# 131 1510 reference books 1 agarwal bl basic

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131 15.10. REFERENCE BOOKS 1) Agarwal, B.L., ‘Basic Statistics’, Wiley Eastern Ltd, New Delhi, 2 nd ed., 1991. 2) Gibbon. J.D., ‘Non -Parametric Statist ical Inference’, McGraw -Hill kogakusha Ltd, Tokyo. 3) W.J.Conover ‘Practical non - parametric statistics’ John Wiley & sons , Thired Ed, 2007. 15.11. LEARNING ACTIVITIES The board of regents of large eastern state university wants to test the hypothesis that the mean SAT scores of students at two branches of the state university are the Federal Aviation Agency (FAA) written examination , arranged according to which method was used in their training video cassette, audio cassette and class room training. The FAA is interested in evaluating the effectiveness of these three training methods. To test the hypothesis that the mean written examination scores of student pilots trained by each of these three methods are equal to apply the Kruskal-Wallis test to this problem. 15.12. KEY WORDS 1) Independent samples 2) Median 3) Ranking sum 4) Scale measurement 5) U- statistic 6) H-Statistic.

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132 LESSON 16 CHI-SQUARE TEST 16.1. INTRODUCTION Testing of hypothesis is an important tool of statistics. There are many test used in statistical analysis. But some are more frequently used than others. Chi-square test is one of the most frequently used test. The reason being that it is applicable in a large number of sciences like Biology, Agriculture, Psychology, education, Management, etc. Chi-square test makes use of the Chi-square distribution, that is why it is called chi-square test. The chi-square distribution is utilized to determine the critical values of the chi-square variate at various level of significance. Like other tests chi-square test also entails null and alternative hypothesis, two types of error in test of hypothesis leading to level significance and power of the test, degree of freedom. The details of these are omitted here. Chi-square test is applicable to test the hypothesis about the variance of a normal population, test of goodness of fit of a theoretical distribution, test of independence of attributes when the frequencies are presented in a two way table according to two attributes classified in various categories known as the contingency table. Chi-square test dated back to 1900, when Karl Pearson gave the test statistics for frequencies classified into K-mutually exclusive categories. 16.2. OBJECTIVES To use the chi-square distribution to see if two classifications of the same data are independent of each other. To use a chi-square test to check. Whether a particular collection of data is well described by a specified distribution. 16.3. CONTENTS 16.3.1. Characteristics of Chi-square Distribution 16.3.2. Working Rule for Chi-square Test 16.3.3. The 2 -Test for Goodness of Fit 16.3.4. Contingency Table of Order 2 2 16.3.1. CHARACTERISTICS OF CHI-SQUARE DISTRIBUTION 1) Chi-square curve is always positively skewed, i.e.
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