100 STATISTICAL TESTS phần 10 ppt

Table 20 Critical values of U for the Wilcoxon inversion testn1= number of elements in the largest sample; n2= number of elements in the smallest sample... Table 21 Critical values of th

Table 20 Critical values of U for the Wilcoxon inversion test

n1= number of elements in the largest sample;

n2= number of elements in the smallest sample

Level of significance α Level of significance α

Two-sided 0.10 0.05 0.02 0.01 Two-sided 0.10 0.05 0.02 0.01One-sided 0.05 0.025 0.01 0.005 One-sided 0.05 0.025 0.01 0.005

Table 21 Critical values of the smallest rank sum for the Wilcoxon–Mann–Whitney test

n1= number of elements in the largest sample;

n2= number of elements in the smallest sample

Level of significance α Level of significance α

Two-sided 0.20 0.10 0.05 0.01 Two-sided 0.20 0.10 0.05 0.01One-sided 0.10 0.05 0.025 0.005 One-sided 0.10 0.05 0.025 0.005

Table 21 continued

Level of significance α Level of significance α

Two-sided 0.20 0.10 0.05 0.01 Two-sided 0.20 0.10 0.05 0.01One-sided 0.10 0.05 0.025 0.005 One-sided 0.10 0.05 0.025 0.005

Table 22 The Kruskal–Wallis test

Critical region: H≥ tabulated value.

Sample α= 0.05 α= 0.01 Sample α= 0.05 α= 0.01 Sample α= 0.05 α= 0.01

Table 23 Critical values for the rank sum difference test (two-sided)

Table 24 Critical values for the rank sum maximum test

Table 25 Critical values for the Steel test

7 0.05 37 36 35 35 34 34 33 330.01 32 31 30 30 29 29 29 29

8 0.05 49 48 47 46 46 45 45 440.01 43 42 41 40 40 40 39 39

9 0.05 63 62 61 60 59 59 58 580.01 56 55 54 53 52 52 51 51

10 0.05 79 77 76 75 74 74 73 720.01 71 69 68 67 66 66 65 65

11 0.05 97 95 93 92 91 90 90 890.01 87 85 84 83 82 81 81 80

12 0.05 116 114 112 111 110 109 108 1080.01 105 103 102 100 99 99 98 98

13 0.05 138 135 133 132 130 129 129 1280.01 125 123 121 120 119 118 117 117

14 0.05 161 158 155 154 153 152 151 1500.01 147 144 142 141 140 139 138 137

15 0.05 186 182 180 178 177 176 175 1740.01 170 167 165 164 162 161 160 160

16 0.05 213 209 206 204 203 201 200 1990.01 196 192 190 188 187 186 185 184

17 0.05 241 237 234 232 231 229 228 2270.01 223 219 217 215 213 212 211 210

18 0.05 272 267 264 262 260 259 257 2560.01 252 248 245 243 241 240 239 238

19 0.05 304 299 296 294 292 290 288 2870.01 282 278 275 273 271 270 268 267

20 0.05 339 333 330 327 325 323 322 3200.01 315 310 307 305 303 301 300 299

Table 26 Critical values of r s for the Spearman

rank correlation test

Table 27 Critical values of S for the Kendall rank

Table 28 Critical values of D for the adjacency test

Columns a denote the lower boundaries or the left-sided critical values.

Columns b denote the upper boundaries or the right-sided critical values.

Table 29 Critical values of r for the serial correlation test

Columns a denote the lower boundaries or the left-sided critical values.

Columns b denote the upper boundaries or the right-sided critical values.

Table 30 Critical values for the run test on successive

differences

Columns a denote the lower boundaries or the left-sided critical values.

Columns b denote the upper boundaries or the right-sided critical values.

Table 31 Critical values for the run test (equal sample sizes)

Columns a denote the lower boundaries or the left-sided critical values.

Columns b denote the upper boundaries or the right-sided critical values.

Level of significance α

Two-sided 0.10 0.05 0.02 0.01One-sided 0.05 0.025 0.01 0.005

Table 32 Critical values for the Wilcoxon–Wilcox

Table 33 Durbin–Watson test bounds

d Ldenotes the lower boundary or left-sided critical values

d U denotes the upper boundary or right-sided critical values

Example: for n = 20, α = 0.01, and two independent variables,

Table 34 Modified Rayleigh test (V -test)

Table 35 Watson’s U n2 -test

Table 36 Watson’s two-sample U2 -test

n and m are sample sizes.

Table 37 Maximum likelihood estimate ˆk for

given ¯R in the von Mises case

For the solution k = A−1(ρ), replace ˆk by k, ¯ R by ρ.

0.00 0.00000 0.35 0.74783 0.70 2.013630.01 0.02000 0.36 0.77241 0.71 2.076850.02 0.04001 0.37 0.79730 0.72 2.143590.03 0.06003 0.38 0.82253 0.73 2.214250.04 0.08006 0.39 0.84812 0.74 2.289300.05 0.10013 0.40 0.87408 0.75 2.369300.06 0.12022 0.41 0.90043 0.76 2.454900.07 0.14034 0.42 0.92720 0.77 2.546860.08 0.16051 0.43 0.95440 0.78 2.646130.09 0.18073 0.44 0.98207 0.79 2.753820.10 0.20101 0.45 1.01022 0.80 2.871290.11 0.22134 0.46 1.03889 0.81 3.000200.12 0.24175 0.47 1.06810 0.82 3.142620.13 0.26223 0.48 1.09788 0.83 3.301140.14 0.28279 0.49 1.12828 0.84 3.479010.15 0.30344 0.50 1.15932 0.85 3.680410.16 0.32419 0.51 1.19105 0.86 3.910720.17 0.34503 0.52 1.22350 0.87 4.177030.18 0.36599 0.53 1.25672 0.88 4.488760.19 0.38707 0.54 1.29077 0.89 4.858710.20 0.40828 0.55 1.32570 0.90 5.30470.21 0.42962 0.56 1.36156 0.91 5.85220.22 0.45110 0.57 1.39842 0.92 6.53940.23 0.47273 0.58 1.43635 0.93 7.42570.24 0.49453 0.59 1.47543 0.94 8.61040.25 0.51649 0.60 1.51574 0.95 10.27160.26 0.53863 0.61 1.55738 0.96 12.76610.27 0.56097 0.62 1.60044 0.97 16.92660.28 0.58350 0.63 1.64506 0.98 25.25220.29 0.60625 0.64 1.69134 0.99 50.24210.30 0.62922 0.65 1.73945 1.00 ∞0.31 0.65242 0.66 1.78953

0.32 0.67587 0.67 1.841770.33 0.69958 0.68 1.896370.34 0.72356 0.69 1.95357

Source: Mardia, 1972

Table 38 Mardia–Watson–Wheeler test

n1= smaller of the two sample sizes n1, n2; n = n1+ n2

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Hartley’s test 73

Hotelling’s T2test 48 hypothesis testing 2

independence test 91 interaction effect 142, 161 inversion test 97

level of significance 3 likelihood ratio test 18, 164 Link–Wallace test 67 log odds ratio 156

Mardia–Watson–Wheeler test 180

mean 55, 61, 95, 96 mean angles 18, 178 median test 93, 94, 98, 99, 171 modified Rayleigh test 174 multinomial distribution 137 multiple comparison 65, 67, 106 multiple regression 18, 158

Neave 2

non-additivity 17, 139 normal distribution 16,

25, 44 normality 74 null hypothesis 1, 4, 17

outliers 54, 75

paired observations 9, 35, 46, 96,

109, 110 Poisson distribution 28, 60 probabilistic model 18, 172

q-test 65 Q-test 88

random effects model 18, 160 randomness 118, 120, 121,

122, 123, 124, 126, 128,

129, 174 rank correlation test 109, 110,

129, 133 rank sum difference test 106 rank sum maximum test 107 rectangular population

18, 164 regression 37, 151, 153 run test 123, 124, 126

sequential contingencies 156 sequential probability ratio test 168

sequential test 18, 112, 114,

116, 166 serial correlation test 120 Siegel–Tukey rank sum dispersion test 102

sign test 93, 94 signed rank test 95, 96 significance level 2 skewness 51, 53 Spearman rank correlation test 109

standard deviation 114 Steel test 108 Studentized range 65, 74

Student’s t distribution 29, 31, 33,

Yates correction 85

Z-test 5, 6, 21, 23, 25, 26, 27, 28,

40, 42, 57, 155, 156

Z-transformation 194