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Table D.9 Critical Values for the Durbin–Watson d Statistic (α = .01)

Table D.9 Critical Values for the Durbin–Watson d Statistic (α = .01)

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772 Appendix D Useful Statistical Tables

Table D.10 Critical values for the χ 2 Statistic

Degrees of
Freedom
1
2
3
4
5
6
7
8
9
10
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
150
200
300
400
500

2
χ.995

2
χ.990

2
χ.975

2
χ.950

2
χ.900

.0000393
.0100251
.0717212
.206990
.411740
.675727
.989265
1.344419
1.734926
2.15585
2.60321
3.07382
3.56503
4.07468
4.60094
5.14224
5.69724
76.26481
6.84398
7.43386
8.03366
8.64272
9.26042
9.88623
10.5197
11.1603
11.8076
12.4613
13.1211
13.7867
20.7065
27.9907
35.5346
43.2752
51.1720
59.1963
67.3276
109.142
152.241
240.663
330.903
422.303

.0001571
.0201007
.114832
.297110
.554300
.872085
1.239043
1.646482
2.087912
2.55821
3.05347
3.57056
4.10691
4.66043
5.22935
5.81221
6.40776
7.01491
7.63273
8.26040
8.89720
9.54249
10.19567
10.8564
11.5240
12.1981
12.8786
13.5648
14.2565
14.9535
22.1643
29.7067
37.4848
45.4418
53.5400
61.7541
70.0648
112.668
156.432
245.972
337.155
429.388

.0009821
.0506356
.215795
.484419
.831211
1.237347
1.68987
2.17973
2.70039
3.24697
3.81575
4.40379
5.00874
5.62872
6.26214
6.90766
7.56418
8.23075
8.90655
9.59083
10.28293
10.9823
11.6885
12.4011
13.1197
13.8439
14.5733
15.3079
16.0471
16.7908
24.4331
32.3574
40.4817
48.7576
57.1532
65.6466
74.2219
117.985
162.728
253.912
346.482
439.936

.0039321
.102587
.351846
.710721
1.145476
1.63539
2.16735
2.73264
3.32511
3.94030
4.57481
5.22603
5.89186
6.57063
7.26094
7.96164
8.67176
9.39046
10.1170
10.8508
11.5913
12.3380
13.0905
13.8484
14.6114
15.3791
16.1513
16.9279
17.7083
18.4926
26.5093
34.7642
43.1879
51.7393
60.3915
69.1260
77.9295
122.692
168.279
260.878
354.641
449.147

.0157908
.210720
.584375
1.063623
1.61031
2.20413
2.83311
3.48954
4.16816
4.86518
5.57779
6.30380
7.04150
7.78953
8.54675
9.31223
10.0852
10.8649
11.6509
12.4426
13.2396
14.0415
14.8479
15.6587
16.4734
17.2919
18.1138
18.9392
19.7677
20.5992
29.0505
37.6886
46.4589
55.3290
64.2778
73.2912
82.3581
128.275
174.835
269.068
364.207
459.926

(continued overleaf )

Appendix D Useful Statistical Tables

773

Table D.10 (Continued)
Degrees of

2
χ.100

2
χ.050

2
χ.025

2
χ.010

2
χ.500

Freedom
1
2
3
4
5
6
7
8
9
10
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
150
200
300
400
500

2.70554
4.60517
6.25139
7.77944
9.23635
10.6446
12.0170
13.3616
14.6837
15.9871
17.2750
18.5494
19.8119
21.0642
22.3072
23.5418
24.7690
25.9894
27.2036
28.4120
29.6151
30.8133
32.0069
33.1963
34.3816
36.5631
36.7412
37.9159
39.0875
40.2560
51.8050
63.1671
74.3970
85.5271
96.5782
107.565
118.498
172.581
226.021
331.789
436.649
540.930

3.84146
5.99147
7.81473
9.48773
11.0705
12.5916
14.0671
15.5073
16.9190
18.3070
19.6751
21.0261
22.3621
23.6848
24.9958
26.2962
27.5871
28.8693
30.1435
31.4104
32.6705
33.9244
35.1725
36.4151
37.6525
38.8852
40.1133
41.3372
42.5569
43.7729
55.7585
67.5048
79.0819
90.5312
101.879
113.145
124.342
179.581
233.994
341.395
447.632
553.127

5.02389
7.37776
9.34840
11.1433
12.8325
14.4494
16.0128
17.5346
19.0228
20.4831
21.9200
23.3367
24.7356
26.1190
27.4884
28.8454
30.1910
31.5264
32.8523
34.1696
35.4789
36.7807
38.0757
39.3641
40.6465
41.9232
43.1944
44.4607
45.7222
46.9792
59.3417
71.4202
83.2976
95.0231
106.629
118.136
129.561
185.800
241.058
349.874
457.305
563.852

6.63490
9.21034
11.3449
13.2767
15.0863
16.8119
18.4753
20.0902
21.6660
23.2093
24.7250
26.2170
27.6883
29.1413
30.5779
31.9999
33.4087
34.8053
36.1908
37.5662
38.9321
40.2894
41.6384
42.9798
44.3141
45.6417
46.9630
48.2782
49.5879
50.8922
63.6907
76.1539
88.3794
100.425
112.329
124.116
135.807
193.208
249.445
359.906
468.724
576.493

7.87944
10.5966
12.8381
14.8602
16.7496
18.5476
20.2777
21.9550
23.5893
25.1882
26.7569
28.2995
29.8194
31.3193
32.8013
34.2672
35.7185
37.1564
38.5822
39.9968
41.4010
42.7956
44.1813
45.5585
46.9278
48.2899
49.6449
50.9933
52.3356
53.6720
66.7659
79.4900
91.9517
104.215
116.321
128.299
140.169
198.360
255.264
366.844
476.606
585.207

Source: From C. M. Thompson. ‘‘Tables of the Percentage Points of the χ 2 -Distribution.’’ Biometrika, 1941, 32, 188–189.
Reproduced by permission of the Biometrika trustees.

774 Appendix D Useful Statistical Tables

Table D.11 Percentage Points of the Studentized Range q(p, ν), upper 5%
p
2

3

4

5

6

7

8

9

10

11

1

17.97

26.98

32.82

37.08

40.41

43.12

45.40

47.36

49.07

50.59

2

6.08

8.33

9.80

10.88

11.74

12.44

13.03

13.54

13.99

14.39

3

4.50

5.91

6.82

7.50

8.04

8.48

8.85

9.18

9.46

9.72

4

3.93

5.04

5.76

6.29

6.71

7.05

7.35

7.60

7.83

8.03

5

3.64

4.60

5.22

5.67

6.03

6.33

6.58

6.80

6.99

7.17

6

3.46

4.34

4.90

5.30

5.63

5.90

6.12

6.32

6.49

6.65

7

3.34

4.16

4.68

5.06

5.36

5.61

5.82

6.00

6.16

6.30

8

3.26

4.04

4.53

4.89

5.17

5.40

5.60

5.77

5.92

6.05

ν

9

3.20

3.95

4.41

4.76

5.02

5.24

5.43

5.59

5.74

5.87

10

3.15

3.88

4.33

4.65

4.91

5.12

5.30

5.46

5.60

5.72

11

3.11

3.82

4.26

4.57

4.82

5.03

5.20

5.35

5.49

5.61

12

3.08

3.77

4.20

4.51

4.75

4.95

5.12

5.27

5.39

5.51

13

3.06

3.73

4.15

4.45

4.69

4.88

5.05

5.19

5.32

5.43

14

3.03

3.70

4.11

4.41

4.64

4.83

4.99

5.13

5.25

5.36

15

3.01

3.67

4.08

4.37

4.60

4.78

4.94

5.08

5.20

5.31

16

3.00

3.65

4.05

4.33

4.56

4.74

4.90

5.03

5.15

5.26

17

2.98

3.63

4.02

4.30

4.52

4.70

4.86

4.99

5.11

5.21

18

2.97

3.61

4.00

4.28

4.49

4.67

4.82

4.96

5.07

5.17

19

2.96

3.59

3.98

4.25

4.47

4.65

4.79

4.92

5.04

5.14

20

2.95

3.58

3.96

4.23

4.45

4.62

4.77

4.90

5.01

5.11

24

2.92

3.53

3.90

4.17

4.37

4.54

4.68

4.81

4.92

5.01

30

2.89

3.49

3.85

4.10

4.30

4.46

4.60

4.72

4.82

4.92

40

2.86

3.44

3.79

4.04

4.23

4.39

4.52

4.63

4.73

4.82

60

2.83

3.40

3.74

3.98

4.16

4.31

4.44

4.55

4.65

4.73

120

2.80

3.36

3.68

3.92

4.10

4.24

4.36

4.47

4.56

4.64



2.77

3.31

3.63

3.86

4.03

4.17

4.29

4.39

4.47

4.55

(continued overleaf )

Appendix D Useful Statistical Tables

775

Table D.11 (Continued)
p
12

13

14

15

16

17

18

19

20

1

51.96

53.20

54.33

55.36

56.32

57.22

58.04

58.83

59.56

2

14.75

15.08

15.38

15.65

15.91

16.14

16.37

16.57

16.77

3

9.95

10.15

10.35

10.52

10.69

10.84

10.98

11.11

11.24

4

8.21

8.37

8.52

8.66

8.79

8.91

9.03

9.13

9.23

5

7.32

7.47

7.60

7.72

7.83

7.93

8.03

8.12

8.21

6

6.79

6.92

7.03

7.14

7.24

7.34

7.43

7.51

7.59

7

6.43

6.55

6.66

6.76

6.85

6.94

7.02

7.10

7.17

8

6.18

6.29

6.39

6.48

6.57

6.65

6.73

6.80

6.87

9

5.98

6.09

6.19

6.28

6.36

6.44

6.51

6.58

6.64

10

5.83

5.93

6.03

6.11

6.19

6.27

6.34

6.40

6.47

11

5.71

5.81

5.90

5.98

6.06

6.13

6.20

6.27

6.33

12

5.61

5.71

5.80

5.88

5.95

6.02

6.09

6.15

6.21

13

5.53

5.63

5.71

5.79

5.86

5.93

5.99

6.05

6.11

14

5.46

5.55

5.64

5.71

5.79

5.85

5.91

5.97

6.03

15

5.40

5.49

5.57

5.65

5.72

5.78

5.85

5.90

5.96

16

5.35

5.44

5.52

5.59

5.66

5.73

5.79

5.84

5.90

17

5.31

5.39

5.47

5.54

5.61

5.67

5.73

5.79

5.84

18

5.27

5.35

5.43

5.50

5.57

5.63

5.69

5.74

5.79

19

5.23

5.31

5.39

5.46

5.53

5.59

5.65

5.70

5.75

20

5.20

5.28

5.36

5.43

5.49

5.55

5.61

5.66

5.71

24

5.10

5.18

5.25

5.32

5.38

5.44

5.49

5.55

5.59

30

5.00

5.08

5.15

5.21

5.27

5.33

5.38

5.43

5.47

40

4.90

4.98

5.04

5.11

5.16

5.22

5.27

5.31

5.36

60

4.81

4.88

4.94

5.00

5.06

5.11

5.15

5.20

5.24

120

4.71

4.78

4.84

4.90

4.95

5.00

5.04

5.09

5.13



4.62

4.68

4.74

4.80

4.85

4.89

4.93

4.97

5.01

ν

Source: Biometrika Tables for Statisticians, Vol. 1, 3rd ed., edited by E. S. Pearson and H. O. Hartley (Cambridge
University Press, 1966). Reproduced by permission of Professor E. S. Pearson and the Biometrika Trustees.