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I've just received some survey data and I found that the results are highly positively skewed. Most of the questions were answered on a five-point Likert scale, and the mean values of many questions are around 4.3, with standard deviations of 0.5 or 0.6.

Another problem is that in the questionnaire I included several multiple item scales that have been validated previously in the literature. However, some of these have very low Cronbach's alpha values (.4 or even .3) and I'm wondering how much of a problem this indicates.

Do these qualities indicate any intrinsic problems with the data set?

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    $\begingroup$ My first question would be what sort of analysis you want to do on the dataset. Why might the skewness be a problem? I mean, lots of real phenomena are pretty skewed. $\endgroup$
    – generic_user
    Mar 30 '13 at 4:29
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    $\begingroup$ "the mean values of many questions are around 4.3, with standard deviations of 0.5 or 0.6" --- sounds like negative skew to me. $\endgroup$
    – Glen_b
    Mar 30 '13 at 9:21
  • $\begingroup$ You've gotten two good comments about the skewness. Re Cronbach's alpha - did you check whether any items need to be reverse coded? An alpha of 0.3 or 0.4 is quite low. $\endgroup$
    – Peter Flom
    Mar 30 '13 at 10:33
  • $\begingroup$ Thank you for your answers. I would like to run a series ANOVAs and t-tests on the data. Actually, I'm not sure that skewness will be a problem, only that this survey data is much more skewed than I am used to. As to the cronbach's alpha, no items are reverse coded (unfortunately). $\endgroup$
    – kwela12
    Mar 31 '13 at 7:17
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If you have a 5-point Likert scale, you would want to entertain an ordinal logistic regression. The analogues of $t$-test is then a regression with dummy variable coded categorical variables (just one regressor with 0/1 values for the $t$-test, and multiple variables with many categories for ANOVA). Some low categories may have to be collapsed to identify the thresholds.

For more details, see J Scott Long's book on categorical dependent variables.

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