wo indpndnt Sampls his tst is for two indpndnt Populations. h tst is somtims calld th Mann-Whitny U tst or th Rank Sum Wilcoxon. hy ar quivalnt. h main assumption is that th two sampls ar indpndnt and that th variabl masurd is ordinal or continuous. Rad th xampl on p. 87. h data is: im ratmt Cnsord 68.00 MODIFIED 0.00 70.00 MODIFIED 0.00 73.00 MODIFIED 0.00 75.00 MODIFIED 0.00 77.00 MODIFIED 0.00 80.00 MODIFIED 0.00 80.00 MODIFIED 0.00 132.00 MODIFIED 0.00 148.00 MODIFIED 0.00 155.00 MODIFIED 0.00 183.00 MODIFIED 0.00 197.00 MODIFIED 0.00 206.00 MODIFIED 0.00 210.00 MODIFIED 0.00 130.00 COVEIOAL 0.00 139.00 COVEIOAL 0.00 146.00 COVEIOAL 0.00 150.00 COVEIOAL 0.00 161.00 COVEIOAL 0.00 177.00 COVEIOAL 0.00 228.00 COVEIOAL 0.00 242.00 COVEIOAL 0.00 265.00 COVEIOAL 0.00 1
W first xamin th data visually. h book dos doubl sidd stm plots, w can do boxplots. proc sort data=mth567.gomtry; by tratmt; goptions rst=goptions dvic=mf gsfnam=plotg gsfmod=rplac gunit=pct hsiz=17cm vsiz=12.6cm nobordr cback=whit ctxt=black htxt=0.45cm ftxt='arial' ftitl='arial'; filnam plotg "c:\tstgraph.mf"; proc boxplot data=mth567.gomtry; plot tim*tratmt /boxstyl=schmaticid; 300 250 200 IME 150 100 50 COVEIOAL REAM MODIFIED Gt rid of th mf in th abov to s things on th scrn. Can also look at histograms: proc univariat data=mth567.gomtry; var tim; histogram; I still lik th rsults of Proc mans: proc mans data=mth567.gomtry n man mdian stdv min max; var tim; 2
40 R E A M C O V E I O A L M O D I F I E D P r c n t P r c n t 35 30 25 20 15 10 5 0 40 35 30 25 20 15 10 5 0 60 100 140 180 220 260 300 IME Analysis Variabl : IME IME REAM Obs Man Mdian Std Dv Minimum Maximum ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ COVEIOAL 14 14 224.1428571 235.0000000 70.5471551 130.0000000 300.0000000 MODIFIED 14 14 125.2857143 106.0000000 56.5976740 68.0000000 210.0000000 proc npar1way data=mth567.gomtry wilcoxon; var tim; xact; h PAR1WAY Procdur Wilcoxon Scors (Rank Sums) for Variabl IME Classifid by Variabl REAM Sum of Expctd Std Dv Man REAM Scors Undr H0 Undr H0 Scor 3
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ COVEIOAL 14 269.0 203.0 21.701254 19.214286 MODIFIED 14 137.0 203.0 21.701254 9.785714 Avrag scors wr usd for tis. Wilcoxon wo-sampl st Statistic (S) 269.0000 ormal Approximation Z 3.0183 On-Sidd Pr > Z 0.0013 wo-sidd Pr > Z 0.0025 t Approximation On-Sidd Pr > Z 0.0027 wo-sidd Pr > Z 0.0055 Exact st On-Sidd Pr >= S 8.222E-04 wo-sidd Pr >= S - Man 0.0016 Z includs a continuity corrction of 0.5. Confidnc Intrval for δ - th additiv ffct. If w want to know what th 95% confidnc intrval is for how strong th improvmnt is, w can subtract 50 sconds from th convntional folks and s if it compars now to th modifid folks. data mth567.gomtry2; st mth567.gomtry; if tratmt="coveioal" thn tim2=tim-50; ls tim2=tim; proc npar1way data=mth567.gomtry2 wilcoxon; var tim2; xact; Whn w run this cod, w gt th output Statistic (S) 251.0000 ormal Approximation Z 2.1897 On-Sidd Pr > Z 0.0143 wo-sidd Pr > Z 0.0285 So thr is still a significant diffrnc. W can try 60 sconds. data mth567.gomtry2; st mth567.gomtry; 4
if tratmt="coveioal" thn tim2=tim-60; ls tim2=tim; proc npar1way data=mth567.gomtry2 wilcoxon; var tim2; xact; Statistic (S) 241.5000 ormal Approximation Z 1.7513 On-Sidd Pr > Z 0.0399 wo-sidd Pr > Z 0.0799 W would continu to do this to find th uppr bound of th diffrnc. h book shows that uppr bound is around 159 sconds. So th 95% confidnc intrval for th ffct siz of this chang in prsnting this matrial is (58, 159) scond improvmnt ovr convntional mthods. So w could us th midpoint of this intrval 107.5 as th stimatd ffct siz. 4.3.1 Prmutation sts th O-ring data is a vry vry intrsting cas. W hav dividd th data into two groups: launch tmpratur blow 65 and abov 65. In ordr w hav, Undr 65, w hav 1,1,1,3 Abov 65, w hav 17 0 s, 1,1,2. hr ar too many tis for our Wilcoxon and no way is th data normal. On thing is to xamin how far apart ar ths mans with a prmutation tst. Statistics Lowr CL Uppr CL Lowr CL Uppr CL Variabl LAUCH Man Man Man Std Dv Std Dv Std Dv Std Err ICIDES COOL 4-0.091 1.5 3.0912 0.5665 1 3.7285 0.5 ICIDES WARM 20-0.045 0.2 0.4448 0.3978 0.5231 0.7641 0.117 ICIDES Diff (1-2) 0.6065 1.3 1.9935 0.4722 0.6105 0.8641 0.3344 -sts Variabl Mthod Variancs DF t Valu Pr > t ICIDES Poold Equal 22 3.89 0.0008 ICIDES Sattrthwait Unqual 3.34 2.53 0.0769 Equality of Variancs 5
Variabl Mthod um DF Dn DF F Valu Pr > F ICIDES Foldd F 3 19 3.65 0.0622 6