# Shapiro-Wilk Tables

Table 1 contains the weights ai for any given sample size n. Table 2 contains the p-values for Shapiro-Wilk Test. See Shapiro-Wilk Test for more details.

Table 1 – Coefficients

Correction: The a13 value for n = 49 should be 0.0919 instead of 0.9190.

Table 2 – p-values

### 25 Responses to Shapiro-Wilk Tables

1. Bourgeois Thomas says:

Hi Charles,
Thanks a lot for the very helpful explanation.
However, I’m a bit confused.

For n=25, I obtain W=0.97, thus p-value of 0.6.
For alpha=5%, therefore, my hypothesis is not rejected.
However, the more I diminish the alpha (1%, 0.5%, etc.) the more the hypothesis is “not rejected” as alpha is further away from the p-value. I’m confused, shouldn’t it be harder and harder to have a “non rejection” when I diminish the level of error ?

Isn’t there a mistake and it should be that the p-value should be below alpha (and not higher than) for a non-rejection ?

Thomas

• Charles says:

Thomas,
The lower the value of alpha, the harder it should be to reject the null hypothesis (i.e. the tail beyond the critical value is smaller).
Charles

2. Maximilian Hugo says:

Dear Dr. Zaiontz,

am I right by assuming the Shapiro-Wilk-Tables presented on this page are only applicable for Tests within a Significance Level of 5 %?

Thank you for providing this knowlege and also for this great webside.

Best regards
Max

• Charles says:

Table 1 is applicable for any significance level. Table 2 is applicable for .01, .02, .05, etc. significance levels.
Charles

3. annisa says:

I really need to know the reference of this table. Thank you

• Charles says:

Annisa,
The reference is the original paper by Shapiro, S.S. & Wilk, M.B. (1965). See Bibliography for details.
Charles

4. ann says:

hi,
i need the values for n=60 and n=100. but i can´t find them nowhere. and p-values,of course. can you help me? unfortunately my knowledge of math isn´t that good.
thanks.
anna

• Charles says:

Ann,
I don’t know of a table with such high values of n. For values of n larger than 50, you could use the Real Statistics SWPROB function (or better yet the SWTEST function) instead of statistics table. See the following webpage
Shapiro-Wilk Test
Charles

• Vivian Fernandes says:

You can download the Sisvar software, it gives you all values you need.

5. Huchesh H B says:

Hello sir
How to calculate ai values by manual? I tried to calculate the covariance but could not. please help me

6. Jolie says:

Hi, is it possible to know how do you get the p-values table??????? Very curious! Thanks!

• Charles says:

If I remember correctly, I believe I got it from the original Shapiro-Wilk paper. See the Bibliography for details.
Charles

7. M says:

Thanks for the great instructions! However, my results in SPSS and other stats tools yield different p-values (W value is the same) than this example. The first example gives a p-value of 0.873, but SPSS and other tools gives the p-value of 0.922. Is there a reason for this difference?

• Charles says:

The website gives two ways of calculating the p-value for the Shapiro-Wilk test. The original method gives a p-value of .873 based on a linear interpolation, while the Royston method gives a value of .922, which is the same as that provided by SPSS.
Charles

8. Johanna says:

Hello Dr. Zaiontz,

Thank you, this really helped!

I would like to ask, what if your W value is lower and out of the table? Example: n=20, computed W=0.8222. I looked at the table and the value at p=0.01 is 0.868

What should I do to find the p-value?

Thank you.

• Charles says:

Johanna,
From the table all that you can conclude is that p < .01. In the next release of the Real Statistics Resource Pack you will be able to use the Royston approximation to compute a more exact value, which in this case will be .001888. I hope to have the next release out this week, hopefully tomorrow if I have time enough to complete all the testing. Charles

9. Raphaela says:

Hi Charles,
I just started to study statistics and I am trying to calculate Shapiro-Wilk (W) by myself. For this task I need to find the coefficient table 1 for n= 78 from a1 untill a35. Could you help me? Thank you
Raphaela

10. Amelia says:

Hi Dr. Zaiontz,

Thank you so much for creating this website! It’s very helpful!

I wonder how we can generate the p values using the W score and other results from Shapiro-Wilk without looking up this table?

Best,
Amelia

11. Gudiel Roblero says:

Thanks, is very useful your information!
I have a doubt, ¿how i can get the p value? you are mention about interpolation but i undestnad this proces whit this tables.
thanks.

12. Tim says:

Table 1: (n=50, a25) Should this be “0.0035”? I didn’t see any excel file links for the tables, so I’m making my own file for future ‘copy/paste’ of ai values.

Thanks for the whole site. Very helpful.

• Charles says:

Tim,

Thanks for catching this typo. You are correct; the value should be 0.0035. I will correct it on the website and in the Real Statistics Resource Pack and Examples file shortly.