17 * 3 = 51) minus the total number of categories (N - a*b). In this example, the denominator df are 45 (51 - 2*3).