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Statistical Methods and Computing

by: Cullen Conn

Statistical Methods and Computing 22S 105

Marketplace > University of Iowa > Natural Sciences and Mathematics > 22S 105 > Statistical Methods and Computing
Cullen Conn
GPA 3.72

Mary Cowles

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Mary Cowles
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This 5 page Class Notes was uploaded by Cullen Conn on Friday October 23, 2015. The Class Notes belongs to 22S 105 at University of Iowa taught by Mary Cowles in Fall. Since its upload, it has received 21 views. For similar materials see /class/228075/22s-105-university-of-iowa in Natural Sciences and Mathematics at University of Iowa.

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Date Created: 10/23/15
22S105 Statistical Methods and Computing More on ttests Lecture 17 Mar 107 2006 Kate Cowles 374 SH7 33570727 kcowles statuiowaedu data normtemp infile normtempdat input temp gender heart run proc means n mean stddev clm alpha 05 var temp run Variable N Mean Std Dev Lower 950 Upper 950 CLM CLlVl temp 130 98249 0733 98122 98376 Note that o The 95 con dence interval for n does not contain 986 o The prvalue is less than 05 so we can reject the null hypothesis 2 SAS for onesample ttests 0 SAS automatically does a tworsided test HOIMM0 HaZM7 M0 Example Using the normtempdat data on body temperatures measured on 130 healthy adults7 we will test the hypotheses H0 n 986 Ha n 7 986 at the 05 signi cance level 4 Example 2 We will use the same dataset to test a hypothesis regarding heart rates7 namely H0M73 Han73 at the 05 signi cance level Analysis Variable HEART N Mean Std Dev Lower 950 CLM Upper 950 CLM 130 737615385 70620767 725360699 749870071 Note that o The 95 con dence interval for n does con tain 73 o The prvalue is greater than 05 so we cannot reject the null hypothesis 5 6 Onesample ttests using proc univari Twosample ttests ate So far we have talked about drawing inference data normemp about a single population mean it based on data infile groupftppubkcowlesdatasetsnomtempdat input temp gender heart contained in one sample drawn from that pop format gender sexfmt ulation run proc univariate muO 986 data nomtemp Now we will consider procedures for comparing var temp two dzjj erent population means run The UNIVARIATE Procedure There are different procedures depending on whether Variable temp the samples are 0 paired Tests for Location Mu0986 0 independent Test Statistic p Value iiii W Student s t t 7545482 Pr gt ltl lt0001 Sign M 721 Pr gt lMl 00002 Signed Rank 3 1963 Fr gt Isl lt0001 7 E Paired samples 0 self pairing two measurements are taken on each subject oWe are interested in the unknown popula tion means M1 and pg of two different poput lations systolic blood pressure sbp upon entry into a clinical study Example 0 In our sample7 each observation drawn from the rst population is matched up with an observation drawn from the second popula tion sbp after 1 month on treatment The population means of interest are 7m mean sbp of untreated patients of this type 7M2 mean sbp of patients of this type after 1 month of treatment with the study regimen The question of interest is whether the treatment lowers blood pressure7 ie is 2 lt 17 9 o matched pairs investigator matches each subject in one treatment group with one sub ject in another treatment group so that meme bers of a pair are as alike as possible The population means of interest are 7 M1 mean response say sbp at 1 month of patients receiving treatment 1 7 M2 mean response of patients receiving treatment 2 i The question of interest is whether M1 M2 11 come OC users This subgroup will be the study sample 0 Measure the sbp of the study sample at the followrup visit 0 We will compare the baseline and followrup sbps of the women in the study sample 10 Paired ttest To carry out the hypothesis test of interest7 we apply onesample procedures to the di erences between values measured on members of each pair Example 0 We are interested in whether the use of oral contraceptive 00 drugs affects the level of systolic blood pressure sbp in women 0 We identify a group of nonpregnant7 premenopausal women aged 16749 from a prepaid health plan who are not currently OC users and measure their sbp7 which we will refer to as baseline sbp 0 We rescreen these women 1 year later to as certain a subgroup who have remained none pregnant throughout the year and have be 12 We will do a twosided test7 because we do not know in advance whether to expect M1 mean sbp in OC users to be higher or lower than M2 mean sbp in nonrusers H0 I Hi M2 Ha M1 M2 or equivalently H0 I Hi i 2 0 Ha I Hi i 2 at 0 or equivalently H0 2 6 0 Ha 6 7 0 where 6 denotes M1 7 M2 13 We will use the observed di erences between the before and after values observed on each woman as our data to to carry out the hypother sis test regarding 6 at the 05 signi cance level We will compute the sample mean of the dis 2 1239 T and the sample standard deviation of the dis 3 Ed 32 8d proc means data sbpoc var diff run Analysis Variable DIFF N Mean Std Dev Minimum Maximum 10 4800 4 5655716 20000 130000 14 data sbpoc infile groupftppubkcowlesdatasetssbpocdat input sbpnooc sbpoc diff sbpoc sbpnooc run proc print run OBS SBPNOOC SBPOC DIFF 1 115 128 13 2 112 115 3 3 107 106 1 4 119 128 9 5 115 122 7 6 138 145 7 7 126 132 6 8 105 109 4 9 104 102 2 10 115 117 2 16 Then the t statistic is tigim 851 W From our data7 34m 3d 4566 7 4 456am 332 Using Table A7 we see that the value that cuts off the upper 025 area under a t distribution with 9 degrees of freedom is 2262 Because 332 gt 2262 our result is more exr treme than the required cutoff7 we can reject the null hypothesis at the 05 level 17 We could use SAS to nd the exact prvalue7 Which is 00089 Note that the onersample trtest in proc univariate by default tests the null hypothesis that M 0 proc univariate data sbpoc var diff run The UNIVARIATE Procedure Variable temp Tests for Location Mu00 Test Statistic p Value iiii W Student s t t 3324651 Pr gt ltl 00089 Sign 3 Fr gt IMI 01094 Signed Rank S 24 Pr gt ISI 00117


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