Appendix x^2 : Upper Percentage Points of the x^2 Distribution 697Appendix x^2 : Upper Percentage Points
of the x^2 Distribution
df1 2 3 4 5 6 7 8 910
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
50
60
70
80
90
100
0.9500.00
0.10
0.35
0.71
1.15
1.64
2.17
2.73
3.33
3.94
4.57
5.23
5.89
6.57
7.26
7.96
8.67
9.39
10.12
10.85
11.59
12.34
13.09
13.85
14.61
15.38
16.15
16.93
17.71
18.49
26.51
34.76
43.19
51.74
60.39
69.13
77.930.9950.00
0.01
0.07
0.21
0.41
0.68
0.99
1.34
1.73
2.15
2.60
3.07
3.56
4.07
4.60
5.14
5.70
6.26
6.84
7.43
8.03
8.64
9.26
9.88
10.52
11.16
11.80
12.46
13.12
13.78
20.67
27.96
35.50
43.25
51.14
59.17
67.300.9000.02
0.21
0.58
1.06
1.61
2.20
2.83
3.49
4.17
4.87
5.58
6.30
7.04
7.79
8.55
9.31
10.09
10.86
11.65
12.44
13.24
14.04
14.85
15.66
16.47
17.29
18.11
18.94
19.77
20.60
29.06
37.69
46.46
55.33
64.28
73.29
82.360.9900.00
0.02
0.11
0.30
0.55
0.87
1.24
1.65
2.09
2.56
3.05
3.57
4.11
4.66
5.23
5.81
6.41
7.01
7.63
8.26
8.90
9.54
10.19
10.86
11.52
12.20
12.88
13.56
14.26
14.95
22.14
29.68
37.46
45.42
53.52
61.74
70.050.7500.10
0.58
1.21
1.92
2.67
3.45
4.25
5.07
5.90
6.74
7.58
8.44
9.30
10.17
11.04
11.91
12.79
13.68
14.56
15.45
16.34
17.24
18.14
19.04
19.94
20.84
21.75
22.66
23.57
24.48
33.67
42.95
52.30
61.70
71.15
80.63
90.140.9750.00
0.05
0.22
0.48
0.83
1.24
1.69
2.18
2.70
3.25
3.82
4.40
5.01
5.63
6.26
6.91
7.56
8.23
8.91
9.59
10.28
10.98
11.69
12.40
13.12
13.84
14.57
15.31
16.05
16.79
24.42
32.35
40.47
48.75
57.15
65.64
74.220.5000.45
1.39
2.37
3.36
4.35
5.35
6.35
7.34
8.34
9.34
10.34
11.34
12.34
13.34
14.34
15.34
16.34
17.34
18.34
19.34
20.34
21.34
22.34
23.34
24.34
25.34
26.34
27.34
28.34
29.34
39.34
49.34
59.34
69.34
79.34
89.33
99.330.2501.32
2.77
4.11
5.39
6.63
7.84
9.04
10.22
11.39
12.55
13.70
14.85
15.98
17.12
18.25
19.37
20.49
21.60
22.72
23.83
24.93
26.04
27.14
28.24
29.34
30.43
31.53
32.62
33.71
34.80
45.61
56.33
66.98
77.57
88.13
98.65
109.140.1002.71
4.61
6.25
7.78
9.24
10.64
12.02
13.36
14.68
15.99
17.28
18.55
19.81
21.06
22.31
23.54
24.77
25.99
27.20
28.41
29.62
30.81
32.01
33.20
34.38
35.56
36.74
37.92
39.09
40.26
51.80
63.16
74.39
85.52
96.57
107.56
118.490.0503.84
5.99
7.82
9.49
11.07
12.59
14.07
15.51
16.92
18.31
19.68
21.03
22.36
23.69
25.00
26.30
27.59
28.87
30.14
31.41
32.67
33.93
35.17
36.42
37.65
38.89
40.11
41.34
42.56
43.77
55.75
67.50
79.08
90.53
101.88
113.14
124.340.0255.02
7.38
9.35
11.14
12.83
14.45
16.01
17.54
19.02
20.48
21.92
23.34
24.74
26.12
27.49
28.85
30.19
31.53
32.85
34.17
35.48
36.78
38.08
39.37
40.65
41.92
43.20
44.46
45.72
46.98
59.34
71.42
83.30
95.03
106.63
118.14
129.560.0106.63
9.21
11.35
13.28
15.09
16.81
18.48
20.09
21.66
23.21
24.72
26.21
27.69
29.14
30.58
32.00
33.41
34.81
36.19
37.56
38.93
40.29
41.64
42.98
44.32
45.64
46.96
48.28
49.59
50.89
63.71
76.17
88.40
100.44
112.34
124.13
135.820.0057.88
10.60
12.84
14.86
16.75
18.55
20.28
21.96
23.59
25.19
26.75
28.30
29.82
31.31
32.80
34.27
35.72
37.15
38.58
40.00
41.40
42.80
44.18
45.56
46.93
48.29
49.64
50.99
52.34
53.67
66.80
79.52
91.98
104.24
116.35
128.32
140.190 2Source: The entries in this table were computed by the author.