STAT371 DISCUSSION 10 November 10 2002 1 Comparison of Paired Samples In a paired design the observations Y1 Y2 occur in pairs not independent Instead of considering Y1 and Y2 independently we consider the DIFFERENCE d defined as d Y1 Y2 Relationship between sample means and population means d y 1 y 2 d 1 2 Standard error of d is sd SEd nd t Test H 0 d 0 d 0 ts SEd 1 Confidence Interval for d is d t 2 SEd e g If 10 then 90 confidence interval of d is d t0 05 SEd 2 Analysis of Categorical Data The chi square goodness of fit test H0 Pr categorical 1 p1 Pr categorical 2 p2 HA At least one of the probabilities specified in H0 is incorrect Chi square Statistics is 2s 1 X O E 2 E where the summation is over all the categories O represents the observed frequency of the category and E represents the expected frequency For categorial i E n pi where n is the total numP ber of observations n O Under H0 if the sample size is large enough the distribution of 2s can be approximated by 2 distribution with degree of freedom as df number of categories 1 The chi square test for the 2 2 contingency table H0 p 1 p 2 The Chi squate statistics is 2s X O E 2 E where the sum is taken over all four cells in the contingency table O represents the observed frequency and E represents the correspondint expected frequency according to H0 and E Row total Column total Grand total The degree of freedom is df 1 2
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