# 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. 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.

An Excel version of the table is available for free download. It is included in the Real Statistics Examples file. You can download this file from the webpage http://www.real-statistics.com/free-download/real-statistics-examples-workbook/.

Charles

2. 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.

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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.

10. 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

11. 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

12. 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 ?

Thanks for your help,
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