The table gives the critical values *D _{n,α}* as described in Kolmogrov-Smirnov Test.

### Real Statistics Resources

### Current Section

- Statistics Tables
- Wilcoxon Rank-Sum Table
- Mann-Whitney Table
- Wilcoxon Signed-Ranks Table
- Runs Test Table
- Kolmogorov-Smirnov Table
- Shapiro-Wilk Tables
- Two Sample Kolmogorov-Smirnov Table
- Studentized Range q Table
- Spearman’s Rho Table
- Kendall’s Tau Table
- Durbin-Watson Table
- Lilliefors Test Table
- Anderson-Darling Test Table
- Pearson’s Correlation Table
- Dunnett’s Table
- Augmented Dickey-Fuller Table
- Interpolation

- Statistics Tables

Thank you for your help.

Hi Charles, how i get the Kolmogorov-Smirnov Table for two samples?

Adrian,

I have found a few versions of the two-sample KS table, but they are all different, and so I have been reluctant to put one of these on the website. For this reason I provided a distribution function to calculate these values, as described on the webpage

Two Sample Kolmogorov-Smirnov Test.

Charles

Charles,

In the Kolmogorov-Smirnov table, the critical value of D increases as alpha (1-P) decreases for a given N. This would imply that if a sample K-S statistic is < the critical D value at say the .05 level, then it must also be < the critical D value at the .01 level. This does not seem logical to me – what am I missing?

Robert

Robert,

We reject the null hypothesis that the data comes from a specific distribution when the sample K-S statistic > the critical value (not less than it).

Charles

Charles,

Yes, I agree – so if the sample K-S statistics is critical D at 0.05, so we must then accept the null hypothesis at the 0.01 level, and then at the 0.01 level, etc.

Put another way, would we reject the null hypothesis at the 0.05 level but accept it at the 0.01 level if the the sample,K-S statistic lay between these values (ie D.01 > K-S statistic > D.05)? Robert

Charles – sorry, “>” was missing on the first line; should read “… K-S statistic is > critical D …then accept H0 at the 0.01 level…”. Apologies, Robert

I meant “<" of course – I'm confusing myself! Robert

Robert,

If you reject a null hypothesis at the 1% level, then clearly you reject it also at the 5% level. Thus if you retain the null hypothesis at the 5% level you also retain it at the 1% level.

Charles

Charlies – thank you for your patience, Robert

For n25 alpha 0.05 is 0.264….

Sorry….for n25..alpha o.o5=0.264

The numbers that you have reported for D_n is in contrast with the values at the wiki page :

https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test

Look at the “Two-sample Kolmogorov–Smirnov test” at the wiki page, for two samples of different sizes n and n’, If one defines n=n’, she will get D_n bigger than what you have reported for n over 50 in this page…with a factor of sqrt(2). which one is correct?

The Wikipedia page that you reference provides the exact same values as the

onesample KS table on my site. In any case, the Wikipedia table is referring to the two sample test whereas as the referenced table on my site is for the one sample test. I describe the two sample KS test on the following webpageTwo Sample Kolmogorov-Smirnov Test

Charles

Thank you so much for your quick response. That was so helpful.

How can we “accept” the null hypothesis H0? We fail to reject the alternative,

not less, not more. The NHST was not constructed to accept whatever H0 or Ha.

Think that the procedure is completely unfair to Ha, in fact we not reject it

unless the pvalue is less than 1-alpha, that is 0.05 , 0.01.

So there are a lot of cases that p>0.05 (say) notwithstanding H0 is untrue.

“Accepted?”.

Bibliography

https://statistics.laerd.com/…/hypothesis-testing-3.ph…

. . . shows that the significance level is below the cut-off value we have set (e.g., either 0.05 or 0.01), we reject the null hypothesis and accept the alternative hypothesis. Alternatively, if the significance level is above the cut-off value, we fail to reject the null hypothesis and cannot accept the alternative hypothesis. You should note that you cannot accept the null hypothesis, but only find evidence against it.

My observed value Dn=0.0462, n=100. How to calculate p-value? Thanks in advance.

You can use the KSPROB function as described on the following webpage:

http://www.real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/kolmogorov-smirnov-test/

Charles

Sir charles? How can we identify the critical value in the kolmogorov smornov test

Please.

Eliza,

This is covered on the website. I suggest that you type Kolmogorov into the Search bar (under the topic menu on the right side of any webpage) to see how the critical value of the KS test is used.

Charles

I would like to learn if I could use K-S test for normality, for big figures like 1.4 E10, 2.04 E09, 4.6E09 (Estimated bacteria amount in milk etc.) without taking log.

Alberto,

You can probably use the KS test for normality, but in general I suggest that you use Shapiro-Wilk test.If you do use the KS test and estimate the mean and standard deviation from the sample, then you should use the Lilliefors table.

Charles

Sir,

How to estimate the mean and standard deviation from the sample

Neeraj,

See

http://www.real-statistics.com/descriptive-statistics/measures-central-tendency/

http://www.real-statistics.com/descriptive-statistics/measures-variability/

Charles

“Charles,

Yes, I agree – so if the sample K-S statistics is critical D at 0.05, so we must then accept the null hypothesis at the 0.01 level, and then at the 0.01 level, etc.

Put another way, would we reject the null hypothesis at the 0.05 level but accept it at the 0.01 level if the the sample,K-S statistic lay between these values (ie D.01 > K-S statistic > D.05)? Robert” I’ve a same problem too.

My alpha 0.2 is more restrict than 0,01. Why?

The critical region for alpha = .01 is smaller than the critical region for alpha = .05. You could reject the null hypothesis at the .05 level, but retain it at the .01 level.

Charles