MULTIPLE COMPARISONS AMONG 5 TREATMENTS.docx
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MULTIPLECOMPARISONSAMONG5TREATMENTS
www.math.wustl.edu/~sawyer/s475f03/onewaymc.lst
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME1
LET'SVISUALIZETHEDATABEFOREPROCEEDING
21:
01Monday,September22,2003
Frequency
15+EEEEEEEEEE
|DDDDDEEEEE
|DDDDDEEEEE
|DDDDDEEEEE
|DDDDDDDDDD
10+CCCCCDDDDD
|CCCCCDDDDD
|CCCCCBBBBBCCCCC
|CCCCCBBBBBCCCCC
|CCCCCBBBBBCCCCC
5+BBBBBBBBBBCCCCCEEEEE
|BBBBBBBBBBBBBBBEEEEE
|AAAAAAAAAABBBBBEEEEE
|AAAAAAAAAAAAAAADDDDD
|AAAAAAAAAAAAAAAAAAAADDDDDEEEEE
------------------------------------------------------------------
125150175200225250
YYMidpoint
SymbolTREATSymbolTREATSymbolTREAT
ATrt1BTrt2CTrt3
DTrt4ETrt5
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME2
THETREATMENTMEANSARE:
21:
01Monday,September22,2003
AnalysisVariable:
YY
TREATNObsNMeanStdDevMinimumMaximum
---------------------------------------------------------------------------
Trt199164.666666722.5000000118.0000000193.0000000
Trt299175.777777816.2617479150.0000000203.0000000
Trt399178.777777822.3482537148.0000000208.0000000
Trt499200.333333323.2540319171.0000000237.0000000
Trt599210.000000019.7040605183.0000000246.0000000
---------------------------------------------------------------------------
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME3
AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?
MULTIPLECOMPARISONTESTS:
21:
01Monday,September22,2003
GeneralLinearModelsProcedure
ClassLevelInformation
ClassLevelsValues
TREAT5Trt1Trt2Trt3Trt4Trt5
Numberofobservationsindataset=45
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME4
AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?
MULTIPLECOMPARISONTESTS:
21:
01Monday,September22,2003
GeneralLinearModelsProcedure
DependentVariable:
YY
SumofMean
SourceDFSquaresSquareFValuePr>F
Model412538.53333134.63337.130.0002
Error4017593.1111439.8278
CorrectedTotal4430131.6444
R-SquareC.V.RootMSEYYMean
0.41612511.2807020.9721185.911
SourceDFTypeISSMeanSquareFValuePr>F
TREAT412538.53333134.63337.130.0002
SourceDFTypeIIISSMeanSquareFValuePr>F
TREAT412538.53333134.63337.130.0002
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME5
AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?
MULTIPLECOMPARISONTESTS:
21:
01Monday,September22,2003
GeneralLinearModelsProcedure
Ttests(LSD)forvariable:
YY
NOTE:
ThistestcontrolsthetypeIcomparisonwiseerrorratenotthe
experimentwiseerrorrate.
Alpha=0.05df=40MSE=439.8278
CriticalValueofT=2.02
LeastSignificantDifference=19.981
Meanswiththesameletterarenotsignificantlydifferent.
TGroupingMeanNTREAT
A210.0009Trt5
A
A200.3339Trt4
B178.7789Trt3
B
B175.7789Trt2
B
B164.6679Trt1
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME6
AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?
MULTIPLECOMPARISONTESTS:
21:
01Monday,September22,2003
GeneralLinearModelsProcedure
Duncan'sMultipleRangeTestforvariable:
YY
NOTE:
ThistestcontrolsthetypeIcomparisonwiseerrorrate,notthe
experimentwiseerrorrate
Alpha=0.05df=40MSE=439.8278
NumberofMeans2345
CriticalRange19.9821.0121.6822.17
Meanswiththesameletterarenotsignificantlydifferent.
DuncanGroupingMeanNTREAT
A210.0009Trt5
A
A200.3339Trt4
B178.7789Trt3
B
B175.7789Trt2
B
B164.6679Trt1
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME7
AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?
MULTIPLECOMPARISONTESTS:
21:
01Monday,September22,2003
GeneralLinearModelsProcedure
Student-Newman-Keulstestforvariable:
YY
NOTE:
ThistestcontrolsthetypeIexperimentwiseerrorrateunderthe
completenullhypothesisbutnotunderpartialnullhypotheses.
Alpha=0.05df=40MSE=439.8278
NumberofMeans2345
CriticalRange19.98126324.06253726.49951428.236284
Meanswiththesameletterarenotsignificantlydifferent.
SNKGroupingMeanNTREAT
A210.0009Trt5
A
A200.3339Trt4
B178.7789Trt3
B
B175.7789Trt2
B
B164.6679Trt1
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME8
AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?
MULTIPLECOMPARISONTESTS:
21:
01Monday,September22,2003
GeneralLinearModelsProcedure
Tukey'sStudentizedRange(HSD)Testforvariable:
YY
NOTE:
ThistestcontrolsthetypeIexperimentwiseerrorrate,but
generallyhasahighertypeIIerrorratethanREGWQ.
Alpha=0.05df=40MSE=439.8278
CriticalValueofStudentizedRange=4.039
MinimumSignificantDifference=28.236
Meanswiththesameletterarenotsignificantlydifferent.
TukeyGroupingMeanNTREAT
A210.0009Trt5
A
BA200.3339Trt4
B
BC178.7789Trt3
BC
BC175.7789Trt2
C
C164.6679Trt1
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME9
AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?
MULTIPLECOMPARISONTESTS:
21:
01Monday,September22,2003
GeneralLinearModelsProcedure
Scheffe'stestforvariable:
YY
NOTE:
ThistestcontrolsthetypeIexperimentwiseerrorratebut
generallyhasahighertypeIIerrorratethanREGWFforall
pairwisecomparisons
Alpha=0.05df=40MSE=439.8278
CriticalValueofF=2.60597
MinimumSignificantDifference=31.919
Meanswiththesameletterarenotsignificantlydifferent.
ScheffeGroupingMeanNTREAT
A210.0009Trt5
A
BA200.3339Trt4
BA
BAC178.7789Trt3
BC
BC175.7789Trt2
C
C164.6679Trt1
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME10
AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?
MULTIPLECOMPARISONTESTS:
21:
01Monday,September22,2003
GeneralLinearModelsProcedure
Ttests(LSD)forvariable:
YY
NOTE:
ThistestcontrolsthetypeIcomparisonwiseerrorratenotthe
experimentwiseerrorrate.
Alpha=0.005df=40MSE=439.8278
CriticalValueofT=2.97
LeastSignificantDifference=29.374
Meanswiththesameletterarenotsignificantlydifferent.
TGroupingMeanNTREAT
A210.0009Trt5
A
BA200.3339Trt4
B
BC178.7789Trt3
BC
BC175.7789Trt2
C
C164.6679Trt1
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME11
AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?
MULTIPLECOMPARISONTESTS:
21:
01Monday,September22,2003
GeneralLinearModelsProcedure
DependentVariable:
YY
ContrastDFContrastSSMeanSquareFValuePr>F
C1withavofC2C31954.24074954.240742.170.1486
C4withavofC2C313189.351853189.351857.250.0103
C5withavC2C3C414231.259264231.259269.620.0035
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME12
PLOTOFRESIDUALS21:
01Monday,September22,2003
PlotofRESID*TREAT.SymbolisvalueofTRTSYM.
RESID|
|
40+
|45
|
|123
|13
20+
|135
|25
|245
|12
0+1345
|134
|2
|45
|124
-20+345
|23
|45
|3
|
-40+
|
|1
|
|
-60+
|
---+------------+------------+------------+------------+--
Trt1Trt2Trt3Trt4Trt5
TREAT
NOTE:
6obshidden.
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME13
PROCUNIVARIATE:
Testingnormality21:
01Monday,September22,2003
LOOKFORWSTATISTIC
UnivariateProcedure
Variable=RESID
Moments
N45SumWgts45
Mean0Sum0
StdDev19.99609Variance399.8434
Skewness0.028618Kurtosis-0.49279
USS17593.11CSS17593.11
CV.StdMean2.98084
T:
Mean=00Pr>|T|1.0000
Num^=045Num>022
M(Sign)-0.5Pr>=|M|1.0000
SgnRank-8.5Pr>=|S|0.9248
W:
Normal0.975412PrQuantiles(Def=5)
100%Max36.6666799%36.66667
75%Q314.2222295%36
50%Med-0.7777890%28.33333
25%Q1-14.333310%-25.7778
0%Min-46.66675%-29.3333
1%-46.6667
Range83.33333
Q3-Q128.55556
Mode-25.7778
Extremes
LowestObsHighestObs
-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)
MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME14
PROCUNIVARIATE:
Testingnormality21:
01Monday,September22,2003
LOOKFORWSTATISTIC
UnivariateProcedure
Variable=RESID
StemLeaf#Boxplot
36773|
3|
257894|
241|
151|
1034445+-----+
077894||
001334|+|
-0443115*-----*
-0862||
-1433205+-----+
-198654|
-221|
-297664|
-311|
-3|
-4|
-471|
----+----+----+----+
MultiplyStem.Leafby10**+1
NormalProbabilityPlot
37.5+**++
|++
|****+
|*++
|+*+
|****
|***
|+**
|***
|+**
|***
|***
|+*
|*+**
|*++
|+++
|++
-47.5++++*
+----+----+----+----+----+----+----+----+----+----+
-2-10+1+2