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How to check the normality of data collected on 5 point Likert scale?

As it is ordinal numbers not continuous. Using SPSS the Shapiro Wilk or Kolmogorov-Smirnov test indicate my data is not normal.

I am validating the existing frameworks so most of the values (mean) are between 3.5- 4.5

Can I go ahead with factor analysis? If yes then are there any constraints for the same?

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    $\begingroup$ Likert scale data is not normal. It's discrete, so it can't be normal. It's bounded on both sides, so it can't be normal. It's ordinal. It's not normal. Why would you test it, which can at best tell you what you already know? $\endgroup$ – Glen_b Oct 14 '14 at 11:42
  • $\begingroup$ The big question isn't whether your data are normal (we know it's not), it's how much the non-normality you have impacts any inference in your factor analysis. $\endgroup$ – Glen_b Oct 14 '14 at 18:38
  • $\begingroup$ This question seems like a potential duplicate. $\endgroup$ – Glen_b Oct 14 '14 at 18:41
  • $\begingroup$ In addition to the preceding comments, there are methods to handle categorical variables with ordered levels that do not rely on classical multivariate normal assumptions in CFA, as implemented in, e.g., Mplus, or using an alternative statistical framework, e.g., IRT modeling. $\endgroup$ – chl Oct 14 '14 at 19:59
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If you know how to use R, you can use sem and polycor packages to do exploratory or confirmatory analysis based on ordinal data. See the manual here. It first computes a polychoric correlation matrix as input. If you are not familiar with polychoric correlation, see this Wikipedia article about its assumptions and examples.

If you do not know how to use R, you can compute polychoric correlations among the ordinal variables and submit the correlation matrix to SPSS/AMOS as input. I do believe SPSS/AMOS takes a correlation matrix as input. It seems, though, you need the SPSS Categories Module to compute polychoric correlations.

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