Introductory Applied Statistics for the Life Sciences
Introductory Applied Statistics for the Life Sciences STAT 371
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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 371 at University of Wisconsin - Madison taught by Nicholas Keuler in Fall. Since its upload, it has received 35 views. For similar materials see /class/205072/stat-371-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
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Date Created: 09/17/15
Qi Tang 1276 MSC qitang statlwiscledu STAT 371 Discussion 10 April 19 2006 1 Analysis of varianceone way anova 0 Notation yij the jth observation in the ith group I the number of groups n the ith sample size m 39 yquot 37 a the mean of the 1th sample 71139 I 71 the total number of observations i1 I 211 221 yij yi the grand mean 71 o The ANOVA Table Source df SSSum of Squares MSMean Square 7 I I 1 7 2 SSbetween Between groups I 1 21 ny dfbetween l l SS within Wlthm groups 71 7 I ELI 21yij 7 yi2 Total m 7 1 2 21y 7 3quot SStotalSSbetweenSSwithin dftotaldfwithindfbetween o The F Statistic 7 The F statistic is the ratio of the mean square between over the mean square within MSbetween MSwithin 7 If the populations are normal the population means are all equal the standard devia tions are all equal and all observations are independent then the F statistic has an F distribution with I 7 1 and n 7 I degrees of freedom 7 An F distribution is positive and skewed right like the chi square distribution but it has two separate degrees of freedom the numerator degrees of freedom and the denominator degrees of freedom 0 Newman Keuls 7 The Newman Keuls procedure is based on the distribution of the differences of order statistics of sample means when all population means are equal and sample sizes 11 are equal 7 The order statistics are the sample means sorted from smallest to largest 7 The procedure is as follows Sort the sample means in increasing order Compute critical values R q x spooled n f Here spooled MSwithin q is provided by the Table 11 and with dfdfwithin Of ce hours M 100200and T 9301030 1276 MSC 1 httpwwwlstatlwiscleduNqitang Qi Tang 1276 MSC qitang statiwisciedu Make pairwise comparisons 2 Examples 0 Example 1 Invent examples of data with SSbetween0 and SSwithm gt 0 0 Example 2 1137 on page 516 Ten treatments were compared for their effect on the liver in mice There were 13 animals in each treatment group The ANOVA gave MSwithin 05842 The mean liver weights are given in the table Treatment Mean Liver Weightg 5 omxlouo39l w wwwwwwwwww 00 us Use the Newman Keuls method to compare treatment 1amp 27 treatment 4 amp 10 of means at 04 005 Of ce hours M 100200and T 9301030 1276 MSC 2 httpwwwistatlwiscieduNqitang
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