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note14 - Chapter 5 Tests for Trends and Association 4...

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Chapter 5: Tests for Trends and Association 4. Permutation Tests for Contingency Tables A two-way contingency table : the counts of individuals who fall into each of the categories that are determined by the two characteristics being studied. Data layout for an R × C contingency table Column 1 Column 2 . . . Column c Row Totals Row 1 n 11 n 12 . . . n 1 c n 1 . Row 2 n 21 n 22 . . . n 2 c n 2 . . . . . . . . . . . . . . . . . . . Row r n r 1 n r 2 . . . n rc n r. Column Totals n . 1 n . 2 . . . n .c n Hypotheses to Be Tested and the χ 2 Statistic definitions the expected cell proportions p ij = E ( n ij ) n the row and column proportions p i. = c summationdisplay j =1 p ij p .j = r summationdisplay i =1 p ij the conditional probability of column j given row i p j | i = p ij p i. hypothesis test: a test of association between the row and column factors Case 1: · all n individuals are selected at random from a population and cross-classified according to row and column characteristics · hypothesis H 0 : p ij = p i. p .j (independence) H a : p ij negationslash = p i. p .j at least one row and column (association between row and column characteristics) 1
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Case 2: · a fixed number n i. is selected according to row characteristic i ( i = 1 , . . . , r ) and classified according to the column character- istics · hypothesis H 0 : p j | i = p j | i (homogeneity of row distribution) H a : p j | i
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  • Spring '08
  • Staff
  • Null hypothesis, Statistical hypothesis testing, Statistical tests, Pearson's chi-square test, pj, Fisher's exact test

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