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Analy Of Variance

by: Carmen Mayer

Analy Of Variance STA 106

Carmen Mayer
GPA 3.69


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This 3 page Class Notes was uploaded by Carmen Mayer on Tuesday September 8, 2015. The Class Notes belongs to STA 106 at University of California - Davis taught by Staff in Fall. Since its upload, it has received 30 views. For similar materials see /class/191920/sta-106-university-of-california-davis in Statistics at University of California - Davis.


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Date Created: 09/08/15
Sta106 Winter 2009 for extra study purposes only written by TA EXAMPLE 39 39 39 intervals 39 39 Consider Dataset in your textbook CH17TA02 see data CD of chapter 17 for information Suppose that the data represent time in seconds it takes for a technician to assemble parts Consider that in 4 different branches of the company 10 randomly selected technicians are evaluated The goal of the study is to compare the assembly time between 4 branches Suppose single factor ANOVA model is appropriate Yij u an i14 j1 10 cu 7 N002 r 4 n 10 for all i The tted values are eaerage assemb1y time in seconds Y14047 Y24313 Y36795 Y48944 Analysis of Variance Table ResponseY Df Sum Sq Mean Sq F value PrgtF X 3159535 53178 86612 lt22e 16 Residuals 36 2210 61 From ANOVA table MSE61 1 Construct 95 simultaneous con dence intervals for all pairWise comparisons of type D u up where i7 i using Tukey procedure The estimate ofthe pairWise comparisonis DA so 7 T 172 7 4047 a 4313 7 266 4047 7 6795 2748 Y4 4047 7 8944 4897 4313 7 6795 2482 Y4 4313 7 8944 4631 Y4 6795 7 8944 2149 D U U Hgt H H H U U o gt Lngt Agt LAgt Ngt H 9 glt1lt1lt1lt1lt I 5 U Standard error is since group samples are all equal size 10 sDA MSE1ni1nix V61110 110 110 Tukey multiple T 12 q1005440412 381 269 95 simultaneous C1s for D gt DA T sDA D1171 172TsDA gt 266 26911 gt 5619 0299 D2 3043924521 D3 5192946011 D4 2777921861 D5 4926943351 D5 2444918531 Interpretation With 95 con dence the true difference in mean assembly time between branches 1 and 2 is somewhere between 5619 seconds and 0299 seconds between 1 and 2 is somewhere between 30439 seconds and 24521 seconds and so on obviously the standard interpretation of the con dence interval is a rather dull statement which is dif cult to understand Inference The con dence interval D1 suggests with 95 con dence that the mean assembly time in branch 1 is not signi cantly different from that of branch 2 Alternatively con dence intervals D2 through D6 suggest the mean assembly times between all other branches differ signi cantly More speci cally with 95 con dence the mean assembly time is shorter in branch 1 when compared to branches 3 and 4 it is also shorter in branch 2 when compared with branches 3 and 4 and is it also shorter in branch 3 than in branch 4 This conclusion was made since the rst con dence interval includes zero implying that the two treatment means are the same and all other con dence intervals do not include zero and are negative implying that the two treatment means are different 2 Construct 95 simultaneous con dence intervals for contrasts L1 04M1 06m 7 071 7 03 L l3u1 l3u2 13 7 L4 Le 2u170u27ui 2u4 2u17ui 2u4 using both Scheffe and Bonferroni procedures Which procedure would you prefer The estimate of the contrast is LA 2617 so L91 04171 06172 07173 03174 7 044047 064313 7 076795 7 038944 7 32331 m 171 m7 Z 7174 7 134047 134313 1367957 8944 7 389233 L93 7 mi 17 mi 7 044047 064313 7 076795 7 038944 7 2995 Standard error is sLA 7 VMSEEcizni sLAl 7 6104210 06210 07210 03210 7 61011 7 0819 sLAZ 7 6113210 13210 13210 1210 7 6101333 7 0902 gm 7 V6112210 1210 13210 7 V61015 7 0956 Scheffe multiple S V14F1005 41 404 32866 293 95 simultaneous C1s for L1 L2 L3 using Scheffe LA S sLA L1 04171 06Z 707173 703174 s sLAl 7gt 32331 2930819 7gt 34730672993133 Ll 41566163628044 L3 579608019392 Bonferroni multiple B t10052g 404 t100523 404 t09916667 36 251 95 simultaneous C1s for L1 L2 L3 using Bonferroni gt LA B sLA L1 04171 06Z 07173 03E s sLA1 gt 32331 2510819 gt 34386693027531 Ll 41187323665928 L3 539456 059544 Bonferroni method gives a narrower con dence interval thus Bonferroni method is superior to Scheffe method for the comparison of this type


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