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B.Kramer
IntroductiontoMinitab
Throughoutthesemester,youwillfinditnecessarytousespreadsheetsandstatistical
packagestohelpyouanalyzedataobtainedinthelab.Mostcommonly,youwilllikelyuse
MicrosoftExceltoperformnecessarycalculations.Ifyouneedarefresher,directionsfor
usingExceltohelpanalyzedataobtainedintheanalyticallabcanbefoundat
http://chemlab.truman.edu/CHEM222manual/pdf/spreadsheet.pdf.Asaspreadsheet,
Excelisveryusefulfordataorganizationandmanipulation.Whenyouneedtodoa
statisticalanalysis,youwillfindthatitisofteneasierandmoreappropriatetousesoftware
thatisdesignedforthatpurpose.TheprogramwewilluseinthiscourseisMinitab,a
statisticalsoftwarepackageavailableonanycampuscomputerorthroughTruman’s
virtualnetwork.WewilluseMinitabtohelpobtaindescriptivestatisticsandconfidence
intervals,performregressionanalysistocreatecalibrationcurvesandtohelpdisplayour
data.
AccessingMinitab:
Minitabisavailableonanycomputerrunningthecampusimage.ToaccessMinitabonthe
DellDuosinthelab(oryourpersonalcomputerconnectedintotheTrumannetwork),you
mustfirstlogintoTruman’svirtualnetwork.(Ifyouhavenotsetyourcomputerupto
accessTruman’svirtualnetwork,seehttps://secure.truman.edu/its‐s/viewclient/tolearn
howtoconnectbothonandoffcampus.)
OntheDellDuos:
1. OpentheVMWareViewclient(
)tolaunchthenetwork.
2. Ifitisn’talreadyentered,typeview.truman.eduintheboxlabeled“Connection
server”thenclickConnect.
3. EnteryourusernameandpasswordandchooseLogin.
4. ChoosetoDisplayFullScreenorinawindowasyoupreferfromthedropdown
menuandclickConnect.
5. Afterloggingin,openMinitab16fromtheProgramMenu.
Alternatively,youcanaccessthevirtualnetworkthroughanybrowserbygoingto
https://virtualdesktop.truman.edu/,choosingthe“VMwareHorizonViewHTMLAccess”
linkontherightandlogginginusingyourTrumanusernameandpassword.
BriefOverviewofMinitab
Minitabisapowerfulstatisticalsoftware
package.Wewillbeusingjustasmall
portionofthefeaturesoftheprogramin
thisclass.Ifyouareinterestedin
exploringfurther,detailedtutorialsare
availableat
http://case.truman.edu/resources/tutorials.asp ThemainwindowforMinitab(Figure1)
consistsoftwoimportantwindows–
Figure1. Minitabwindowforanewanalysis.
SessionandWorksheet.Youwillenter
dataintotheWorksheetwindowand,after
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performingstatisticalanalysis,resultswillbegivenintheSessionwindow(aswellasin
pop‐upwindows).
Obtainingdescriptivestatisticsandpresentingdata
Inthefollowingexample,youwilluseMinitabtofindthedescriptivestatisticsofthedata
obtainedinanexperimenttocalibrateavolumetricpipetandamicropipet(Table1). Table1.Calibrationdataobtainedforvolumetricpipetandmicropipet
5‐mLvolumetricpipet
Trial
TrueVol(mL)
1
5.2348
2
5.1303
3
4.9237
4
5.0754
5
5.1877
6
5.0226
7
5.0652
8
5.0671
9
5.0799
100‐Lmicropipet
Trial
TrueVol(mL)
1
0.0983
2
0.0986
3
0.0991
4
0.0995
5
0.0992
6
0.0994
7
0.0992
8
0.0993
9
0.0993
1. TypeanameforeachcolumninthegrayboxesdirectlyunderC1andC2.(For
example,onecouldread“5mL”andone“micro”.)
2. Nowenterthetruevolumes(determinedafterbuoyancyanddensitycorrectionin
Excel).Thesedatamaybeenteredbytypingdirectlyorbycopyingthe
correspondinginformationfromExcelandpastingitdirectlyintoMinitab.
3. Underthe“Stat”menu,choose“BasicStatistics”and“DisplayDescriptiveStatistics.”
4. Choosethevariable(s)youwanttoanalyzebyfirstclickingin“Variables”andthen
doubleclickingonthename(s)ofthedataset(s).
5. Clickon“Statistics”toseethetypesofresultsthatwillbedisplayed.Youmay
explorethesedifferentresults,butthemostusefulforourpurposeswillbethe
mean,standarddeviation,minimum,maximum,medianandfirstandthird
quartiles.Click“OK”whentheresultsyouwishtoseearechosen.
6. Ifallyouwanttoseearethedescriptivestatistics,thenclick“OK”again.Ifyouwish
todisplaythedatagraphically,clickon“Graphs.”Inthe“Graph”window,youmay
choosetoseeahistogramofyourdata(withorwithoutanormalcurve),an
individualvalueplotand/oraboxplot.Anyofthesewillgiveyouavisualideaofthe
variationinyourresults.Fornow,chooseallfouroptionssoyoucanseewhattype
ofresultseachshows.Click“OK.”
7. Now,click“OK”intheDisplayDescriptiveStatisticswindowtoseeyourresults.
8. Aseriesofpop‐upwindowswillopendisplayingeachgraph.Youcanclickoneach
componentofagraphtochangethedisplay.Youcanprinteachgraphorcopyand
pasteitintoadocument.
9. IntheSessionwindow,scrolluptothetoptoseealistofthedescriptivestatistics
youselectedforeachofyourvariables.
10. Youcanalsousetheprocedureabovetosimultaneouslyobservetheresultsofsimilar
measurementsfortwoormoredifferentcategoriesofdataononegraph.See
http://case.truman.edu/Documents/Minitab%20Introduction%20to%20Minitab.pdf
formoreinformation.
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Determiningaconfidenceinterval
Inordertodeterminetherangeofresultsinwhichwehaveaspecificprobabilityoffinding
thetruevaluegivenoursampledata,wewilluseMinitabtodetermineaconfidence
intervalforthe5mLpipetandthemicropipet.
1. EnteryourdataintotheWorksheetasbefore.
2. Fromthe“Stat”menu,select“BasicStatistics”andthen“1samplet.”
3. Inthepop‐upmenu,clickintheboxbelow“Samplesincolumns.”Thedataset(s)
youhaveenteredshouldthenappearinthewindowontheleft.
4. Doubleclickonthedatasetonwhichyouwishtoperformtheanalysis.
5. Select“Options.”Inthepop‐upwindow,enteraconfidenceinterval.Most
commonly,youwillenter95.0.Select“OK.”
6. Afterclicking“OK”inthe1‐sampletwindow,scrollbackuptofindyourresultsin
theSessionwindow.Youshouldseethenumberofsamples(N),theirmean,the
standarddeviation,theSE(standarderror)ofthemean(calculatedasthestandard
deviationdividedbythesquarerootofN)andtheintervalindicatingtherangeof
resultswithinwhichthetruevalueislikelytolie(atagivenconfidence)ifallofthe
errorinthedataisrandom.
Hypothesistesting
Often,youwillwanttocomparetheresultsyouhaveobtainedinlabtoa“true”valueorto
comparetheresultsobtainedbytwodifferentmethodsofanalysis.Todothis,wewilluse
Minitabtoperformhypothesistesting.(Seeyouranalyticalorintroductorystatisticsnotes
formoreinformation.)ForadetailedintroductiontousingMinitabforthisprocess,see
http://case.truman.edu/Documents/Minitab%20Hypothesis%20Testing.pdf
Comparingyourresultstoa“true”value:Aretheyequal?(H0: x   ;HA: x   )
1. EnteryourdataintotheWorksheetasbefore.
2. Fromthe“Stat”menu,select“BasicStatistics”andthen“1samplet.”
3. Inthepop‐upmenu,clickintheboxbelow“Samplesincolumns.”Thedataset(s)
youhaveenteredshouldthenappearinthewindowontheleft.
4. Doubleclickonthedatasetonwhichyouwishtoperformtheanalysis.
5. Makesurethebox“Performhypothesistest”ischecked.Enterthe“hypothesized
mean”–inthiscase,itwillbe5.00mLforthevolumetricpipet.
6. Select“Options.”Inthepop‐upwindow,enteraconfidenceinterval.Most
commonly,youwillenter95.0.Forthe“Alternative,”choose“notequal”inthiscase.
Select“OK.”
7. Afterclicking“OK”inthe1‐sampletwindow,scrollbackuptofindyourresultsin
theSessionwindow.Inadditiontotheresultsincludedintheconfidenceinterval
directionsabove,youwillalsoseeavalueof“T”and“P.”Youcanusetheseto
determinewhethertorejectorfailtorejectthenullhypothesis.
Fortheseresults,“T”isthecalculatedvalueofStudent’stforthegivendegreesof
freedom.“P”isthep‐valuethathelpsusdetermineifthenullhypothesisshouldbe
rejectedatthegivenconfidencelevel.Thep‐valuerepresentstheprobabilitythat,
underthegivenconditionsofdegreesoffreedomandstandarddeviation,avalueofthe
samplemean( x ) thisextremeormorewouldbefoundifthenullhypothesisweretrue.
Thesmallerthevalueofp,thelesslikelythatthiswillbepossible.Forourpurposes,if
wewanttomakethecomparisonata95%confidencelevel,wewill“rejectthenull”if
thevalueofpislessthan0.05(thisvalueisfoundas100–confidencelevel).
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B.Kramer
Forthevolumetricpipetdata,thep‐valuewasdeterminedtobe0.020(seeFigure2).In
thiscase,p<0.05.So,werejectthenullhypothesis(thatthemeanisequaltothe“true”
valueof5.00mL).Thisindicatesthat,atthe95%confidencelevel,thereisevidence
thatthereisastatisticallysignificantdifferencebetweenthemeanvolumedispensedby
thispipetandthemanufacturer’sclaimedvolumeof5.00mL.
One-Sample T: 5 mL
Test of mu = 5 vs > 5
Variable
5 mL
N
9
Mean
5.0874
StDev
0.0906
SE Mean
0.0302
95% Lower
Bound
5.0312
T
2.89
P
0.010
Figure2.Resultsobtainedfor1sample,2‐tailed t‐testfor5mLvolumetricpipetinMinitab.
Theexampleaboveonlylookedatwhetherthesampleaveragewasequaltothetruevalue,
notwhetheritwasgreaterorlessthanthetruevalue(a2‐tailedt‐test).Inordertomake
thismeasurement,wemustperforma1‐tailedt‐testasshownbelow.
Comparingyourresultstoa“true”value:Isthesamplebigger(orsmaller)?(H0: x   ;HA: x   )
1. RepeatSteps1‐5fromthepreviousdirections.
2. Select“Options.”Inthepop‐upwindow,enteraconfidenceinterval.Most
commonly,youwillenter95.0.Forthe“Alternative,”choose“greaterthan”inthis
case(i.e.,forourpurposes,wearetryingtoseeiftheaverageof5.0874mLis
greaterthan5.00mL).Select“OK.”
3. Afterclicking“OK”inthe1‐sampletwindow,scrollbackuptofindyourresultsin
theSessionwindow.Inadditiontotheresultsincludedintheconfidenceinterval
directionsabove,youwillalsoseeavalueof“T”and“P.”Youcanusetheseto
determinewhethertorejectorfailtorejectthenullhypothesis.
Forthevolumetricpipetdata,thep‐valueinthiscasewasdeterminedtobe0.010.
Again,herep<0.05.So,werejectthenullhypothesis(thatthemeanisequaltothe
“true”valueof5.00mL).Thisindicatesthat,atthe95%confidencelevel,thereis
evidencethatthemeanvalueisgreaterthanmanufacturer’sclaimedvolumeof5.00
mL.
Foreithercase,ifp>0.05,wewouldfailtorejectthenullhypothesisandhaveno
evidencethatthereisastatisticallysignificantdifferencebetweenourmeasuredvalue
andthemanufacturer’sclaimedvolumeof5.00mL.
Seehttp://case.truman.edu/Documents/Minitab%20Hypothesis%20Testing.pdffor
directionsforusingMinitabtocomparetheaveragesoftwosetsofdataortheresultsof
pairedanalyses.
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B.Kramer
Creatingascatterplot
Toanalyzeyourweighbottleandburetdata,youwillcreateascatterplot(x‐ygraph)in
Minitab.
1. EnteryourdataintotheWorksheetcreatingacolumnforeachvariable.
2. Fromthe“Graph”menu,select“Scatterplot.”
3. Inthepop‐upwindow,choosethetypeofscatterplotyouwouldliketouse.Ifyou
justwishtoobservethedata,choose“Simple.”Inthecaseoftheweighbottledata,
youmaychoose“WithConnectLine”aseachmeasurementwasmadeoneafterthe
nextandistime‐based.Foryourburetdata,choose“WithRegression”inorderto
alsodeterminealineofbestfitforyourdata.Ifyouwishtoplotmorethanoneline
onthesamegraph,chooseoneofthe“Groups”options.Afterchoosingthegraph
style,click“OK.”
4. Inthenextwindow,selectadatasetforthexandyvariablesbyfirstclickinginthe
columnandthendoubleclickingthevariable(orhighlightingitandchoosing
“Select”).
5. Youmayuse“Scale”and“Labels”tochangetheappearanceofyourgraph.These
mayalsobechangedafterthegraphisprepared.
6. Ifperformingaregressionanalysis(foryourburetdata,forexample),choose“Data
View.”Youcanaddaconnectinglineinthe“DataDisplay”windowifitis
appropriate(itisNOTappropriateforyourburetdata).Clickonthe“Regression”
tabandconfirmthat“Linear”ischosenandthat“FitIntercept”isselected.Choose
“OK”ineachwindowtoplotthedata.
7. Inthepop‐upwindow,clickonthetitleandaxeslabelstochangethemtosomething
reasonable.Byplacingyourmouseovertheregressionline,youwillseethe
equationfortheline.Onceagain,youmaycopyandpastetheplotorprintittoa
PDFtolaterincludeitinyourELN.
Performingsimplelinearregression
Toanalyzeyourburetdata,youwillperformaregressionanalysisofyourdata(similarto
findingalineofbestfit)inMinitab.
1. Firstcreateascatterplotasintheprevioussection.
2. Inthe“Stat”menu,choose“Regression”andthen“Regression.”
3. For“Response”chooseyouryvariable(yourdependentvariable).Foryourburet
data,thatshouldbethemass.For“Predictors”chooseyourxvariable(your
independentvariable).Foryourburetdata,thatshouldbethevolume.Hit“OK.”
4. ScrollbackupintheSessionwindowtoseeyourresults.Theregressionequation
willbegivenatthetopintheformat“y=b+mx”withbasthey‐interceptandmas
theslope.Ratherthan“x”and“y,”theactualnameofthevariableswillbegiven.
5. FormoreinformationabouttheremaininginformationpresentedintheSessionwindow,
see:
http://case.truman.edu/Documents/Minitab%20Simple%20Regression%20Analysis.pdf
6. Moreinformationwillbegiveninhowtousetheseresultsinclass.