MULTIPLE COMPARISONS AMONG 5 TREATMENTS.docx

1、MULTIPLE COMPARISONS AMONG 5 TREATMENTSwww.math.wustl.edu/sawyer/s475f03/onewaymc.lstMULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 1LETS VISUALIZE THE DATA BEFORE PROCEEDING 21:01 Monday, September 22, 2003Frequency15 + EEEEE EEEEE | DDDDD EEEEE | DDDDD EEEEE | DDDDD EEEEE | DDDDD DDDDD 10 + CC

2、CCC DDDDD | CCCCC DDDDD | CCCCC BBBBB CCCCC | CCCCC BBBBB CCCCC | CCCCC BBBBB CCCCC 5 + BBBBB BBBBB CCCCC EEEEE | BBBBB BBBBB BBBBB EEEEE | AAAAA AAAAA BBBBB EEEEE | AAAAA AAAAA AAAAA DDDDD | AAAAA AAAAA AAAAA AAAAA DDDDD EEEEE - 125 150 175 200 225 250 YY MidpointSymbol TREAT Symbol TREAT Symbol TR

3、EAT A Trt1 B Trt2 C Trt3 D Trt4 E Trt5MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 2THE TREATMENT MEANS ARE: 21:01 Monday, September 22, 2003Analysis Variable : YYTREAT N Obs N Mean Std Dev Minimum Maximum-Trt1 9 9 164.6666667 22.5000000 118.0000000 193.0000000Trt2 9 9 175.7777778 16.2617479 1

4、50.0000000 203.0000000Trt3 9 9 178.7777778 22.3482537 148.0000000 208.0000000Trt4 9 9 200.3333333 23.2540319 171.0000000 237.0000000Trt5 9 9 210.0000000 19.7040605 183.0000000 246.0000000-MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 3ARE ALL TREATMENT DIFFERENCES SIGNIFICANTLY DIFFERENT?MULTIP

5、LE COMPARISON TESTS: 21:01 Monday, September 22, 2003General Linear Models ProcedureClass Level InformationClass Levels ValuesTREAT 5 Trt1 Trt2 Trt3 Trt4 Trt5Number of observations in data set = 45MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 4ARE ALL TREATMENT DIFFERENCES SIGNIFICANTLY DIFFERE

6、NT?MULTIPLE COMPARISON TESTS: 21:01 Monday, September 22, 2003General Linear Models ProcedureDependent Variable: YY Sum of MeanSource DF Squares Square F Value Pr FModel 4 12538.5333 3134.6333 7.13 0.0002Error 40 17593.1111 439.8278Corrected Total 44 30131.6444 R-Square C.V. Root MSE YY Mean 0.41612

7、5 11.28070 20.9721 185.911Source DF Type I SS Mean Square F Value Pr FTREAT 4 12538.5333 3134.6333 7.13 0.0002Source DF Type III SS Mean Square F Value Pr FTREAT 4 12538.5333 3134.6333 7.13 0.0002MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 5ARE ALL TREATMENT DIFFERENCES SIGNIFICANTLY DIFFEREN

8、T?MULTIPLE COMPARISON TESTS: 21:01 Monday, September 22, 2003General Linear Models ProcedureT tests (LSD) for variable: YYNOTE: This test controls the type I comparisonwise error rate not the experimentwise error rate.Alpha= 0.05 df= 40 MSE= 439.8278Critical Value of T= 2.02Least Significant Differe

9、nce= 19.981Means with the same letter are not significantly different.T Grouping Mean N TREAT A 210.000 9 Trt5 A A 200.333 9 Trt4 B 178.778 9 Trt3 B B 175.778 9 Trt2 B B 164.667 9 Trt1MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 6ARE ALL TREATMENT DIFFERENCES SIGNIFICANTLY DIFFERENT?MULTIPLE C

10、OMPARISON TESTS: 21:01 Monday, September 22, 2003General Linear Models ProcedureDuncans Multiple Range Test for variable: YYNOTE: This test controls the type I comparisonwise error rate, not the experimentwise error rateAlpha= 0.05 df= 40 MSE= 439.8278Number of Means 2 3 4 5Critical Range 19.98 21.0

11、1 21.68 22.17Means with the same letter are not significantly different.Duncan Grouping Mean N TREAT A 210.000 9 Trt5 A A 200.333 9 Trt4 B 178.778 9 Trt3 B B 175.778 9 Trt2 B B 164.667 9 Trt1MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 7ARE ALL TREATMENT DIFFERENCES SIGNIFICANTLY DIFFERENT?MUL

12、TIPLE COMPARISON TESTS: 21:01 Monday, September 22, 2003General Linear Models ProcedureStudent-Newman-Keuls test for variable: YYNOTE: This test controls the type I experimentwise error rate under the complete null hypothesis but not under partial null hypotheses.Alpha= 0.05 df= 40 MSE= 439.8278Numb

13、er of Means 2 3 4 5Critical Range 19.981263 24.062537 26.499514 28.236284Means with the same letter are not significantly different.SNK Grouping Mean N TREAT A 210.000 9 Trt5 A A 200.333 9 Trt4 B 178.778 9 Trt3 B B 175.778 9 Trt2 B B 164.667 9 Trt1MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 8

14、ARE ALL TREATMENT DIFFERENCES SIGNIFICANTLY DIFFERENT?MULTIPLE COMPARISON TESTS: 21:01 Monday, September 22, 2003General Linear Models ProcedureTukeys Studentized Range (HSD) Test for variable: YYNOTE: This test controls the type I experimentwise error rate, but generally has a higher type II error

15、rate than REGWQ.Alpha= 0.05 df= 40 MSE= 439.8278Critical Value of Studentized Range= 4.039Minimum Significant Difference= 28.236Means with the same letter are not significantly different.Tukey Grouping Mean N TREAT A 210.000 9 Trt5 A B A 200.333 9 Trt4 B B C 178.778 9 Trt3 B C B C 175.778 9 Trt2 C C

16、 164.667 9 Trt1MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 9ARE ALL TREATMENT DIFFERENCES SIGNIFICANTLY DIFFERENT?MULTIPLE COMPARISON TESTS: 21:01 Monday, September 22, 2003General Linear Models ProcedureScheffes test for variable: YYNOTE: This test controls the type I experimentwise error ra

17、te but generally has a higher type II error rate than REGWF for all pairwise comparisonsAlpha= 0.05 df= 40 MSE= 439.8278Critical Value of F= 2.60597Minimum Significant Difference= 31.919Means with the same letter are not significantly different.Scheffe Grouping Mean N TREAT A 210.000 9 Trt5 A B A 20

18、0.333 9 Trt4 B A B A C 178.778 9 Trt3 B C B C 175.778 9 Trt2 C C 164.667 9 Trt1MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 10ARE ALL TREATMENT DIFFERENCES SIGNIFICANTLY DIFFERENT?MULTIPLE COMPARISON TESTS: 21:01 Monday, September 22, 2003General Linear Models ProcedureT tests (LSD) for variab

19、le: YYNOTE: This test controls the type I comparisonwise error rate not the experimentwise error rate.Alpha= 0.005 df= 40 MSE= 439.8278Critical Value of T= 2.97Least Significant Difference= 29.374Means with the same letter are not significantly different.T Grouping Mean N TREAT A 210.000 9 Trt5 A B

20、A 200.333 9 Trt4 B B C 178.778 9 Trt3 B C B C 175.778 9 Trt2 C C 164.667 9 Trt1MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 11ARE ALL TREATMENT DIFFERENCES SIGNIFICANTLY DIFFERENT?MULTIPLE COMPARISON TESTS: 21:01 Monday, September 22, 2003General Linear Models ProcedureDependent Variable: YY C

21、ontrast DF Contrast SS Mean Square F Value Pr FC1 with av of C2 C3 1 954.24074 954.24074 2.17 0.1486C4 with av of C2 C3 1 3189.35185 3189.35185 7.25 0.0103C5 with av C2 C3 C4 1 4231.25926 4231.25926 9.62 0.0035MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 12PLOT OF RESIDUALS 21:01 Monday, Septe

22、mber 22, 2003 Plot of RESID*TREAT. Symbol is value of TRTSYM. RESID | | 40 + | 4 5 | | 1 2 3 | 1 3 20 + | 1 3 5 | 2 5 | 2 4 5 | 1 2 0 + 1 3 4 5 | 1 3 4 | 2 | 4 5 | 1 2 4 -20 + 3 4 5 | 2 3 | 4 5 | 3 | -40 + | | 1 | | -60 + | -+-+-+-+-+- Trt1 Trt2 Trt3 Trt4 Trt5 TREATNOTE: 6 obs hidden.MULTIPLE COMPAR

23、ISONS AMONG 5 TREATMENTS - YOURNAME 13PROC UNIVARIATE: Testing normality 21:01 Monday, September 22, 2003LOOK FOR W STATISTICUnivariate ProcedureVariable=RESID Moments N 45 Sum Wgts 45 Mean 0 Sum 0 Std Dev 19.99609 Variance 399.8434 Skewness 0.028618 Kurtosis -0.49279 USS 17593.11 CSS 17593.11 CV .

24、Std Mean 2.98084 T:Mean=0 0 Pr|T| 1.0000 Num = 0 45 Num 0 22 M(Sign) -0.5 Pr=|M| 1.0000 Sgn Rank -8.5 Pr=|S| 0.9248 W:Normal 0.975412 PrW 0.5969 Quantiles(Def=5) 100% Max 36.66667 99% 36.66667 75% Q3 14.22222 95% 36 50% Med -0.77778 90% 28.33333 25% Q1 -14.3333 10% -25.7778 0% Min -46.6667 5% -29.33

25、33 1% -46.6667 Range 83.33333 Q3-Q1 28.55556 Mode -25.7778 Extremes Lowest Obs Highest Obs -46.6667( 1) 28.33333( 9) -30.7778( 19) 29.22222( 27) -29.3333( 28) 36( 45) -27( 37) 36.66667( 35) -25.7778( 20) 36.66667( 36)MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 14PROC UNIVARIATE: Testing norma

26、lity 21:01 Monday, September 22, 2003LOOK FOR W STATISTICUnivariate ProcedureVariable=RESID Stem Leaf # Boxplot 3 677 3 | 3 | 2 5789 4 | 2 4 1 | 1 5 1 | 1 03444 5 +-+ 0 7789 4 | | 0 0133 4 | + | -0 44311 5 *-* -0 86 2 | | -1 43320 5 +-+ -1 9865 4 | -2 2 1 | -2 9766 4 | -3 1 1 | -3 | -4 | -4 7 1 | -+-+-+-+ Multiply Stem.Leaf by 10*+1 Normal Probability Plot 37.5+ * *+ | + | *+ | *+ | +*+ | * | * | +* | * | +* | * | * | +* | *+* | *+ | + | + -47.5+* +-+-+-+-+-+-+-+-+-+-+ -2 -1 0 +1 +2