Introductory Applied Statistics for the Life Sciences
Introductory Applied Statistics for the Life Sciences STAT 371
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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 Quoc Tran in Fall. Since its upload, it has received 32 views. For similar materials see /class/205074/stat-371-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
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Date Created: 09/17/15
Quoc Tran B248D MSC tran statwiscedu STAT 371 Discussion 7 Testing Without normality 1 Two independent samples Wilcoxon Mann Whitney Test Sect 711 0 Applicability when we have two independent samples without normality 0 Statement of H0 and HA H0 The population distribution of Y1 and Y2 are the same HA The population distribution of Y1 and Y2 are different Steps to do a Sort data in Y1 and Y2 b Determine K1 and K2 as follows i The K1 count for each observation in sample 17 we count the number of observations in sample 2 that are smaller in value We count 12 for each tied observation The sum of all counts in sample 1 is K1 7 The K2 count for each observation in sample 27 we count the number of observations in sample 1 that are smaller in value We count 12 for each tied observation The sum of all counts in sample 2 is K2 7 Check if the work is correct7 K1 K2 711712 c Test statistics US is the larger of K1 and K2 US mazK17K2 d P value are bracketed from Table 6 with n the larger sample size7 and n7 the smaller sample size e Conclusion reject H0 when p 7 value lt a o Directional alternative if the HA is directional rather than nondirectional7 the WMW has two steps a Step 1 Check to see if data deviate from H0 in the direction speci ed by HA lf not7 p value is greater than 05 and we can not reject H0 lf so7 proceed to step 2 b Step 2 The p value are bracketed from the one tail title instead of the two tail as in the nondirectional 0 Conditions for use of WMW we still need randomness and independence of data 0 Example Prob 780 in the text book P 297 2 Paired Samples Sign Test Sect 94 o The sign test is a nonparametric test that does not depend on a normal assumption for the population of differences To carry out a sign test7 we ignore the magnitude of differences and just record whether each difference is positive or negative 0 P values are then computed from a binomial distribution with p 05 Technically7 the sign test is not testing equality of population means Instead7 a sign test is testing ifthe differences are equally likely to be positive versus either a nondirectional or directional alternative Of ce hours Mon 300 500pm l httpwwwstatwiscedutran Quoc Tran B248D MSC tran statwiscedu o Bracketing the p value The sign test statistic BS may be exactly equal to an entry in Table 77 and in such a case the Pivalue is less than the column heading Also7 some critical values appear more than once in the same row This feature is also due to the discreteness of the null distribution and does not cause any particular dif culty to bracket the P7 value7 we move to the right in Table 7 as far as possible7 stop when the next critical value in the table is larger than the observed value B5 Bracket this column7s title and the next7s 0 Example Prob 922 in the text book P 371 Of ce hours Mon 300 500pm 2 httpwwwstatwiscedutran