Nonparametric Tests

Kolmogorov-Smirnov Table: Critical Values of D

Exact critical values for the one-sample Kolmogorov-Smirnov test of whether data follow a fully specified distribution.

n = 1 to 100
Exact values
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Kolmogorov-Smirnov Table

Rows: sample size n · Columns: two-sided α · Cells: critical D. Reject H₀ if D ≥ the cell.

Kolmogorov-Smirnov Table (One-Sample Critical Values)
Two-sided α → n ↓	0.2	0.15	0.1	0.05	0.02	0.01	0.001
1	0.9000	0.9250	0.9500	0.9750	0.9900	0.9950	0.9995
2	0.6838	0.7261	0.7764	0.8419	0.9000	0.9293	0.9776
3	0.5648	0.5958	0.6360	0.7076	0.7846	0.8290	0.9206
4	0.4927	0.5248	0.5652	0.6239	0.6889	0.7342	0.8505
5	0.4470	0.4744	0.5094	0.5633	0.6272	0.6685	0.7814
6	0.4104	0.4353	0.4680	0.5193	0.5774	0.6166	0.7248
7	0.3815	0.4050	0.4361	0.4834	0.5384	0.5758	0.6793
8	0.3583	0.3806	0.4096	0.4543	0.5065	0.5418	0.6410
9	0.3391	0.3601	0.3875	0.4300	0.4796	0.5133	0.6085
10	0.3226	0.3425	0.3687	0.4092	0.4566	0.4889	0.5804
11	0.3083	0.3273	0.3524	0.3912	0.4367	0.4677	0.5559
12	0.2957	0.3141	0.3381	0.3754	0.4192	0.4490	0.5342
13	0.2847	0.3023	0.3255	0.3614	0.4036	0.4325	0.5149
14	0.2748	0.2918	0.3142	0.3489	0.3897	0.4176	0.4975
15	0.2658	0.2823	0.3040	0.3376	0.3771	0.4042	0.4818
16	0.2577	0.2737	0.2947	0.3273	0.3657	0.3920	0.4675
17	0.2503	0.2659	0.2863	0.3180	0.3553	0.3809	0.4544
18	0.2436	0.2587	0.2785	0.3094	0.3457	0.3706	0.4423
19	0.2373	0.2520	0.2714	0.3014	0.3369	0.3612	0.4312
20	0.2315	0.2459	0.2647	0.2941	0.3287	0.3524	0.4209
21	0.2261	0.2402	0.2586	0.2872	0.3210	0.3443	0.4112
22	0.2211	0.2348	0.2528	0.2809	0.3139	0.3367	0.4022
23	0.2164	0.2298	0.2475	0.2749	0.3073	0.3295	0.3938
24	0.2120	0.2251	0.2424	0.2693	0.3010	0.3229	0.3859
25	0.2079	0.2207	0.2377	0.2640	0.2952	0.3166	0.3784
26	0.2040	0.2166	0.2332	0.2591	0.2896	0.3106	0.3714
27	0.2003	0.2127	0.2290	0.2544	0.2844	0.3050	0.3647
28	0.1968	0.2089	0.2250	0.2499	0.2794	0.2997	0.3584
29	0.1934	0.2054	0.2212	0.2457	0.2747	0.2947	0.3524
30	0.1903	0.2021	0.2176	0.2417	0.2702	0.2899	0.3467
31	0.1873	0.1989	0.2141	0.2379	0.2660	0.2853	0.3413
32	0.1844	0.1958	0.2108	0.2342	0.2619	0.2809	0.3361
33	0.1817	0.1929	0.2077	0.2308	0.2580	0.2768	0.3312
34	0.1791	0.1901	0.2047	0.2274	0.2543	0.2728	0.3264
35	0.1766	0.1875	0.2018	0.2242	0.2507	0.2690	0.3219
36	0.1742	0.1849	0.1991	0.2212	0.2473	0.2653	0.3175
37	0.1718	0.1825	0.1965	0.2183	0.2440	0.2618	0.3133
38	0.1696	0.1801	0.1939	0.2154	0.2409	0.2584	0.3093
39	0.1675	0.1779	0.1915	0.2127	0.2379	0.2552	0.3054
40	0.1654	0.1757	0.1891	0.2101	0.2349	0.2521	0.3017
45	0.1562	0.1659	0.1786	0.1984	0.2218	0.2380	0.2849
50	0.1484	0.1575	0.1696	0.1884	0.2107	0.2260	0.2707
60	0.1357	0.1441	0.1551	0.1723	0.1927	0.2067	0.2476
70	0.1258	0.1336	0.1438	0.1597	0.1786	0.1917	0.2296
80	0.1178	0.1251	0.1347	0.1496	0.1673	0.1795	0.2150
90	0.1112	0.1181	0.1271	0.1412	0.1579	0.1694	0.2029
100	0.1056	0.1121	0.1207	0.1340	0.1499	0.1608	0.1927

Tip: click any value to highlight its row and column.

How to read this table

Compute D, the largest vertical distance between the empirical distribution function of your sample and the hypothesised distribution function.
Find the row for your sample size and the column for α.
Reject H₀ if D is greater than or equal to the table value.

Worked example

Twenty-five event times are compared with an exponential distribution with a pre-specified mean, giving D = 0.29. Row n = 25, α = 0.05 gives 0.2640. Because 0.29 ≥ 0.2640, the data are not consistent with that distribution at the 5% level.

Click the underlined links to highlight the value in the table.

Calculator

For values between the rows and columns of the table. Results update as you type.

Formula and how the values were computed

D = sup_x |F_n(x) − F₀(x)|

Values are quantiles of the exact null distribution of D for a continuous, fully specified distribution, computed numerically in double precision.

Frequently asked questions

Can I use this table to test for normality?

Only if the mean and standard deviation are specified in advance. If they are estimated from the same data, these critical values are too large and the test will rarely reject; use the Lilliefors correction or the Shapiro-Wilk test instead.

Why do other tables show slightly different values?

Many older tables use approximations such as 1.36/√n for α = 0.05. This table uses the exact distribution, which matters most for small samples.

Kolmogorov-Smirnov Table: Critical Values of D

Kolmogorov-Smirnov Table

How to read this table

Worked example

Calculator

Formula and how the values were computed

Frequently asked questions

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