By R. S. Aggarwal

ISBN-10: 8121905516

ISBN-13: 9788121905510

This ebook includes all kinds of questions requested in quite a few aggressive examinations; totally solved examples with explanatory solutions

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Extra resources for A Modern Approach to Verbal & Non-Verbal Reasoning

Example text

Consequently, when H0i is true, —2 log pt has a chi-square distribution with two degrees of freedom. Because the sum of independent chi-square variables has a chisquare distribution, we have the very simple and elegant fact that if H0 is true, then - 2 \og(p{p2 · · · pk) = -2 log px 2 log pk has a chi-square distribution with 2k degrees of freedom. Because of this fact, no special tables are needed for the Fisher method. The test procedure becomes k reject H0 if P = -2 £ log p( > C, (3) 38 3. Tests of Combined Results where the critical value C is obtained from the upper tail of the chi-square distribution with 2/c degrees of freedom.

However, they do not always provide a test of the hypothesis of interest to the research reviewer. Such tests do not, for example, support inferences about the average magni­ tude of effects or about consistency of results across studies (see Section D). A. PRELIMINARIES AND NOTATION Consider a collection of k independent studies characterized by parameters 0 l 5 . . , 0 k , such as means, mean differences, or correlations. ,fc, 29 A. Preliminaries and Notation where large values of the test statistic lead to rejection of the null hypothesis.

In fact, the Fisher procedure and the normal procedure are both examples of (12). In the first case F is the chi-square distribution with two degrees of freedom, and in the second case F is the normal distribution. , any chi-square distribution) could also be used. , F~l(p) has a chi-square distribution with k degrees of freedom] is asymptotically ß-optimal. 43 C. ,Fk to provide a weighted statistic whose null distribution is easy to calculate. He suggested the statistic T=Fï1(p1) + ... , ak degrees of freedom, respectively.

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A Modern Approach to Verbal & Non-Verbal Reasoning by R. S. Aggarwal


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