Table 1 contains the weights a_{i} 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**

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.

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

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.

Gudiel,

How to perform linear interpolation is described http://www.real-statistics.com/descriptive-statistics/ranking-function-excel/ (Example 6). You can also use the supplemental function INTERPOLATE which is described at the bottom of http://www.real-statistics.com/excel-capabilities/table-lookup/.

Charles

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

Hi Amelia,

You can do this using the Real Statistics software pack. Please see the webpage http://www.real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/shapiro-wilk-expanded-test/ for how to do this.

Charles

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

Raphaela,

The table I have stops at n = 50. For values n > 50 you can use the Royston approach to Shapiro-Wilk, as described on the webpage http://www.real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/shapiro-wilk-expanded-test/. You can also use the following function provided by the Real Statistics Resource Pack: SWCoeff(n, j) = the jth coefficient for samples of size n.

Charles

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.

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

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?

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

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

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

Charles

Hello sir

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

See the webpage

Shapiro-Wilk Expanded Version

Charles

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

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

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

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

Annisa,

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

Charles

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

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

Charles

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

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