I'm doing a project on measuring customer satisfaction using SERVQUAL. How do you calculate the standard deviation of each statement?

For example, if for one of the questions, there were:

  • 2 respondents as strongly disagree (SD)
  • 5 disagree (D)
  • 20 neutral (N)
  • 21 agree (A)
  • 2 strongly agree (SA) (sample being 50)

How would you calculate the standard deviation if the scale were SD=1, D=2, N=3, A=4 and SA=5?

Also, how do you calculate the standard deviation for one dimension on the whole: e.g., the standard deviation for one of the dimensions in SERVQUAL say, Tangibles which has 4 statements or questions, and the standard deviation for Reliability which has 5 questions, etc.?

  • $\begingroup$ Regarding your second point, if you have an estimate of scale reliability (test-retest measurement, or internal consistency--i.e., Cronbach's alpha), it can be used to compute the standard error of measurement of your scale scores. $\endgroup$ – chl Jul 17 '12 at 19:48

This is a Likert type scale and involves ordinal numbers and since intervals are not defined nor are ratios there is really not a meaningful concept for it. However when scores are averaged there are models such as the Rasch model which allow these averages to be viewed as interval data. I really know nothing about these models but Peter Flom and others at this site have discussed these ideas here yesterday and prior to that. Gung and Peter Flom provide some information on this at this question. Is 0 a valid value in a Likert scale?

If we accept that the average score is interval then the standard formula for the standard error of the mean could be applied to give you an estimate of the standard deviation for the mean. I still would not think an standard deviation for the sample responses makes sense but you could calculate something that looks like a standard deviation by multiplying the standard error of the mean by square root of n where n is the number of independent responders.

  • $\begingroup$ Thank you for answering but are you saying that standard deviation can not be found out for this question only something that looks something like it can be? $\endgroup$ – Tanishka Jul 17 '12 at 19:21
  • $\begingroup$ I am saying that there is theory to support a standard error for the mean based on what others have said. Conceptually I do not see that a standard deviation for the response distribution to individual questions make sense. All I meant by saying square root of n times the standard error looks like a standard deviation is that if you make the analogy to independent interval data the population standard deviation is root n times the standard error. So it is possible to make that calculation and think of it like a standard deviation by analogy. $\endgroup$ – Michael R. Chernick Jul 17 '12 at 19:43
  • $\begingroup$ But conceptually it doesn't make sense to me. I would defer to @gung who seems to be much more well-versed in these types of analyses. $\endgroup$ – Michael R. Chernick Jul 17 '12 at 19:43
  • $\begingroup$ Actually it doesn't make sense to me either. But I noticed such analyses in some other projects for each individual statements and wondered how they did it. $\endgroup$ – Tanishka Jul 17 '12 at 19:48

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