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Experimental Design & Analysis

by: Vance Bode Sr.

Experimental Design & Analysis 22S 158

Vance Bode Sr.
GPA 3.72


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Class Notes
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This 4 page Class Notes was uploaded by Vance Bode Sr. on Friday October 23, 2015. The Class Notes belongs to 22S 158 at University of Iowa taught by Staff in Fall. Since its upload, it has received 57 views. For similar materials see /class/228087/22s-158-university-of-iowa in Natural Sciences and Mathematics at University of Iowa.


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Date Created: 10/23/15
gQO 7 quot I J H gt In J JVAAA A emblem X6 540 f rBoiCCEO 3 0 j 2 2 t J MadL 490 W 41 S r i UL O wfJ U 07va 1 I V LJa M w j 2 539 cc 2 k g j 2 0 UN z 17 m W a M 5 d9 4 Kym 4WWj 409 W I l lIIj oV 5f cw aka m at Q 4574 w 7d 449 3 Kym5 X W La 880 5M 7 42 330 WWVMrdbl 7AA E Mx 39 WW w 7 sayLL 526 CydL 3 m7 ad 3 K3559 31 zM z M c 1 I t 39 399 quot k 7 A I z m 9 i he k 5 R quot39I WF fj bpv wm m rfgigo ga BB 10 bouocf a 5 45 quot 3L 1 a H77 7 77 quotIV TC rtBIGURQBD L KW fti mr W 742630 SWmf I7 cg 0n L me 5001 39 gq z 7 A x quotf r K 1 51 L 4M0 5 955 34 In 3 A I 2 g sz valL k391 Q 6 W h 81801030 Wz WJIOLMl W 5 4 W a 4 39 7 a 4 4 424 bgatf lnm rwcm WW 40U M C 7L CK M WZV7j M 40 39L 4ML quot 4 A K W 4 9 4 WE z w CV w39 W W M I J 225158165 Experimental Design and AnaylsisApplied Statistic H 42409 BIBD Eyedrops example An experimenter is studying the effects of three di erent eyedrop brands for reduction in irritation Six subjects has volunteered for the study and will receive a dose of one brand in the left eye and a dose of another brand in the right eye randomly assigned The set up and observed responses irritation reduction are shown below subject l 1 2 3 4 5 6 A17 A53 B93 A76 A44 B52 B8 C30 C79 B68 C24 C38 R statements for data input and BIBD parameters gt setwdquotDUE165handoutsBIBDquot gt eyesread csvquoteyedrops csvquot gt eyes subject treatment reduction 1 1 A 17 2 1 B 53 3 2 A 93 4 2 C 76 5 3 B 44 6 3 C 52 7 4 A 8 8 4 B 30 9 5 A 79 10 5 C 68 11 6 B 24 12 6 C 38 gt BIBD related parameters gt g3 gt k2 gt b6 gt rbkg gt r 1 4 Every treatment appears 4 times in 4 distinct blocks gt lambdar k 1ltg 1 gt lambda 1 2 Every pairing occurs twice gt Nbk gt N 1 12 R statements for computing SS gt yeyesreduction gt SStotalsumy meany 2 1 gt SStotal g 9 1 7785 W Hr gt blockmeanstapplyyeyessubjectmean r E IV Xi gt SS blockksum blockmeans meany 2 KN COVEIL I Law ebbquot gt SSblock 5711 6 11 6560 SStreatmentadj TRT A in blocks l245 TRT B in blocks l346 TRT c in blocks 2356 treatmentsumstapplyyeyestreatmentsum blocksumstapplyyeyessubjectsum Qivaluestreatmentsums csumblocksumsC1245k sumblocksumsc1346ksumelocksumsc2356k gt Qivalues Adjusted treatment sums A B C 3915 18 3 gt SStreatmentadjksumQivalues 2lambdag gt SStreatmentadj C 1 186 S derailHM U61 sawl a VVVVVVV gt SSESStotalSSblockSStreatmentadj gt MSESSE12 1 5 2 1 f gt MSE U D L 1 25975 gt EBIBDRCBDgk1ltglk gt EBIBDRCBD 5440 Zr W3 1 075 R statements for computing treatment effect estimates gt treatment effect estimates under sumtoezero constraints gt alphahatskQivalueslambdag f f gt alphahats q Q A B c 39 7 5 6 1 tom ElliL C91 3 l UAW7 rim r r Lr R statements for comparing treatments gt Compare treatments 1 and 3 A 1 A gt gammahatalphahats1 alphahats3 gtTquot JVK quot gt gammahat t 4 gt segammahatsqrtklambdag2MSE 9 gt segammahat 9i 11 1315928 gt tstatgammahatsegammahat gt tstat E 0303968 R statements for getting treatment means adjusted gt Treatment mean adjusted gt muhatsumybk gt treatmentmeansmuhatalphahats gt treatmentmeans A B C 435 545 475 gt setreatmentmeansqrtMSEkg 1lambdag 21N gt setreatmentmean 1 8908875 SAS statements for Proc GLM proc glm dataeyes class treatment subject model reductionsubject treatmentsolution estimate trt 1 vs 3 treatment 1 O 1 lsmeans treatmentadjusttukey pdiff stderr output outdiag rresid pyhat run The GLM Procedure Dependent Variable reduction Sum of Source DF Squares Mean Square Model 7 6746000000 963714286 Error 4 1039000000 259 750000 Corrected Total 11 7785000000 1in Wquot a K g 3 i t The GLM Procedure 5 bb Dependent Variable reduction Source DF Typel SSf Mean Square F Value Pr gt F subject 5 7 s 0f000000r 1312000000 505 00709 treatment 2 186000000 93000000 036 07194 Source DF Type 111 SS Mean Square F Value Pr gt F subject 5 5881500000 1176300000 453 00842 treatment 2 lt13 EE 0 00gt 93000000 036 07194 x I 1 7quot 39339 r I gt 3977quot L u7111 a The GLM Procedure Dependent Variable reduction Standard Parameter Estimate Error t Value Pr gt Itl trt 1 VS 3 th 400000000 131592806 030 07763 Standard Parameter Estimate Error t Value Pr gt Itl Intercept 2750000000 B 1315928063 209 01049 subject 1 600000000 B 1740809199 034 07477 subject 2 5900000000 B 1740809199 339 00275 subject 3 1700000000 B 1611676146 105 03510 subject 4 1000000000 B 1740809199 057 05964 subject 5 4800000000 B 1740809199 276 00510 subject 6 000000000 B treatment A 400000000 B 1315928063 030 07763 treatment B 700000000 B 1315928063 053 06229 treatment C 000000000 B NOTE The X X matrix has been found to be singular and a generalized inverse was used to solve the normal equations Terms whose estimates are followed by the letter B are not uniquely estimable The GLM Procedure Least Squares Means Adjustment for Multiple Comparisons TukeyKramer reduction Standard LSMEAN treatment LSMEAN Error Pr gt Itl Number A 435000000 89088751 00081 1 B 545000000 89088751 00036 2 C 475000000 89088751 00060 3 4 Least Squares Means for effect treatment Pr gt tl for H0 LSMeaniLSMeanj Dependent Var iable reduct ion ij 1 2 3 1 07035 09510 2 07035 08606 3 09510 08606 SAS diagnostics 4 1 r e s x 1 d 5 1 I lvi I I I l l 10 15 gtZu 05 J 05 10 15 20 Norm Quantiles res 1 10 b 1 l I r39 Iquot 39 l H 10 0 30 10 50 9 70 80 90


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