Mean Scores

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Mean Scores
Message posted by CJG on October 26, 1999 at 12:00 AM (ET)

I want to create an index by combining variables from a survey in which I used likert scaling for the responses. The variables are ordinal in nature. Is there a problem with cominining them if I total the variables and then compute a mean?

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Re: Mean Scores
Message posted by Jack Tomsky on October 26, 1999 at 12:00 AM (ET)

You can define a statistic any way you want. You might want to consider generalizing this by combining the responses into a linear combination rather than a sum. The coefficients would be chosen so as to maximize the variance between the individuals. You don't need normaility for this and the coefficients can be calculated from the covariance matrix of the responses. Each individual will have a combined score associated with this linear combination.

You can generalize it further by a (snall) set of linear combinations which are uncorrelated and which account for almost all the total variation between individuals. Each individual's responses will then be summarized by a small set of scores. This methodology is known as principal components. You end up with simplifying the data set, while retaining most of the original information.

Re: Mean Scores
Message posted by JG on October 27, 1999 at 12:00 AM (ET)

The most important issue is whether you really have a Likert scale or you just assume that you have one. See an appropriate social science statistics book if the conditions needed to have a Likert scale have been satisfied by your scale.

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