100 Statistical Tests

[...]... distributed, (b) are statistically independent and (c) have equal variances Most of the parametric tests considered in this book have made the assumption that the populations involved have normal distributions Therefore a test should only be carried out when the normality assumption is not violated It is also a necessary part of 4 100 STATISTICAL TESTS the test to check the effect of applying these tests when... its target, but the basis of this process is essentially that suggested above 22 100 STATISTICAL TESTS Numerical calculation ¯ µ0 = 4.0, n = 9, x = 4.6, σ = 1.0 Z = 1.8 Critical value Z0.05 = 1.96 [Table 1] H0 : µ = µ0 , H1 : µ = µ0 (Do not reject the null hypothesis H0 ) H0 : µ = µ0 , H1 : µ > µ0 (Reject H0 ) THE TESTS 23 Test 2 Z-test for two population means (variances known and equal) Object... even need to perform a calculation Notice that we are not doing all possible combination of tests so that we can find a significant result Our test is based on our design of the ‘experiment’ or survey planned before we collect any data Our data do not have a bearing on the form of the testing 24 100 STATISTICAL TESTS Numerical calculation ¯ ¯ n1 = 9, n2 = 16, x1 = 1.2, x2 = 1.7, σ = 1.4405, σ 2 = 2.0750... Critical region Using α = 0.05 [see Table 1] 1 0.025 0.025 –1.96 1.96 2 0.05 1.64 Data Conclusion H0 : µ0 = 4.0 n = 9, x = 4.6 ¯ σ = 1.0 ∴ Z = 1.8 1 Do not reject H0 [see Table 1] 2 Reject H0 6 100 STATISTICAL TESTS Test 3 Z-test for two population means (variances known and unequal) Hypotheses and alternatives 1 2 H0 : µ1 − µ2 H1 : µ1 − µ2 H0 : µ1 − µ2 H1 : µ1 − µ2 Z= Test statistics = µ0 = µ0 = µ0... 0.05 tn –1; 0.05 H0 : µ0 = 4.0 n = 9, x = 3.1 ¯ s = 1.0 ∴ t = −2.7 Data Conclusion 1 2 t8; 0.025 = ±2.306 [see Table 2] Reject H0 t8; 0.05 = −1.860 (left-hand side) [see Table 2] Reject H0 8 100 STATISTICAL TESTS Test 8 t-test for two population means (variance unknown but equal) Htypotheses and alternative H0 : µ1 − µ2 H1 : µ1 − µ2 2 H0 : µ1 − µ2 H1 : µ1 − µ2 1 t= Test statistics = µ0 = µ0 = µ0 >... 0.025 0.025 tn – 1; 0.025 2 0.05 tn – 1; 0.05 n1 = 16, d = 1.0 s = 1.0 ∴ t = 4.0 Data Conclusion 1 2 t15; 0.025 = ±2.131 [see Table 2] Reject H0 t15; 0.05 = 1.753 [see Table 2] Raject H0 10 100 STATISTICAL TESTS Test 15 χ 2 -test for a population variance Hypotheses and 1 alternatives 2 2 = σ0 2 = σ0 2 = σ0 2 > σ0 (n − 1)s2 2 σ0 Given a sample from a normal population with unknown variance χ2 = Test... 1; 0.05 2 2 H0 : σ1 = σ2 n1 = 11, n2 = 2 2 s1 = 6.0, s2 = Data ∴ F = 2.0 Conclusion 16 3.0 F10, 15; 0.025 = 3.06 Do not reject H0 2 F10, 15; 0.05 = 2.54 [see Table 3] Do not reject H0 1 12 100 STATISTICAL TESTS Test 37 χ 2 -test for goodness of fit Hypotheses and alternatives Goodness of fit for Poisson distribution with known mean λ Test statistics χ2 = (Oi − Ei )2 Ei Oi is the ith observed frequency,... significance of the differences between observed frequencies for two dichotomous distributions when the sample sizes are large 15 51 54 55 57 59 60 61 63 65 67 69 71 73 74 75 76 78 79 81 83 85 16 100 STATISTICAL TESTS Test 41 To investigate the significance of the differences between observed frequency distributions with a dichotomous classification Test 42 To investigate the significance of the differences... events Test 84 To test the significance of the difference in sequential connections across groups 17 116 118 120 121 122 123 124 126 128 129 130 131 133 135 137 139 142 145 148 151 153 155 156 18 100 STATISTICAL TESTS Test 85 To test whether the population value of each regression coefficient is zero in a multiple regression model Test 86 To test the variances in a balanced random effects model of random... other with respect to mean angle, angular variance or both Test 100 To test whether the treatment effects of independent samples from von Mises populations differ significantly from each other 158 160 161 164 165 166 168 169 171 172 174 176 177 178 180 182 CLASSIFICATION OF TESTS Test numbers For linear data 1 sample Parametric classical tests for central tendency 1, 7, 19 2 samples K samples 2, 3, 8, . a sourcebook for precise details of some or all the various tests. 100 Statistical Tests lists 100 different inferential tests used to solve a variety of statistical problems. Each test is presented in an. — 2006/6/15 — 15:21 — PAGEi—#1 100 STATISTICAL TESTS GOKA: “FM” — 2006/6/15 — 15:21 — PAGE ii — #2 GOKA: “FM” — 2006/6/15 — 15:21 — PAGE iii — #3 100 STATISTICAL TESTS 3rd Edition Gopal K. Kanji GOKA:. provide a list of all the 100 statistical tests. The fourth section classifies the tests under a variety of headings. This became necessary when we tried to arrange the tests in some logical sequence. Many