101110u - CHI-SQUAREfor a particular number of degrees of...

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Sheet1 Page 1 AGENDA Computer implementation of Chi-square goodness of fit test Review Return tests? Optional homework problems Quiz GOODNESS OF FIT TESTS Based on a comparison of observations between Observed data Theoretical data The comparison utilizes a set of intervals or cells Each cell has a lower and upper boundary values The determination of the boundaries are a function of Theoretical distribution Number of observations in the sample TWO DIFFERENT APPROACHES Approach 1 Used in the book Equal interval approach No cell grouping can have less than 5 expected observations Approach 2 Used in other books Equiprobable approach Maximum number of cells not to exceed 100 such that the expected number of observations is at least 5 = Int ( obs/5 ) Expected number of obs in each cell = obs / cells More statistically robust
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Unformatted text preview: CHI-SQUAREfor a particular number of degrees of freedom TEST STATISTIC NON-PARAMETRIC TEST CONCEPTS Used when the sample data is either Non-normal (from goodness of fit test) Sample is too small to determine normality Rank sum tests Based on the rank order of sorted data sample rather than using the mean and standard deviation Equivalent sets of data with have similar ranks U Test& H Test& PERFORM CALCULATIONS Calculate rank sums W1 is the sum of the ranks of data from set 1 W2 is the sum of the ranks of data from set 2 Calculate U s U1=W1-n1(n1+1)/2 Sheet1 Page 2 U2=W2-n2(n2+1)/2 U1=min (U1,U2) Next& NEXT Calculate the mean of the ranks u = n1*n2/2 Calculate the variance of the ranks Sigma1 squared = n1*n2*(n1+n2+1)/12 Calculate the test statistic Z Z = (U1-u) / sigma1 H-TEST STATISTIC...
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This note was uploaded on 11/21/2010 for the course INDE 2333 taught by Professor Staff during the Fall '08 term at University of Houston.

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101110u - CHI-SQUAREfor a particular number of degrees of...

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