# Thread: Which one should I trust : shapiro test or qq plot?

1. ## Which one should I trust : shapiro test or qq plot?

Good evening everyone,

Sorry if this question already exist, I searched but didn't find an asnwer.

I am using 7-points likert scale for my research. I'm then using the mean for each of them.

Then, before I run any analysis, I wanted to check for assumption of normality to decide if I either use parametric or non parametric test.

When I run my shapiro test, it's > .05 so I can say my distribution is normal

However, my QQ plot looks "almost normal", a few points are not straight though. Which one should I trust?

PS : my sample is really small n = 20.

2. ## Re: Which one should I trust : shapiro test or qq plot?

I would prefer to look at the QQ plot.

But the important thing is if the data (in each group, or the residuals) is roughly normal, so that it does not deviate a lot from normality. Also, the central limit theorem says that sums (like in "parametric estimation") tends to be normally distributed. The way I interpret your results I believe that it is Ok to use the normal model.

Besides, there are many other parametric distributions than the normal.

3. ## Re: Which one should I trust : shapiro test or qq plot?

a QQplot does not to be perfect. Real data rarely is.

You can run the big 4: Shapiro-Wilk, Anderson-Darling, Kolmogorov-Smirnov, and Lilliefors.

In my opinion though, if your shapiro-wilk's test is showing normality, then its a pretty good sign.

4. ## Re: Which one should I trust : shapiro test or qq plot?

It is never possible to show normality. It is only possible to reject normality.

And you know from the start that a seven point Likert scale (I believe you mean Likert item) is not normally distributed, since it is discrete and has a finite range, while the normal distribution goes from minus infinity to plus infinity and it is continuous. What matters is that it is a good model, that it is somewhat bell shaped. And really that the test statistics approximately follows a t-distribution (if that is what you intend to use).

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