# 5 2066 751065 10076 1601065 185 300 215 300 total 460

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30(55.5) 20(66) 75(106.5) 100(76) 160(106.5) 185 300 215 300 Total 460 185 355 1000 Solution

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145 The value of statistic chi-square is, 2 2 2 2 2 125 85 40 34 20 66 160 138 85 34 66 138 2 2 2 2 60 55.5 75 106.5 65 99 50 40 55.5 106.5 99 40 2 2 2 2 100 76 110 138 30 55.5 160 106.5 76 138 55.5 106.5 18.82 1.06 32.06 3.51 0.36 9.32 11.68 2.50 7.58 5.68 11.71 26.88 2 131.16 The value of =131.16 and n=12. So the value of coefficient of contingency 2 2 131.16 0.916 131.16 12 C n The value of C=0.916 is near to unity. Hence, there is a strong association between the type of workers and incentive schemes. 16.4. REVISION POINTS 1) The chi-square is a statistical method of determining the degree of division of the experimental results from the expected results, i.e., predetermined theoretical results. 2) The chi-square test is applied to test the closeness of observed frequency with that of expected frequency. 3) Chi-square test is used to see that the classification of attributes are independent. 16.5. INTEXT QUESTIONS 1) What is chi-square test? Give various uses of chi-square test. 2) What is chi-square test of goodness of fit? What precautions are necessary while using this test? 3) What are the basic conditional for the application of chi-square test? 4) Explain the chi-square test for independence of attributes. 5) Explain with illustration the special properties of chi-square distribution. 16.6. SUMMARY 1) Chi-square test is the most commonly used non-parametric test in social science research. It is computed on the basic of frequencies in a sample and is applied only for qualitative data such as intelligence, colour, immunity, health etc., 2) It is used as a test of significance when data is expressed in frequencies or in terms of percentages chi-square test enables us to determine the degree of deviation between observed frequencies and the theoretical frequencies and conclude whether the deviation between observed frequencies and expected frequencies is due to error of sampling or due to chance. 16.7. TERMINAL EXERCISES
146 1) Explain in brief chi-square test for goodness of fit. 2) Describe significance of chi-square test. 3) What is 2 2 contingency table. 4) What are the properties of chi-square test. 5) What is chi-square test for independence ? Choose the correct answer 1) When observed and expected frequencies completely coincide, chi-square will be a. +1 b. -1 c. 0 d. None of these 2) The calculated value of chi-square is a. Always positive b. Always negative c. Can be either positive or negative d. None of these 3) The number of degrees of freedom in 3 3 contingency table is a. 8 b. 4 c. 3 d. 1 4) The chi-square test was devised by a. Fisher b. Gauss c. Laplace d. Karl Pearson 5) Entries into the cells of contingency table should be a. Frequencies b. Mean values c. Percentages d. Degrees of freedom 16.8. SUPPLEMENTARY MATERIALS 1) 2) 3)

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