Checking normality of a Likert scaling question

Question

I have likert scale responses (1-5 rating) of 20 respondents for a set of 25 questions. So that means that each respondent has answered 25 questions (with 1-5 rating). If I need to check the normality distribution of all the 25 questions together for a particular respondent, how do i do that?

Answer 1

If by "together" you mean the sum of all 25 questions, then the sum still can't be exactly normal, because it is still discrete. But it could be close enough to normal that everything works out OK.

Rather than a test of normality (which are all highly dependent on sample size) I would look at the quantile normal plot, available in R with the qqnorm function.

Answer 2

Analyze // Nonparametric // Legacy dialogs // 1- Sample KS

Well, I felt this one-line answer would be enough. Ok, so this option conducts a KS (Kolmogorov-Smirnov) Test of Normality. Essentially doing the same as the Shapiro-Wilk test previously mentioned. If you need the pros and cons of both tests, wikipedia might give a good answer.

In many cases Likert scales are skewed, since people tend to do yea-saying if the data is from the US. So you will probably standardize each Likert variable by subtracting mean and dividing by standard deviation. You can then conduct the KS test on the transformed variables.

Skewness you can already detect by looking at the descriptives.

Answer 3

If the outcome takes values in {1,2,3,4,5}, then this is clearly not normal because it is a discrete variable. If despite this you still want to use a normal approximation, in R you could use the Shapiro-Wilk normality test

x = rnorm(100,10,3)
shapiro.test(x)

and perhaps reject at a 0.05 level.

I hope this helps.

Best wishes.