Critical Values of the χ² Distribution

p From χ²_Observed

Critical χ² Value

Degrees of Freedom	α Level
Degrees of Freedom	0.05	0.01	0.001
1	3.841	6.635	10.828
2	5.991	9.210	13.816
3	7.815	11.345	16.267
4	9.488	13.277	18.467
5	11.071	15.086	20.516
6	12.592	16.812	22.458
7	14.067	18.475	24.323
8	15.507	20.090	26.125
9	16.919	21.666	27.878
10	18.307	23.209	29.589
Degrees of Freedom	α Level
Degrees of Freedom	0.05	0.01	0.001
11	19.675	24.725	31.265
12	21.026	26.217	32.911
13	22.362	27.688	34.530
14	23.685	29.141	36.125
15	24.996	30.578	37.698
16	26.296	32.000	39.254
17	27.587	33.409	40.792
18	28.869	34.805	42.314
19	30.144	36.191	43.822
20	31.410	37.566	45.316
Degrees of Freedom	α Level
Degrees of Freedom	0.05	0.01	0.001
21	32.671	38.932	46.800
22	33.924	40.290	48.270
23	35.172	41.639	49.730
24	36.415	42.980	51.181
25	37.653	44.314	52.621
26	38.885	45.642	54.054
27	40.113	46.963	55.478
28	41.337	48.278	56.895
29	42.557	49.588	58.303
30	43.773	50.892	59.706
Degrees of Freedom	α Level
Degrees of Freedom	0.05	0.01	0.001
31	44.985	52.192	61.100
32	46.194	53.486	62.490
33	47.400	54.776	63.872
34	48.602	56.061	65.250
35	49.802	57.342	66.621
36	50.999	58.620	67.988
37	52.192	59.893	69.350
38	53.384	61.162	70.706
39	54.572	62.428	72.058
40	55.759	63.691	73.405
Degrees of Freedom	α Level
Degrees of Freedom	0.05	0.01	0.001
41	56.942	64.951	74.748
42	58.124	66.207	76.086
43	59.304	67.460	77.422
44	60.481	68.710	78.754
45	61.656	69.957	80.080
46	62.830	71.202	81.404
47	64.001	72.444	82.723
48	65.171	73.683	84.041
49	66.339	74.920	85.355
50	67.505	76.154	86.664
Degrees of Freedom	α Level
Degrees of Freedom	0.05	0.01	0.001
51	68.669	77.386	87.972
52	69.832	78.616	89.277
53	70.994	79.844	90.577
54	72.153	81.069	91.876
55	73.312	82.293	93.171
56	74.468	83.514	94.464
57	75.624	84.733	95.756
58	76.778	85.951	97.042
59	77.931	87.166	98.328
60	79.082	88.380	99.612
Degrees of Freedom	α Level
Degrees of Freedom	0.05	0.01	0.001
61	80.232	89.592	100.892
62	81.381	90.802	102.171
63	82.529	92.010	103.448
64	83.675	93.217	104.720
65	84.821	94.423	105.993
66	85.965	95.626	107.264
67	87.108	96.828	108.530
68	88.250	98.029	109.796
69	89.391	99.228	111.061
70	90.531	100.426	112.321
Degrees of Freedom	α Level
Degrees of Freedom	0.05	0.01	0.001
71	91.670	101.622	113.582
72	92.808	102.817	114.841
73	93.945	104.010	116.096
74	95.082	105.203	117.351
75	96.217	106.394	118.605
76	97.351	107.583	119.857
77	98.485	108.771	121.105
78	99.617	109.959	122.354
79	100.749	111.145	123.601
80	101.880	112.329	124.844
Degrees of Freedom	α Level
Degrees of Freedom	0.05	0.01	0.001
81	103.010	113.513	126.088
82	104.139	114.696	127.331
83	105.267	115.877	128.569
84	106.395	117.057	129.809
85	107.522	118.236	131.048
86	108.648	119.415	132.285
87	109.773	120.592	133.517
88	110.898	121.768	134.752
89	112.022	122.943	135.985
90	113.145	124.117	137.213
Degrees of Freedom	α Level
Degrees of Freedom	0.05	0.01	0.001
91	114.268	125.290	138.444
92	115.390	126.462	139.673
93	116.511	127.634	140.901
94	117.632	128.804	142.124
95	118.752	129.974	143.350
96	119.871	131.142	144.574
97	120.990	132.310	145.798
98	122.108	133.477	147.016
99	123.225	134.643	148.237
100	124.342	135.807	149.457

Critical Values of the χ2 Distribution

p From χ2Observed

Critical χ2 Value

Critical Values of the χ² Distribution

p From χ²_Observed

Critical χ² Value