2 value is always positive 2 chi square values

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2 value is always positive. 2) Chi-square values increase with the increase in degree of freedom. 3) The standard deviation of 2 distribution is equal to 2 v where v is the degree of freedom. 4) The mean of distribution is the number of degree of freedom. 5) The value of 2 lies between zero and infinity, i.e., 2 0   6) The sum of two 2 distributions is again a 2 distribution. 7) For different degrees of freedom, the shape of curve will be different. 8) Chi-square ( 2 ) is a statistic hypothesis and not a parameter.
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133 Prerequisites of Chi-square Test The are following prerequisites or conditions for using 2 test: 1) Every observations of the sample for this test should be independent of all other observations. 2) The total number of observations used for the test should be large, i.e., 50 n 3) The expected frequency of any item should not be less than 5. 4) The frequencies used in 2 should be absolute and not relative in terms. 5) The observation collected for 2 test should be on random sampling. 6) Chi-square test is used only for drawing inference. It cannot be used for estimation of parameter or any other value. 7) Chi-square test is wholly dependent on degree of freedom. Contingency Table The data are often based on the count of persons, items, units or individuals which possess certain attributes. Here we categories individuals according to attributes say, A and B. Suppose the attribute A has on categories and p has q categories. For example, the attribute A represents Father’s height categorized as tall, medium, gnom e and attribute B as Son’s height categorized as tall, medium, and gnome. The frequencies are to be observed for all combination of Father’s height and Son’s height. A contingency table with attributes A and B having p and q categories is displayed below. Attribute A is taken along rows and B along columns. ij O is the frequency of , th i j cell which represent the number of individual in a group which possess the attributes i A and j B for 1,2,3, .... i p and 1,2,3, .... j q . The contingency table with 2 p and/ or 2 q is called a manifold contingency table. A contingency table with ‘p’ rows and ‘q’ column s is known as the contingency table of order p q . Contingency Table Attribute A Attribute B Total 1 B 2 ..... j B B .......... q B 1 2 . . . . . i p A A A A 11 21 1 1 . . . . . i p O O O O 12 1 22 2 2 2 ...... ...... . . . ...... . . ...... j j i ij p pj O O O O O O O O 1 2 ...... ...... . . . ...... . . ...... q q iq pq O O O O 1 2 . . . . . i p R R R R Total 1 C 2 ...... j C C ...... q C n
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134 The contingency holds certain relations 1 1 p q i j i i r c n Where n is the total number of individuals taken into consideration. Also each of row total or column total is known as marginal total. Test of Hypothesis in Contingency Table: Chi-square test is a test of independence of attributes in a contingency table.
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