Question

Dr. Bellus wants to study how people's perception of attractiveness is affected by the gender of the subjects, and the facial expression of the object. Each participant views six headshots (in random order) of the same person, who demonstrates different facial expressions (joy, surprise, fear, anger, sadness, and disgust) in each picture. The participants are then asked to rate the attractiveness level of each picture. The rating is the dependent variable. Below is the selected output of a two-factor split plot ANOVA.

Source	Type III SS	DF	MS	F
Between subjects
A	226.81	1	226.81	3.04
S	2084.61	28	74.45
Within Subjects
B	18802.53	5	3760.506	38.07
A*B	324.22	5	64.84	0.66
B*S	13829.70	140	98.78

(a) Identify the between-subjects factor and within-subjects factor.

(b) Are the effects significant (α = .05)? What do these results tell us about people's perception of attractiveness?

(c) Is MCP necessary? If so, which effect(s) should we conduct MCP on?

Answer 1

a) To identify the factors we can take some clues from the ANOVA table. Let's do this for the between-subjects factor:

The first clue is that the degrees of freedom (DF) of the factor will be equal to the number of different characteristics or values this can take. We notice that we are looking at the differences in attractiveness in the two genders (male and female), since there are only two "classes" for this factor, it must have DF = 1 so this points us towards A being the between-subjects factor.

We could have also looked at the column labeled F and noticed that the only row with a value for F in the between subjects section is the row for A. Since the F number helps in determining the significance of a factor we can assume that we are looking for the significance of A over S.

Similarly we can find that with 6 treatments (1 for each expression) we must have a within-subjects factor with DF = 5. We discard A*B since this would be the interaction of A with another factor B. We conclude that B must be the within-subjects factor.

b) To determine the significance of the effects we must compare the F statistics given to the values of F in the table for the corresponding degrees of freedom. For example, for A, we take:

F3.04

And we look up on the F table that for degrees of freedom 1 and 28 we have the value 7.6356. We conclude that A is not significant since

F-3.047.6356

F Distribution ( 0.01 in the Right Tail) Numerator Degrees of Freedom df df 4052.2 4999.5 5763.6 5859.0 5928.4 6022.5 98.503 99.000 30.817 99.299 28.237 15.522 99.333 99.388 29,457 28.710 15.207 10.672 11.392 16.258 13.274 10.925 8.2600 6.9928 8.7459 8.4661 6.7188 7.0061 6.4221 5.9943 5.6683 6.6318 6.0569 5.6363 5.3160 5.0643 4.8616 6.3707 5.8018 5.3858 6.0289 10.561 8.0215 6.9919 6.5523 6.2167 5.9525 5.2001 5.0567 4.7445 9.6460 9.3302 9.0738 8.8616 8.6831 8.5310 7.2057 6.9266 6.7010 6.5149 6.3589 6.2262 4.3875 5.2053 4.4410 4.2779 4.3021 5.5639 5.2922 5.0919 4.4558 4.5556 4.4374 4.8932 4.0045 3.8948 3.7804 3.6822 3.5971 3.5225 3.4567 3.3981 3.3458 4.2016 3.7910 3.7054 3.9267 8.2854 8.1849 6.0129 4.5003 20 4.9382 4.8740 3.8714 3.8117 3.6987 8.0166 7.9454 4.0421 3.5056 3.5867 3.5390 4.7649 3.4057 7.8229 3.8951 3.8550 3.7848 3.6667 3.2560 4.6755 3.3239 5.5263 5.4881 3.4210 3.3882 3.3581 3.3303 3.3045 3.1818 3.5580 3.5276 3.2558 3.2259 3.1982 3.1726 2.9930 2.8233 4.5681 4.5378 4.0740 3.0920 7.5625 5.3903 3.8283 3.2910 7.0771 6.8509 6.6349 3.3389 2.9530 4.7865 4.6052 3.9491 3.4795 2.6393 2.5113 2.4073