Question

How does gender and occupational prestige affect credibility? Graduate students in a public health program are asked to rate the strength of a paper about the health risks of childhood obesity. In reality, all student raters are given the same paper, but the name and degree associated with the author are changed. The student raters are randomly assigned to one group from the following name ("John Lake", "Joan Lake") and degree (M.D., R.N., Ph.D.) combination. The raters score the paper from 1 to 5 on clarity, strength of argument, and thoroughness. The total scores (the sum of the three scores) are given in the table below. What can be concluded with an α of 0.05?

John Lake / M.D.	John Lake / R.N.	John Lake / Ph.D.	Joan Lake / M.D.	Joan Lake / R.N.	Joan Lake / Ph.D.
12 15 13 15 14	15 16 12 13 13	11 8 13 12 9	15 10 12 14 12	10 7 8 10 6	11 11 12 8 8

Compute the corresponding effect size(s) and indicate magnitude(s).
Name: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect  

Degree: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect  
Interaction: η² =   ;  ---Select--- na trivial effect small effect medium effect large effect  

Answer 1

Name: η² = 0.2221; large effect
Degree: η² = 0.2229; large effect
Interaction: η² = 0.18113; large effect

Explanation:

The data values are,

	M.D.	R.N.	Ph.D.
John	12	15	11
	15	16	8
	13	12	13
	15	13	12
	14	13	9
Joan	15	10	11
	10	7	11
	12	8	12
	14	10	8
	12	6	8

The two way ANOVA table for the data table is shown below,

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Name	45.63333	1	45.63333	14.26042	0.000925	4.259677
Degree	45.8	2	22.9	7.15625	0.003651	3.402826
Interaction	37.26667	2	18.63333	5.822917	0.008678	3.402826
Within	76.8	24	3.2
Total	205.5	29

Now, the effect size for each factor and interaction is obtained as follows,

For factor Name,

The effect size value 0.2221 indicates that, 22.21% of the variance is account for by factor Name.

For factor Degree,

The effect size value 0.2221 indicates that, 22.29% of the variance is account for by factor Degree

For interaction,

The effect size value 0.1813 indicates that, 18.13% of the variance is account for by interaction of Name and Degree.

(The η² value greater than 0.14 shows a large effect while η² value around 0.01 shows a small effect and 0.06 shows a medium effect)