MULTIPLE COMPARISONS AMONG 5 TREATMENTS.docx

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MULTIPLE COMPARISONS AMONG 5 TREATMENTS.docx

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MULTIPLE COMPARISONS AMONG 5 TREATMENTS.docx

MULTIPLECOMPARISONSAMONG5TREATMENTS

www.math.wustl.edu/~sawyer/s475f03/onewaymc.lst

MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME1

LET'SVISUALIZETHEDATABEFOREPROCEEDING

21:

01Monday,September22,2003

Frequency

15+EEEEEEEEEE

|DDDDDEEEEE

|DDDDDDDDDD

10+CCCCCDDDDD

|CCCCCDDDDD

|CCCCCBBBBBCCCCC

5+BBBBBBBBBBCCCCCEEEEE

|BBBBBBBBBBBBBBBEEEEE

|AAAAAAAAAABBBBBEEEEE

|AAAAAAAAAAAAAAADDDDD

|AAAAAAAAAAAAAAAAAAAADDDDDEEEEE

------------------------------------------------------------------

125150175200225250

YYMidpoint

SymbolTREATSymbolTREATSymbolTREAT

ATrt1BTrt2CTrt3

DTrt4ETrt5

MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME2

THETREATMENTMEANSARE:

21:

01Monday,September22,2003

AnalysisVariable:

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:

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:

NOTE:

ThistestcontrolsthetypeIcomparisonwiseerrorratenotthe

experimentwiseerrorrate.

Alpha=0.05df=40MSE=439.8278

CriticalValueofT=2.02

LeastSignificantDifference=19.981

Meanswiththesameletterarenotsignificantlydifferent.

TGroupingMeanNTREAT

A210.0009Trt5

A200.3339Trt4

B178.7789Trt3

B175.7789Trt2

B164.6679Trt1

MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME6

AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?

MULTIPLECOMPARISONTESTS:

21:

01Monday,September22,2003

GeneralLinearModelsProcedure

Duncan'sMultipleRangeTestforvariable:

NOTE:

ThistestcontrolsthetypeIcomparisonwiseerrorrate,notthe

experimentwiseerrorrate

Alpha=0.05df=40MSE=439.8278

NumberofMeans2345

CriticalRange19.9821.0121.6822.17

Meanswiththesameletterarenotsignificantlydifferent.

DuncanGroupingMeanNTREAT

A210.0009Trt5

A200.3339Trt4

B178.7789Trt3

B175.7789Trt2

B164.6679Trt1

MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME7

AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?

MULTIPLECOMPARISONTESTS:

21:

01Monday,September22,2003

GeneralLinearModelsProcedure

Student-Newman-Keulstestforvariable:

NOTE:

ThistestcontrolsthetypeIexperimentwiseerrorrateunderthe

completenullhypothesisbutnotunderpartialnullhypotheses.

Alpha=0.05df=40MSE=439.8278

NumberofMeans2345

CriticalRange19.98126324.06253726.49951428.236284

Meanswiththesameletterarenotsignificantlydifferent.

SNKGroupingMeanNTREAT

A210.0009Trt5

A200.3339Trt4

B178.7789Trt3

B175.7789Trt2

B164.6679Trt1

MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME8

AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?

MULTIPLECOMPARISONTESTS:

21:

01Monday,September22,2003

GeneralLinearModelsProcedure

Tukey'sStudentizedRange（HSD）Testforvariable:

NOTE:

ThistestcontrolsthetypeIexperimentwiseerrorrate,but

generallyhasahighertypeIIerrorratethanREGWQ.

Alpha=0.05df=40MSE=439.8278

CriticalValueofStudentizedRange=4.039

MinimumSignificantDifference=28.236

Meanswiththesameletterarenotsignificantlydifferent.

TukeyGroupingMeanNTREAT

A210.0009Trt5

BA200.3339Trt4

BC178.7789Trt3

BC175.7789Trt2

C164.6679Trt1

MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME9

AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?

MULTIPLECOMPARISONTESTS:

21:

01Monday,September22,2003

GeneralLinearModelsProcedure

Scheffe'stestforvariable:

NOTE:

ThistestcontrolsthetypeIexperimentwiseerrorratebut

generallyhasahighertypeIIerrorratethanREGWFforall

pairwisecomparisons

Alpha=0.05df=40MSE=439.8278

CriticalValueofF=2.60597

MinimumSignificantDifference=31.919

Meanswiththesameletterarenotsignificantlydifferent.

ScheffeGroupingMeanNTREAT

A210.0009Trt5

BA200.3339Trt4

BAC178.7789Trt3

BC175.7789Trt2

C164.6679Trt1

MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME10

AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?

MULTIPLECOMPARISONTESTS:

21:

01Monday,September22,2003

GeneralLinearModelsProcedure

Ttests（LSD）forvariable:

NOTE:

ThistestcontrolsthetypeIcomparisonwiseerrorratenotthe

experimentwiseerrorrate.

Alpha=0.005df=40MSE=439.8278

CriticalValueofT=2.97

LeastSignificantDifference=29.374

Meanswiththesameletterarenotsignificantlydifferent.

TGroupingMeanNTREAT

A210.0009Trt5

BA200.3339Trt4

BC178.7789Trt3

BC175.7789Trt2

C164.6679Trt1

MULTIPLECOMPARISONSAMONG5TREATMENTS-YOURNAME11

AREALLTREATMENTDIFFERENCESSIGNIFICANTLYDIFFERENT?

MULTIPLECOMPARISONTESTS:

21:

01Monday,September22,2003

GeneralLinearModelsProcedure

DependentVariable:

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

|45

|124

-20+345

|23

|45

-40+

-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

Mean=00Pr>|T|1.0000

Num^=045Num>022

M（Sign）-0.5Pr>=|M|1.0000

SgnRank-8.5Pr>=|S|0.9248

Normal0.975412Pr

Quantiles（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|

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

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