Introduction to Statistical Methods
Introduction to Statistical Methods STAT 301
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Mrs. Triston Collier
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This 2 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 301 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/205083/stat-301-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
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Date Created: 09/17/15
STAT 301 TA Lisa Chung lchungstatwiscedu DISCUSSION 12 Mar 18 2004 Several Samples Proportions 0 Suppose two general categorical variables I J having r and c categories respectively H0 There is no association between categoties ofl and those of J vs H1 There is an association between I and J Observed value OH I i J j Expected valueEj R j where Ri On 022 Oic Cj 017 027 O r r 02 iEi 2 Test statistic X2 2am 2 N X39r71c71 Goodness of t test Consider one of the treatment categories alone Assume we wish to test the null hypothesis that there is no signi cant difference in responses For i12k groups nsample size Observed value OiExpected valueEi mu 1 1 r 2 02397Ei 2 2 Test statistic X 7 Z N inl MeansANOVA table 0 ANOVA focuses on a comparison of more than two population or treatment means 0 Null and alternative hypothesis 7H03ILL1IU2ILLI 7 Ha At least one of the His are different 0 Basic Assumptions The k population or treatment distributions are all normal with the same 2 039 0 ANOVA table Source df Sum of squares Mean square F Treatments k 7 1 2 mm 7 a MSTr SSTrk 7 1 Error 71 7 k 2101 7 1s MSE SSEn 7 k Total 77 71 Emmi17 7 EV where 7 z and 31 sample mean and sample sd in it sample i12k 7 Fundamental Identity of Sum of Squares SST SST SSE 7 Test statistic F has an F distribution with 11 k 7 1 and 12 n 7 k when H0 is true and the basic assumptions are satis ed 7 P value PF12 gt F0179 Reject H0 when P value a Of ce 1335 MSC 263 5948 10f ce Hour Wed100 200 and Thurs 1100 1200 STAT 301 TA Lisa Chung 1chung statwiscedu Examples 1 Goodness of Fit test with random number game 2 p473 38 and 39 3 p 483 45 4 See Practice Problem 610 in Lecture Note Of ce 1335 MSC7 263 5948 2 Of ce Hour Wed100 200 and Thurs 1100 1200
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