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Student ratings of college instructors is common and widespread across the USA. Often such ratings consist of several instructional dimensions such as course organization, clarity of presentation, utility of course material, etc. Often the overall mean of responses to these items are used as a summary measure of teaching effectiveness for tenure, promotion, and merit pay evaluations.

Of interest to many faculty is whether factors other than instructional activities predict (or possibly affect) the overall mean instructional rating. Assume a college instructor wishes to know whether

(a) perceived autonomy among students,

(b) student efficacy for the course material, and

(c) student rating of the utility of the course content to their future studies or career predict mean instructional ratings.

The instructor is unsure how these three predictors may relate to mean ratings, so the instructor wishes to select a sample that would give a $90 \%$ chance of detecting a moderate relationship (say $\mathrm{d}=.5$ ) between mean ratings and any of the three predictors with alpha set at $.05$. What size sample is needed?
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To determine the needed sample size for the multiple regression study, use this regression sample size calculator:
$\underline{\text { http://www.danielsoper.com/statcalc/calc01.aspx }}$
or the Excel file here:
http://www.bwgriffin.com/samplesize

To use this, we must know four parameters:

(a) alpha,

(b) number of predictors,

(c) effect size f-squared, and

(d) power. Each of these are:

(a) alpha $=.05$ (as set by the researcher above)
(b) number of predictors is 3 (perceived autonomy, student efficacy, and utility rating)
(d) power $=.90$ (i.e., "90\% chance of detecting a moderate relationship")
(c) effect size f-square can be determined from $\mathrm{d}=.50$. To find f-square value for a $\mathrm{d}=.50, \mathrm{~d}$ must be converted to f-square. Use this spreadsheet to find f-squared: http:/www.bwgriffin.com/gsu/courses/edur9131/content/sample_size_effect_size_conversion.xls
In the yellow column find "d" and enter the value of $.5$. The resulting f-square is reported as .0625. Enter .0625 as the Anticipated Effect Size $\left(\mathbf{f}^{2}\right)$.
The resulting sample size to detect an moderate effect of $.5$ is about 177 evaluations.
by Diamond (89,036 points)

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