For a variable I have tested the normality by shapiro test and I get the result below. So it seems normally distributed,

Shapiro-Wilk normality test

data:  bowel$normal
W = 0.98112, p-value = 1.62e-07

enter image description here

But the homoscedasticity doesnt look ok. How come?

enter image description here

  • $\begingroup$ One tests for normal distribution, the other tests for homoscedasticity, these two are not really related. Also, the plot looks... OK. $\endgroup$ Mar 6, 2020 at 10:25
  • $\begingroup$ @user2974951 Ok! So you think its ok with a parametric model, or should I turn to a non-parametric model? $\endgroup$ Mar 6, 2020 at 10:36

1 Answer 1


1) The p-value of the Shapiro-Wilk test is very small, so actually normality is rejected. (As opposed to user2974951 in the comments to the question I don't believe that the plots look OK for normality or homoscedasticity. They may at best be just about OK for expecting a method based on these assumptions to give a still somewhat reasonable approximation. However this depends on what exactly was done here, apparently some kind of regression, and several other things that we cannot assess from the information given, like number and distribution of explanatory variables etc.)

2) Even if Shaprio-Wilk was not rejected, that wouldn't be a positive proof/assurance of normality. It would only mean that the test statistic value is compatible with what is expected under the normal. It could still be something else.

3) Normality is about the distributional shape of a single variable (probably residuals here but I don't know), whereas homoscedasticity is about how the variance changes over values of some explanatory variable or time. These are different features of the model; there may be heteroscedastic but normal data, and non-normal but homoscedastic data. One additional thing is that if you're using Shapiro-Wilk to test normality of residuals (assuming that this is the kind of regression I believe it is, but we don't know), this already assumes homoscedasticity, meaning that if the data are in fact heteroscedastic, Shapiro-Wilk is not informative and shouldn't be used.


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