Statistics Reference

Chi-Square Table for α = 0.01 (χ² Critical Values)

The strict column: upper-tail critical values at the 1% significance level for every degree of freedom from 1 to 100, with the matching lower critical values. Used when false alarms are expensive or many tests run at once — and for 98% variance confidence intervals.

How to Read This Table

Rows are degrees of freedom from 1 to 100 — every integer, finer than the stepped rows of the main table. The upper critical value leaves probability 0.01 above it (the standard rejection cutoff); the lower critical value leaves the same probability below it (for lower-tailed tests and two-sided procedures).

The die-fairness test (df = 5, χ² = 13.4) held to the 1% standard:

Row df = 5, upper critical column: 15.086.
13.4 < 15.086 — significant at 5% (11.070) but not at 1%.
Report the exact p-value (0.020) so readers can apply their own threshold.

Common uses of this level:

Confirmatory chi-square tests at the strict 1% level
Conservative testing under multiple comparisons
98% confidence intervals for a variance (0.01 per tail)

χ² Critical Values, α = 0.01, df 1–100

Chi-square critical values at tail area 0.01 for degrees of freedom 1 to 100
df	Lower critical (area 0.01 below)	Upper critical (area 0.01 above)
1	0.000	6.635
2	0.020	9.210
3	0.115	11.345
4	0.297	13.277
5	0.554	15.086
6	0.872	16.812
7	1.239	18.475
8	1.646	20.090
9	2.088	21.666
10	2.558	23.209
11	3.053	24.725
12	3.571	26.217
13	4.107	27.688
14	4.660	29.141
15	5.229	30.578
16	5.812	32.000
17	6.408	33.409
18	7.015	34.805
19	7.633	36.191
20	8.260	37.566
21	8.897	38.932
22	9.542	40.289
23	10.196	41.638
24	10.856	42.980
25	11.524	44.314
26	12.198	45.642
27	12.879	46.963
28	13.565	48.278
29	14.256	49.588
30	14.953	50.892
31	15.655	52.191
32	16.362	53.486
33	17.074	54.776
34	17.789	56.061
35	18.509	57.342
36	19.233	58.619
37	19.960	59.893
38	20.691	61.162
39	21.426	62.428
40	22.164	63.691
41	22.906	64.950
42	23.650	66.206
43	24.398	67.459
44	25.148	68.710
45	25.901	69.957
46	26.657	71.201
47	27.416	72.443
48	28.177	73.683
49	28.941	74.919
50	29.707	76.154
51	30.475	77.386
52	31.246	78.616
53	32.018	79.843
54	32.793	81.069
55	33.570	82.292
56	34.350	83.513
57	35.131	84.733
58	35.913	85.950
59	36.698	87.166
60	37.485	88.379
61	38.273	89.591
62	39.063	90.802
63	39.855	92.010
64	40.649	93.217
65	41.444	94.422
66	42.240	95.626
67	43.038	96.828
68	43.838	98.028
69	44.639	99.228
70	45.442	100.425
71	46.246	101.621
72	47.051	102.816
73	47.858	104.010
74	48.666	105.202
75	49.475	106.393
76	50.286	107.583
77	51.097	108.771
78	51.910	109.958
79	52.725	111.144
80	53.540	112.329
81	54.357	113.512
82	55.174	114.695
83	55.993	115.876
84	56.813	117.057
85	57.634	118.236
86	58.456	119.414
87	59.279	120.591
88	60.103	121.767
89	60.928	122.942
90	61.754	124.116
91	62.581	125.289
92	63.409	126.462
93	64.238	127.633
94	65.068	128.803
95	65.898	129.973
96	66.730	131.141
97	67.562	132.309
98	68.396	133.476
99	69.230	134.642
100	70.065	135.807

Other Significance Levels

The chi-square table overview carries the classic multi-column grid, degrees-of-freedom rules, and the variance-interval walkthrough. The other levels each have a dedicated page:

Frequently Asked Questions

When should chi-square tests use α = 0.01?

When a false rejection is costly - confirmatory studies, quality-critical processes - or when many categories or tables are tested at once and an informal multiplicity guard is wanted. The price is power: real deviations need to be larger to clear the higher bar.

How much larger are the 0.01 critical values than the 0.05 ones?

Roughly 20-70% larger in the working range, with the biggest relative gap at small degrees of freedom: df = 1 moves from 3.841 to 6.635 (+73%), df = 5 from 11.070 to 15.086 (+36%), df = 30 from 43.773 to 50.892 (+16%).

A statistic significant at 0.05 but not 0.01 - what should I conclude?

The evidence is moderate: the data would arise less than 5% but more than 1% of the time under the null hypothesis. Rather than leaning on the labels, report the exact p-value and the per-cell contributions, and let the cost of error in your context set the threshold.