# What test is appropriate for normality?

I would like to check the normality of nearly 400 individuals. I tried many test like Shapiro test, etc...but, not much expected results. So, Could you please tell me what is the appropriate test for Normality.

• What do you expect when saying "not much expected results"? Dec 24 '20 at 20:51
• I am getting shapiro P value nearly 0.03...It is also less than 0.05. Dec 26 '20 at 0:15

> x = replicate(1000,{shapiro.test(rt(1000,30))$p.value<0.05}) > mean(x) [1] 0.194  If I were to reject the null of the test from these data, would that mean that treating the data as normal would be a gross error? Clearly no. What's my point? Basing the legitimacy of an assumption based on a statistical test can lead to erroneous decisions, which is ironic because presumably you're conducting the test to obtain support for certain assumptions. Here is an excellent time to parrot my favourite phrase: Statistics is not an algorithmic truth generating processes. It isn't a decision tree in which you follow certain sets of instructions which are guaranteed to provide you error free inference. You need to take more things into context, including but not limited to : • The support of the data • How it was collected • The size of the data among other things. Generally, my advice would be the following: Plot qq plots of the data and compare the plotted quantiles to the qqline for a normal. If the quantiles match the normal closely, then normality may be a good assumption. I've made such a plot below for the student t data I mentioned earlier. The data used to make this plot would reject the null of the Shapiro test, and yet I think a normal approximation would be fine. • +1 for excluding the legend in the two distributions comparison plot. Dec 24 '20 at 21:47 • +1 for very simple example. Dec 24 '20 at 23:45 • One may add that normality is always false, so if$p >.05\$ by S-W or any other test, it is simply a Type II error. Jan 6 '21 at 18:35