# Factorial experiment, fixed model and mixed model using SAS

In the construction of a projective test, 40 more or less ambiguous pictures of two or more human figures were used. In each picture, the sex of at least one of the figures was only vaguely suggested. In a study of the influence of the introduction of extra cues into the pictures, one set of 40 was retouched so that the vague figure looked slightly more like a woman; in another set each was retouched to make the figure look slightly more like a man. A third set of the original pictures was used as a control. The forty pictures were administered to a group of 18 men college students and an independent group of 18 women college students. Six members of each group saw the pictures with female cues, six the pictures with males cues, and six the original picture. Each subject was scored according to the number of pictures in which he interpreted the indistinct figure as a female. The results follow:

(See data table in attached file)

Using σ = 0.05 for each overall test, state and verify the assumptions for (a) and (b) below and assuming all assumptions are satisfied:

a) Analyze the experiment assuming a fixed ANOVA model

b) Analyze the experiment assuming a mixed ANOVA model where cues are fixed and gender is random.

Please see the attachment.

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I have attached three file to this response, A word document ...

#### Solution Summary

This solution shows how to use SAS to analyze a two factor factorial experiment. Two analyses were completed. The first analysis assumed a fixed ANOVA model and the second assumed a mixed ANOVA model.

I have attached three file to this response, A word document containing the SAS program used to solve this probem, A word document with the output of that program, and a Word document with explanations of assumptions and detailed explanation of the SAS output.