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

Shapiro-Wilk Weights 1

Shapiro-Wilk Weights 2Shapiro-Wilk Weights 3

Shapiro-Wilk Weights 4

Shapiro-Wilk coefficients n50

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.

  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.

  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?


  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

  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:

      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.

  7. Jolie says:

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

  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:

    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.

    • Charles says:

      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

    • 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

  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

    • Charles says:

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

  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,

    • Charles says:

      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).

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