Dear all,
I am working on analyzing data from a survey on student satisfaction. The survey contains items with a 7-point Likert response format that produce 12 scales related to different areas of student satisfaction. Scale scores are calculated for each respondent by taking the mean of their ratings to the items making up each scale.
My understanding is that the mean of each scale is calculated by taking the mean of all responses to the items making up the scale; it is not calculated by taking the mean of all the scale scores for the particular scale (in other words, it is not the average of the averages). My question is, would the scales’ standard deviations be derived in a similar fashion? Would one derive the standard deviation of a given scale by calculating the standard deviation of the matrix of all responses to the items that make up the scale? Would it be appropriate or not to derive a scale’s standard deviation by calculating the standard deviation of all the scale scores for the scale (i.e. taking the standard deviation of the averages)?
Referring to the attached image, which would be the correct way to derive the standard deviation of the theoretical 3-item scale—the formula in cell I3, or the one in cell I5 (or some third option)?
Thanks,
Colin
Believe it or not, both are actually valid methods, but the most commonly used is "standard deviation of scale scores" (or mean scores per respondent), where you first calculate the mean for each respondent for the items that make up the scale, and then you calculate the SD for these mean scores
The standard deviation corresponding to the mean scores of individual respondents to a scale is almost never computed because it's found no practical application.
What is expected is the standard deviation corresponding to the mean scores of samples of respondents.
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