100 Statistical Tests

100 Statistical Tests
Gopal K Kanji | ISBN-13 978 1 4129 2376 7 | Pdf | 257 pgs | 2 mb

Having collected together a number of tests, it is necessary to consider what can be tested, and we include here some very general remarks about the general problem of hypothesis testing. Students regard this topic as one full of pitfalls for the unwary, and even teachers and experienced statisticians have been known to misinterpret the conclusions of their analysis.

Broadly speaking there are two basic concepts to grasp before commencing. First, the tests are designed neither to prove nor to disprove hypotheses.We never set out to prove anything; our aim is to show that an idea is untenable as it leads to an unsatisfactorily small probability. Second, the hypothesis we are trying to disprove is always chosen to be the one in which there is no change; for example, there is no difference between the two population means, between the two samples, etc. This is why it is usually referred to as the null hypothesis, H0. If these concepts were firmly held in mind, we believe that the subject of hypothesis testing would lose a lot of its mystique. (However, it is only fair to point out that some hypotheses are not concerned with such matters.)
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LIST OF TESTS

• Test 1 To investigate the significance of the difference between an assumed
  population mean and sample mean when the population variance is known.
• Test 2 To investigate the significance of the difference between the means of two samples when the variances are known and equal.
• Test 3 To investigate the significance of the difference between the means of two samples when the variances are known and unequal.
• Test 4 To investigate the significance of the difference between an assumed proportion and an observed proportion.
• Test 5 To investigate the assumption that the proportions of elements from two populations are equal, based on two samples, one from each population.
• Test 6 To investigate the significance of the difference between two counts.
• Test 7 To investigate the significance of the difference between an assumed population mean and a sample mean when the population variance is unknown.
• Test 8 To investigate the significance of the difference between the means of two populations when the population variances are unknown but equal.
• Test 9 To investigate the significance of the difference between the means of two populations when the population variances are unknown and unequal.
• Test 10 To investigate the significance of the difference between two population means when no assumption is made about the population variances.
• Test 11 To investigate the significance of the regression coefficient.
• Test 12 To investigate whether the difference between the sample correlation coefficient and zero is statistically significant.
• Test 13 To investigate the significance of the difference between a correlation coefficient and a specified value.
• Test 14 To investigate the significance of the difference between the correlation coefficients for a pair of variables occurring from two different populations.
• Test 15 To investigate the difference between a sample variance and an assumed population variance.
• Test 16 To investigate the significance of the difference between two population variances.
• Test 17 To investigate the difference between two population variances when there is correlation between the pairs of observations.
• Test 18 To compare the results of two experiments, each of which yields a multivariate result. In other words, we wish to know if the mean pattern obtained from the first experiment agrees with the mean pattern obtained for the second.
• Test 19 To investigate the origin of one series of values for random variates, when one of two markedly different populations may have produced that particular series.
• Test 20 To investigate the significance of the difference between a frequency distribution based on a given sample and a normal frequency distribution with the same mean and the same variance.
• Test 21 To investigate the significance of the difference between a suspicious extreme value and other values in the sample.
• Test 22 To test the null hypothesis that the K samples came from K populations with the same mean.
• Test 23 To investigate the significance of the difference between two correlated proportions.
• Test 24 To investigate the significance of the difference between population variance and an assumed value.
• Test 25 To investigate the significance of the difference between two counted results.
• Test 26 To investigate the significance of the difference between the overall mean of K subpopulations and an assumed value for the population mean.
• Test 27 To investigate which particular set of mean values or linear combination of mean values shows differences with the other mean values.
• Test 28 To investigate the significance of all possible differences between
  population means when the sample sizes are unequal.
• Test 29 To investigate the significance of all possible differences between population means when the sample sizes are equal.
• Test 30 To investigate the significance of the differences when several treatments are compared with a control.
• Test 31 To investigate the significance of the differences between the variances of samples drawn from normally distributed populations.
• Test 32 To investigate the significance of the differences between the variances of normally distributed populations when the sample sizes are equal.
• Test 33 To investigate the significance of the difference between a frequency distribution based on a given sample and a normal frequency distribution.
• Test 34 To investigate the significance of the difference between one rather large variance and other variances.
• Test 35 To investigate the significance of the difference between an observed distribution and specified population distribution.
• Test 36 To investigate the significance of the difference between two population distributions, based on two sample distributions.
• Test 37 To investigate the significance of the differences between observed frequencies and theoretically expected frequencies.
• Test 38 To investigate the significance of the differences betweencounts.
• Test 39 To investigate the significance of the differences between observed frequencies for two dichotomous distributions.
• Test 40 To investigate the significance of the differences between observed frequencies for two dichotomous distributions when the sample sizes are large.
• 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 between distributions of alternative data.
• Test 43 To investigate the significance of the differences between two distributions based on two samples spread over some classes.
• Test 44 To investigate the difference in frequency when classified by one attribute after classification by a second attribute.
• Test 45 To investigate the significance of the difference between the population median and a specified value.
• Test 46 To investigate the significance of the difference between the medians of two distributions when the observations are paired.
• Test 47 To investigate the significance of the difference between a population mean and a specified value.
• Test 48 To investigate the significance of the difference between the means of two similarly shaped distributions.
• Test 49 To test if two random samples could have come from two populations with the same frequency distribution.
• Test 50 To test if two random samples could have come from two populations with the same frequency distribution.
• Test 51 To test if K random samples could have come from K populations with the same frequency distribution.
• Test 52 To test if two random samples could have come from two populations with the same means.
• Test 53 To test if two random samples could have come from two populations with the same variance.
• Test 54 To test if K random samples could have come from K populations with the same mean.
• Test 55 To test if K random samples came from populations with the same mean.
• Test 56 To investigate the difference between the largest mean and K − 1 other population means.
• Test 57 To test the null hypothesis that all treatments have the same effect as the control treatment.
• Test 58 To investigate the significance of the correlation between two series of observations obtained in pairs.
• Test 59 To investigate the significance of the correlation between two series of observations obtained in pairs.
• Test 60 To test the null hypothesis that the mean μ of a population with known variance has the value μ0 rather than the value μ1.
• Test 61 To test the null hypothesis that the standard deviation σ of a population with a known mean has the value σ0 rather than the value σ1.
• Test 62 To test the null hypothesis that the parameter of a population has the value p0 rather than p1.
• Test 63 To test the null hypothesis that the fluctuations in a series have a random nature.
• Test 64 To test the null hypothesis that the fluctuations in a series have a random nature.
Series could be serially correlated.
• Test 65 To test the null hypothesis that the variations in a series are independent of the order of the observations.
• Test 66 To test the null hypothesis that the fluctuations of a sample are independent of the order in the sequence.
• Test 67 To test the null hypothesis that observations in a sample are independent of the order in the sequence.
• Test 68 To test the null hypothesis that two samples have been randomly selected from the same population.
• Test 69 To test the significance of the order of the observations in a sample.
• Test 70 To test the random occurrence of plus and minus signs in a sequence of observations.
• Test 71 To test that the fluctuations in a sample have a random nature.
• Test 72 To compare the significance of the differences in response for K treatments applied to n subjects.
• Test 73 To investigate the significance of the differences in response for K treatments applied to n subjects.
• Test 74 To investigate the significance of the correlation between n series of rank numbers, assigned by n numbers of a committee to K subjects.
• Test 75 To test a model for the distribution of a random variable of the continuous type.
• Test 76 To test the equality of h independent multinomial distributions.
• Test 77 To test for non-additivity in a two-way classification.
• Test 78 To test the various effects for a two-way classification with an equal number of observations per cell.
• Test 79 To test the main effects in the case of a two-way classification with unequal numbers of observations per cell.
• Test 80 To test for nestedness in the case of a nested or hierarchical classification.
• Test 81 To test the presence of regression of variable Y on the observed value X.
• Test 82 To test the linearity of regression between the X variable and the Y variable.
• Test 83 To test the significance of the reduction of uncertainty of past events.
• Test 84 To test the significance of the difference in sequential connections across groups.
• 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 variables.
• Test 87 To test the interaction effects in a two-way classification random effects model with equal number of observations per cell.
• Test 88 To test a parameter of a rectangular population using the likelihood ratio method.
• Test 89 To test a parameter of an exponential population using the uniformly most powerful test method.
• Test 90 To test the parameter of a Bernoulli population using the sequential test method.
• Test 91 To test the ratio between the mean and the standard deviation of anormal population where both are unknown, using the sequential method.
• Test 92 To test whether the error terms in a regression model are autocorrelated.
• Test 93 To test the medians of two populations.
• Test 94 To test whether a proposed distribution is a suitable probabilistic model for the sample data.
• Test 95 To test whether the observed angles have a tendency to cluster around a given angle, indicating a lack of randomness in the distribution.
• Test 96 To test whether the given distribution fits a random sample of angular values.
• Test 97 To test whether two samples from circular observations differ significantly from each other with respect to mean direction or angular variance.
• Test 98 To test whether the mean angles of two independent circular observations differ significantly from each other.
• Test 99 To test whether two independent random samples from circular observations differ significantly from each 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.

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