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A StepbyStep Guide to Analysis and Interpretotion
Brian C. Cronk
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Notice SPSSis a registeredtrademarkof SPSS,Inc. Screenimages@ by SPSS,Inc. and MicrosoftCorporation.Usedwith permission. This book is not approvedor sponsoredby SPSS.
"PyrczakPublishing"is an imprintof FredPyrczak,Publisher, A CaliforniaCorporation. Althoughtheauthorandpublisherhavemadeeveryeffortto ensuretheaccuracyand for no responsibility completeness of informationcontainedin thisbook,we assume herein.Any slightsof people, errors,inaccuracies, omissions, or anyinconsistency places,or organizations areunintentional. ProjectDirector:MonicaLopez. ConsultingEditors:GeorgeBumrss,JoseL. Galvan,MatthewGiblin,DeborahM. Oh, JackPetit.andRichardRasor. providedby CherylAlcorn,RandallR. Bruce,KarenM. Disner, Editdrialassistance BrendaKoplin,EricaSimmons,andSharonYoung. Coverdesignby RobertKibler andLarryNichols. Printedin theUnitedStates of Americaby Malloy,Inc. All rights Publisher. Copyright@2008,2006,2004,2002,1999 by FredPyrczak, in anyform or by any or transmitted reserved. No portionof thisbookmaybe reproduced meanswithouttheprior writtenpermission of thepublisher. r s B N l 8 8 4 s8 5 79 5
Tableof Contents Introduction to theFifth Edition
v
What'sNew? Audience Organization SPSSVersions Availabilityof SPSS Conventions Screenshots PracticeExercises Acknowledgments'/ ChapterI Ll t.2 1.3 1.4 1.5 1.6 1.7 Chapter2
2.1 ') ') Chapter3
3.1 3.2 3.3 3.4 3.5 Chapter4 4.1 4.2 4.3 4.4 4.5 4.6 Chapter5
5.1 5.2 5.3 5.4
v v v vi vi vi vi vii vii
GettingStarted
I
StartingSPSS EnteringData DefiningVariables LoadingandSavingDataFiles RunningYour FirstAnalysis ExaminingandPrintingOutputFiles Modi$ing DataFiles
I I 2 5 6 8
EnteringandModifyingData VariablesandDataRepresentation Transformation andSelection of Data
ll t2
Descriptive Statistics
l7
Frequency Distributions andpercentileRanksfor a singlevariable Frequency Distributions andpercentileRanksfor Multille variables Measuresof CentralTendencyandMeasuresof Dispersion for a SingleGroup Measures of CentralTendency andMeasures of Dispersion for MultipleGroups StandardScores
t7 20
ll
2l 24 )7
GraphingData
29
GraphingBasics TheNew SPSSChartBuilder Bar Charts,Pie Charts,andHistograms Scatterplots AdvancedBarCharts EditingSPSSGraphs
29 29 3l 33 36 39
Predictionand Association
4l
PearsonCorrelation Coeffi cient SpearmanCorrelation Coeffi cient Simple Linear Regression Multiple Linear Regression
4l 43 45 49
u,
Chapter6
Parametric InferentialStatistics
53
Reviewof BasicHypothesis Testing SingleSample t Test IndependentSamples I Test PairedSamples t Test OneWayANOVA FactorialANOVA RepeatedMeasures ANOVA MixedDesign ANOVA Analysisof Covariance MultivariateAnalysisof Variance(MANOVA)
53 )) 58 6l 65 69 72 75 79 8l
Chapter7
Nonparametric InferentialStatistics
85
7.1 7.2 7.3 7.4 7.5 7.6
ChiSquare Goodness of Fit ChiSquareTestof Independence MannWhitney UTest WilcoxonTest KruskalWallis,F/Test FriedmanTest
85 87 .90 93 95 97
6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10
Chapter8 8.1 8.2 8.3 8.4
TestConstruction
99
ItemTotalAnalysis Cronbach's Alpha TestRetestReliability CriterionRelated Validiw
99 100 l0l t02
AppendixA
Effect Size
103
AppendixB
PracticeExerciseDataSets
r 09
PracticeDataSet I PracticeDataSet2 PracticeDataSet3
109 ll0 ll0
AppendixC
Glossary
lt3
AppendixD
SampleDataFilesUsedin Text
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COINS.sav GRADES.sav HEIGHT.sav QUESTIONS.sav RACE.sav SAMPLE.sav SAT.sav OtherFiles
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AppendixE
Informationfor Usersof EarlierVersionsof SPSS
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AppendixF
GraphingDatawith SPSS13.0and 14.0
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ChapterI
GettingStarted Section1.1 StartingSPSS
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Startup proceduresfor SPSS will differ slightly, dependingon the exact configurationof the machine on which it is installed.On most computers,you can start SPSS by clicking on Start, then clicking on Programs, then on SPSS. On many installations,there will be an SPSSicon on the desktopthat you can doubleclick to start the program. When SPSS is started,you may be presentedwith the dialog box to the left, depending on the optionsyour systemadministratorselected for your version of the program. If you have the dialog box, click Type in data and OK, which will presenta blank data window.' If you were not presentedwith the dialog box to the left, SPSSshould open automatically with a blank data window. The data window and the output window provide the basic interface for SPSS. A blank data window is shownbelow.
Section1.2 EnteringData One of the keys to success with SPSSis knowing how it stores .:g H*ng:fH"gxr__}rry".** r! *9*_r1_*9lt and uses your data. To illustrate the rtlxlel&l *'.1 rtl ale lgj'Slfil Hl*lml sl el*l I basics of data entry with SPSS,we will useExample1.2.1. Example 1.2.1 A surveywas given to several students from four different classes (Tues/Thurs momings, Tues/Thurs afternoons, Mon/Wed/Fri mornings, and afternoons). Mon/Wed/Fri The students were asked ' Items that appearin the glossaryare presentedin bold. Italics areusedto indicatemenu items.
ChapterI GeningStarted
whether or not they were "morning people" and whether or not they worked. This survey also asked for their final grade in the class (100% being the highest gade possible).The responsesheetsfrom two studentsarepresentedbelow:
Response SheetI ID: Dayof class: Classtime: Are you a morningperson? Finalgradein class: Do youwork outsideschool?
4593 MWF Morning Yes
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Our goal is to enterthe data from the two studentsinto SPSSfor use in future analyses. The first stepis to determinethe variablesthatneedto be entered.Any informaExample tion that can vary amongparticipantsis a variablethat needsto be considered. 1.2.2liststhevariables we will use. Example1.2.2 ID Dayof class Classtime Morningperson Finalgrade Whetheror not the studentworksoutsideschool particivariablesandrowsrepresent In the SPSSdata window,columnsrepresent (variables) rows and two pants.Therefore,we will be creatinga datafile with six columns (students/participants). Section1.3 Defining Variables Beforewe can enterany data,we must first entersomebasicinformationabout eachvariableinto SPSS.For instance, variablesmustfirst be givennamesthat: o beginwith a letter; o do not containa space.
Chapter I Getting Started
Thus, the variable name "Q7" is acceptable,while the variable name "7Q" is not. Similarly, the variable name "PRE_TEST" is acceptable, but the variable name "PRE TEST" is not. Capitalizationdoes not matter, but variable namesare capitalizedin this text to make it clear when we are referring to a variable name, even if the variable name is not necessarilycapitalizedin screenshots. To define a variable.click on the Variable View tab at thebottomofthema inscre e n .Th is wills h o wy o u t h e V a ri@ able View window. To return to the Data View window. click on the Data View tab. Fb m u9* o*.*Trqll
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From the Variable View screen,SPSSallows you to createand edit all of the variables in your data file. Each column representssome property of a variable, and each row representsa variable. All variablesmust be given a name. To do that, click on the first empty cell in the Name column and type a valid SPSSvariable name. The program will then fill in default valuesfor most of the other properties. One usefulfunctionof SPSSis the ability to definevariableand value labels.Variable labels allow you to associatea descriptionwith each variable.Thesedescriptionscan describethe variablesthemselvesor the valuesof the variables. Value labelsallow you to associatea descriptionwith eachvalue of a variable.For example,for most procedures,SPSSrequiresnumerical values.Thus, for data such as the day of the class (i.e., Mon/Wed/Fri and Tues/Thurs),we need to first code the values as numbers.We can assignthe number I to Mon/Wed/Friand the number2to Tues/Thurs. To help us keep track of the numberswe have assignedto the values,we use value labels. To assignvalue labels,click in the cell you want to assignvaluesto in the Values column. This will bring up a small gray button (seeanow, below at left). Click on that button to bring up the Value Labelsdialog box. When you enter a iv*rl** v& 12 Jil value label, you must click L.b.f ll6rhl s*l !!+  Add after eachentry. This will J::::*.,.Tl
mOVe the value and itS associated label into the bottom section of
the window. When all labels have been added, click OK to return to the Variable View window.
ChapterI Gening Starred
In additionto namingand labelingthe variable,you havethe option of definingthe variabletype. To do so, simply click on the Type, Width,or Decimals columns in the Variable View window. The default value is a numeric field that is eight digits wide with two decimalplacesdisplayed.If your dataare more than eight digits to the left of the decimal place,they will be displayedin scientificnotation(e.g.,the number2,000,000,000 will be displayedas 2.00E+09).'SPSSmaintainsaccuracybeyondtwo decimalplaces,but all output will be roundedto two decimal placesunlessotherwiseindicatedin the Decimals column. In our example,we will be usingnumericvariableswith all of the defaultvalues. Practice Exercise Createa data file for the six variablesand two samplestudentspresentedin Example 1.2.1.Name your variables:ID, DAY, TIME, MORNING, GRADE, and WORK. You should code DAY as I : Mon/Wed/Fri,2 = Tues/Thurs.Code TIME as I : morning, 2 : afternoon.CodeMORNING as 0 = No, I : Yes. Code WORK as 0: No, I : PartTime,2 : FullTime. Be sure you enter value labels for the different variables.Note that because value labelsare not appropriatefor ID and GRADE, theseare not coded.When done,your Variable View window should look like the screenshotbelow: J rtrr,d
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Click on the Data View tab to open the dataentryscreen.Enter data horizontally, beginningwith the first student'sID number.Enter the code for eachvariable in the appropriate column; to enterthe GRADE variablevalue,enterthe student'sclassgrade.
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Chapter I Getting Started
Thepreviousdata window canbe changedto look insteadlike the screenshot bel*.bv clickingon the ValueLabelsicon(seeanow).In this case,the cellsdisplayvalue labelsratherthanthe corresponding codes.If datais enteredin this mode,it is not necessaryto entercodes,asclickingthebuttonwhichappearsin eachcell asthe cell is selected will presenta dropdownlist of thepredefined lablis. You may useeithermethod,according to yourpreference.
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Instead of clicking the Value Labels icon, you may optionallytogglebetweenviews by clicking valueLaiels under the Viewmenu.
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Section1.4 Loading and SavingData Files Onceyou haveenteredyour data,you will need to saveit with a uniquenamefor later useso that you canretrieveit whennecessary. Loadingand savingSpSSdatafiles worksin the sameway as most Windowsbased software.Underthe File menu, there are Open, Save, and Save As commands.SPSSdata files have a .,.sav" extension. which is addedby defaultto the end of the filename. ThistellsWindowsthatthefile is anSpSSdatafile.
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Save Your Data When you save your data file (by clicking File, then clicking Save or SaveAs to specify a unique name),pay specialattentionto where you saveit. trrtist systemsdefault to the.location.You will probably want to saveyour data on a floppy disk, cDR, or removableUSB drive so that you can taie the file withvou.
Load YourData When you load your data (by clicking File, then clicking Open, thenData, or by clicking the open file folder icon), you get a similar window. This window lists all files with the ".sav" extension.If you have trouble locating your saved file, make sure you are D{l lriifqffi looking in the right directory.
ChapterI GeningStarted
Practice Exercise To be surethat you havemastered saving and openingdata files, nameyour sample datafile "SAMPLE" andsaveit to a removable
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storagemedium. Once it is saved,SPSSwill display the name of the file at the top of the data window. It is wise to save your work frequently,in caseof computer crashes.Note that filenamesmay be upper or lowercase.In this text, uppercaseis usedfor clarity. After you have saved your data, exit SPSS (by clicking File, then Exit). Restart SPSSand load your databy selectingthe "SAMPLE.sav"file you just created.
Section1.5 RunningYour First Analysis Any time you open a data window, you can mn any of the analysesavailable.To get started,we will calculatethe students'averagegrade.(With only two students,you can easily checkyour answerby hand,but imaginea data file with 10,000studentrecords.) The majority of the available statistical tests are under the Analyze menu. This menu displaysall the optionsavailablefor your versionof the SPSSprogram (the menusin this book were createdwith SPSSStudentVersion 15.0).Otherversionsmay haveslightly different setsof options.
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To calculatea mean (average),we are asking the computerto summarizeour data set. Therefore,we run the commandby clicking Analyze, then Descriptive Statistics,then Descriptives. This brings up the Descriptives dialog box. Note that the left side of the box containsa OAY list of all the variablesin our data file. On the right .Sr ql is an area labeled Variable(s), where we can 3s,l specifythe variableswe would like to use in this particularanalysis. A*r*.. I f 9mloddrov*p*vri*lq
Chapter I Getting Started
l:rt.Ij We want to compute the mean for the variable called GRADE. Thus, we need to select the variable name in the left window (by clicking ;F*  on it). To transfer it to the right window, click on t:g.J the right arrow between the two windows. The !tJ arrow always points to the window opposite the f Smdadr{rdvdarvai& PR:l highlighted item and can be used to transfer selectedvariablesin either direction.Note that doubleclickingon the variable name will also transfer the variable to the opposite window. Standard Windows conventions of "Shift" clicking or "Ctrl" clicking to selectmultiplevariablescan be usedas well. When we click on the OK button, the analysiswill be conducted,and we will be readyto examineour output.
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Section1.6 Examiningand PrintingOutput Files After an analysis is performed, the output is placed in the output window, and the output window becomesthe active window. If this is the first analysis you have conducted since starting SPSS, then a new output window will be created.If you have run previous analyses and savedthem,your
outputis addedto theendof yourpreviousoutput. To switchbackandforthbetweenthedata window andtheoutput window,select thedesiredwindowfrom the Windowmenubar(seearrow,below). The output window is split into two sections. The left sectionis an outlineof the (SPSS "outline output refersto this asthe view").Theright sectionis theoutputitself. H. Ee lbw A*t
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The sectionon the left of the output window provides an outline of the entire output window. All of the analysesare listed in the order in which they were conducted.Note that this outline can be used to quickly locate a sectionof the output. Simply click on the sectionyou would like to see,and the right window will jump to the appropriateplace.
ChapterI GeningStarted
Clicking on a statisticalprocedurealso selectsall of the output for that command. By pressingtheDeletekey, that outputcan be deletedfrom the output window. This is a quick way to be sure that the output window containsonly the desiredoutput. Output can also be selectedand pastedinto a word processorby clicking Edit, then Copy Objecls to copy the output.You can then switch to your word processorand click Edit, thenPaste. To print your output, simply click File, then Print, or click on the printer icon on the toolbar. You will have the option of printing all of your output or just the currently selected section. Be careful when printing! Each time you mn a command, the output is addedto the end of your previous output. Thus, you could be printing a very large output file containinginformation you may not want or need. One way to ensurethat your output window containsonly the resultsof the current commandis to createa new output window just before running the command.To do this, click File, then New, then Outpul. All your subsequentcommandswill go into your new output window. Practice Exercise Load the sampledata file you createdearlier (SAMPLE.sav). Run the Descriptives command for the variable GRADE and print the output. Your output should look like the exampleon page7. Next, selectthe data window and print it.
Section1.7 ModifyingData Files Once you have createda data file, it is really quite simple to add additional cases (rows/participants) or additionalvariables(columns).ConsiderExample1.7.1.
Example1.7.1 Two morestudents provideyou with surveys. Theirinformationis: ResponseSheet3 ID: Day of class: Classtime: Are you a morningperson? Final gradein class: Do you work outsideschool?
ResponseSheet4 ID: Day of class: Classtime: Are you a morning person? Final gradein class: Do you work outsideschool?
8734 MWF Morning Yes
X TTh Afternoon XNo
80% Parttime
Fulltime No
1909 X MWF X Morning X Yes 73% Full+ime No
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Parttime
Chapter I Getting Started
To add thesedata, simply place two additionalrows in the Data View window (after loading your sampledata).Notice that as new participantsare added,the row numbers becomebold. when done,the screenshouldlook like the screenshothere. j
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New variables can also be added.For example, if the first two participantswere given specialtraining on time management,and the two new participantswere not, the data file can be changedto reflect this additionalinformation.The new variable could be called TRAINING (whether or not the participant receivedtraining), and it would be coded so that 0 : No and I : Yes. Thus, the first two participantswould be assigneda "1" and the Iast two participantsa "0." To do this, switch to the Variable View window, then add the TRAINING variable to the bottom of the list. Then switch back to the Data View window to updatethe data. f+rilf,t

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Adding data and adding variablesare just logical extensionsof the procedureswe used to originally createthe data file. Save this new data file. We will be using it again later in the book.
Chapter I Getting Started
Practice Exercise Follow the exampleabove(whereTRAINING is the new variable).Make the modifications to your SAMPLE.savdatafile andsaveit.
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Chapter2
EnteringandModifying Data In Chapter 1, we learnedhow to createa simple data file, save it, perform a basic analysis,and examine the output. In this section,we will go into more detail about variablesand data.
Section2.1 Variablesand DataRepresentation In SPSS,variablesare representedas columns in the data file. Participantsare representedas rows. Thus, if we collect 4 piecesof information from 100 participants,we will have a data file with 4 columnsand 100 rows. Measurement Scales There are four types of measurementscales:nominal, ordinal, interval, and ratio. While the measurementscalewill determinewhich statisticaltechniqueis appropriatefor a given set of data, SPSSgenerally does not discriminate.Thus, we start this section with this warning: If you ask it to, SPSSmay conduct an analysis that is not appropriatefor your data.For a more completedescriptionof thesefour measurementscales,consultyour statisticstext or the glossaryin Appendix C. Newer versionsof SPSS allow you to indicate which types of Measure data you have when you define your variable. You do this using the Measurecolumn. You can indicateNominal, Ordinal, or Scale(SPSS @Nv doesnot distinguishbetweeninterval and ratio scales). f $cale .sriltr Look at the sampledata file we createdin Chapter l. We calcur Nominal lated a mean for the variable GRADE. GRADE was measuredon a ra
summarystatistic(assumingthat the distribution tio scale,andthe mean is an acceptable is normal). We could have had SPSScalculatea mean for the variableTIME insteadof here. GRADE.If we did, we wouldgettheoutputpresented The outputindicatesthat the averageTIME was 1.25.Rememberthat TIME was coded as an ordinal variable ( I = m or ni ngcla ss,2a fte rnoon trlllql eilr $lg class).Thus, the mean is not an *lq]eH"Nql*l appropriatestatisticfor an ordinal :* Sl astts .l.:D gtb scale,but SPSScalculatedit any:$sh way. The importance of considering the type of data cannot be overemphasized. Just because ht6x0tMn SPSS will compute a statistic for you doesnot mean that you should .6M6.ffi
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Chapter2 Enteringand Modifying Data
use it. Later in the text, when specificstatisticalproceduresare discussed,the conditions underwhich they are appropriatewill be addressed. Missing Data Often, participantsdo not provide completedata.For some students,you may have a pretestscore but not a posttestscore.Perhapsone studentleft one question blank on a survey,or perhapsshe did not stateher age.Missing data can weakenany analysis.Often, a singlemissingquestioncan eliminatea subject from all analyses. ql total If you have missing data in your data 2.00 2.Bn 4.00 set, leave that cell blank. In the example to 3.00 1.0 0 4.00 the left, the fourth subject did not complete Question2. Note that the total score(which is 4.00 3.00 7.00 calculatedfrom both questions)is also blank becauseof the missing data for Question 2. 2.00 SPSS representsmissing data in the data 1 .0 0 2.UB 3.00 window with a period (althoughyou should not enter a periodjust leave it blank).
Section2.2 Transformationand Selectionof Data We oftenhavemoredatain a datafile thanwe wantto includein a specificanalysis.For example,our sampledatafile containsdatafrom four participants, two of whom receivedspecialtrainingand two of whom did not. If we wantedto conductan analysis usingonly the two participants who did not receivethe training,we wouldneedto specify theappropriate subset. Selectinga Subset F! Ed vl6{ , O*. lr{lrfum An*/& e+hr O*fFV{ldrr PrS!tU6.,. CoptO.tafropc,tir3,..
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We can use the SelectCasescommandto specify a subset of our data. The Select Cases command is located under the Data menu. When you select this command,the dialog box below will appear. q*d:" """"****""*^*l 6 Alce a llgdinlctidod ,r l
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You can specify which cases(participants) you want to select by using the selection criteria, which appearon the right side of the SelectCasesdialog box.
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Chapter2 Enteringand Modifying Data
By default,All caseswill be selected.The most common way to selecta subsetis to click If condition is satisfied, then click on the button labeledfi This will bring up a new dialog box that allowsyou to indicatewhich casesyou would like to use. You can enter the logic used to select the subset in the upper section. If the logical statement is true for a given case, then that case will be U;J;J:.1glL1 E{''di',*tI 'Je.l,'JlJ.!JEl[aasi"Eo,ti , selected.If the logical statement is false. that case will not be 0 U IAFTAN(r"nasl ,Jl _!JlJ selected.For example, you can sl"J=tx s*t"lBi!?Blt1trb :r select all casesthat were coded ?Ais"I c't I Ht I as Mon/Wed/Fri by entering the formula DAY = I in the upperright part of the window. If DAY is l, thenthe statementwill be true,and SPSSwill select the case.If DAY is anything other than l, the statementwill be false, and the casewill not be selected.Once you have enteredthe logical statement,click Continue to return to the SelectCasesdialog box. Then,click OK to returnto the data window. After you have selectedthe cases,the data window will changeslightly. The casesthat were not selectedwill be markedwith a diagonalline through the casenumber. For example,for our sampledata, the first and third casesare not selected.only the secondand fourth casesare selectedfor this subset.
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.05). No significant differenceexistsamongpretest(m: 63.33,sd = 8.93),midterm(m:78.62, sd:9.66), andfinal(m:86.14, sd: 9.63)means. Practice Exercise Use PracticeData Set 3 in Appendix B. Determine if the anxiety level of participants changedover time (regardlessof which treatmentthey received) using a oneway repeatedmeasures ANOVA and protecteddependentI tests.Write a statementof results. Section 6.8 MixedDesign ANOVA Description The mixeddesignANOVA (sometimescalled a splitplot design) teststhe effects of more than one independentvariable. At leastone of the independentvariables must
75
Chapter6 ParametricInferentialStatistics
be withinsubjects(repeatedmeasures). At leastone of the independentvariables must be betweensubjects. Assumptions The dependent variable shouldbe normally distributedand measuredon an interval or ratio scale. SPSS Data Format The dependent variable shouldbe representedas one variable for each level of the withinsubjectsindependentvariables.Anothervariableshouldbe presentin the datafile for each betweensubjectsvariable. Thus, a 2 x 2 mixeddesignANOVA would require three variables,two representingthe dependent variable (one at each level), and one representingthe betweensubjects independentvariable. Running the Command The GeneralLinear Model commandruns the MixedDesign ANOVA command. Click Analyze, then General Linear Model, then Repeated Measures. Note that this procedure requires an optional module. If you do not have this command, you do not have the proper module installed. This procedure is NOT included in the st u dent versi on o/,SPSS.
lAnqtr:l g{hs Udear Addgnr Uhdorn Rqprto r oitchfiy. $rtBtlca i T.d*t Cocpa''UF46
@
)
ilrGdtilod6b
)
iifr.{*r &rfcrgon tAdhraf
} l i
The RepeatedMeasures command shouldbe used if any of the independent gfitsrf*drvdbbht IK variables are repeatedmeasures(withinter I subjects). s*i I This example also uses the t*., GRADES.sav data file. Enter PRETEST, 34 1 MIDTERM, and FINAL in the lhthinSubjects Variables block. (See the RepeatedMeasuresANOVA command in Section 6.7 for an explanation.) This exampleis a 3 x 3 mixeddesign.There are two independent variables (TIME and INSTRUCT), each with three levels. Uoo*..I cotrl... I 8q... I Podg*. I Sm..  8e4.. I We previously enteredthe information for TIME in the RepeatedMeasures Define Factorsdialog box. We needto transferINSTRUCT into the BetweenSubjects Factor(s) block. Click Options and selectmeansfor all of the main effectsand the interaction (see oneway ANOVA in Section6.5 for more details about how to do this). Click OK to run the command.
mT
76
Chapter6 ParametricInferentialStatistics
Readingthe Output
f
measures command,the GLM procedureprovidesa As with the standardrepeated ANOVA, we are interestedin two secwe will For mixeddesign lot of output not use. a Effects. tions.The first is Testsof WithinSubjects Tests ot WrtlrilrSuuectsEflects M eas u re : Typelll Sum of Squares sphericity Assumed 6 5673.74 Gre e n h o u s e Ge i s s el 5673.746 HuynhFeldt 6 5673.74 Lowerbound 6 5673.74 time' instruct Sphericily Assumed 806.063 0 re e n h o u s e Ge i s s e r 806.063 HuynhFeldt 3 806.06 Lowerbound 806.063 Erro(time) Sphericity Assumed 124857 Gre e n h o u sGe e isser 124.857 HuynhFeldt 124.857 Lowerbound 124.857 S our c e time
df
2
1.181 1.356 1.000 4 2.363 2.f' t2 2.000 36 21.265 24.41'. 18.000
MeanS ouare 2836.873 4802.586 4' t83.583 5673.746 201.516 341.149 297.179 403.032 3.468 5.871 5.115 6.S37
F
817.954 817.954 817.954 817.954 58.103 58.103 58.103 58.103
sis 000 000 000 000 .000 .000 .000 .000
This sectiongives two of the threeanswerswe need (the main effect for TIME and the interactionresult for TIME x INSTRUCTOR). The secondsectionof output is Testsof BetweensubjectsEffects (sample output is below). Here, we get the answersthat do not contain any withinsubjects effects. For our example, we get the main effect for INSTRUCT. Both of thesesectionsmust be combinedto oroduce the full answer for our analysis. Eltecls Testsot BetryeenSill)iects Me a s u re M:EA SU R1E ransformed Variable: Typelll Sum S o u rc e of Squares Intercepl 3 6 4 19 2 .0 6 3 inslrucl 18 .6 9 8 En o r 43 6 8 .5 7 1
df I
2 18
F MeanS ouare 364192.063 1500.595 9.349 .039 242.6S 8
Siq.
.000 .962
If we obtain significant effects, we must perform some sort of posthoc analysis. Again, this is one of the limitations of SPSS.No easyway to perform the appropriatepost(withinsubjects)factors is available. Ask your instructor hoc test for repeatedmeasures for assistance with this. When describingthe results,you should include F, the degreesof freedom,and the significancelevel for eachmain effect and interaction.In addition,somedescriptivestatistics must be included(eithergive meansor includea figure). Phrasing Results That Are Significant There are three answers(at least) for all mixeddesignANOVAs. Pleasesee Section 6.6 on factorial ANOVA for more detailsabouthow to interpretand phrasethe results.
77
Chapter6 ParametricInferentialStatistics
For the aboveexample,we could statethe following in the resultssection(note that this assumesthat appropriateposthoctestshave beenconducted): A 3 x 3 mixeddesignANOVA was calculatedto examinethe effectsof the instructor(Instructors1,2, and,3)and time (pretest,midterm, and final) on scores.A significant time x instructor interactionwas present(F(4,36) = 58.10, p .05).Upon examinationof the data,it appears that Instructor3 showedthe most improvementin scoresover time. With significant interactions, it is often helpful to provide a graph with the descriptive statistics.By selectingthe Plotsoption in the main dialog box, you can make graphsof the interaction like the one below. Interactionsadd considerable complexityto the interpretationof statisticalresults.Consult a researchmethodstext or ask your instructor for more help with interactions. ilme

E@rdAs
I, I lffi_ sw&t.tc
f Crtt"l
l
cd.r_J
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3
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.
ia E
, ,,,:;',,1. "l ","11::::J
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Phrasing Results That Are Not SigniJicant If our resultshad not beensignificant,we could statethe following (note that the .F valuesare fictitious): A 3 x 3 mixeddesignANOVA was calculatedto examinethe effectsof the instructor(lnstructors1,2, and 3) and time (pretest,midterm, and final) on scores.No significant main effects or interactionswere found. The time x instructor interaction(F(4,36) = 1.10,p > .05), the main effect for time (F(2,36)= I .95,p > .05),andthe main effectfor instructor(F(2,18): .039,p > .05) were all not significant.Exam scoreswere not influencedby either time or instructor. Practice Exercise Use PracticeData Set 3 in AppendixB. Determineif anxiety levels changedover time for each of the treatment(CONDITION) types. How did time changeanxiety levels for eachtreatment?Write a statementof results.
78
Chapter6 ParametricInferentialStatistics
Section6.9 Analysisof Covariance Description Analysis of covariance(ANCOVA) allows you to remove the effect of a known covariate. In this way, it becomesa statisticalmethod of control. With methodological controls (e.g., random assignment),internal validity is gained.When such methodological controlsare not possible,statisticalcontrolscan be used. ANCOVA can be performed by using the GLM command if you have repeatedmeasuresfactors. Becausethe GLM commandis not included in the Base Statisticsmodule, it is not includedhere.
Assumptions ANCOVA requiresthatthe covariatebe significantlycorrelatedwith the dependent variable.The dependentvariableandthecovariateshouldbe at theinterval or ratio levels.In addition.bothshouldbe normallydistributed. SPS,SData Format The SPSSdatafile mustcontainonevariablefor eachindependentvariable,one variablerepresenting thedependentvariable,andat leastonecovariate. Running the Command The Factorial ANOVA commandis tsr.b"" GrqphrUUnbr,wrndowl.lab usedto run ANCOVA. To run it, click AnaReports lyze, then General Linear Model, then UniDascrl$lveSt$stks variate. Follow the directionsdiscussedfor factorial ANOVA, using the HEIGHT.sav sampledata file. Placethe variableHEIGHT as your DependentVariable.Enter SEX as your Fixed Factor, then WEIGHT as the CoDogrdrfvdirt{c variate.This last stepdeterminesthe differt{od.L. I l.:r [7mencebetweenregularfactorialANOVA and c**1 ANCOVA. Click OK to run theANCOVA. llr,.. I 'rii l.ri
till Crd{'r.t{r}
td f;'l wlswc0't l 'ffi
j.*.1,q*J*lgl
79
I
*l*:" I q&,, I
Chapter6 ParametricInferentialStatistics
Reading the Output The outputconsistsof onemain sourcetable(shownbelow).This tablegivesyou the main effects and interactionsyou would have receivedwith a normal factorial ANOVA. In addition,thereis a row for eachcovariate.In our example,we haveonemain effect(SEX)andonecovariate(WEIGHT).Normally,we examinethe covariateline only to confirmthatthecovariateis significantlyrelatedto thedependentvariable. Drawing Conclusions This sampleanalysiswas performedto determineif malesand femalesdiffer in height,afterweightis accounted for. We knowthatweightis relatedto height.Ratherthan matchparticipants or usemethodological controls,we canstatisticallyremovethe effectof weight. When giving the resultsof ANCOVA, we must give F, degreesof freedom,and significancelevelsfor all main effects,interactions,and covariates.If main effectsor interactions are significant,posthoctests must be conducted.Descriptive statistics (meanandstandarddeviation)for eachlevelof theindependentvariable shouldalsobe given. Tests of BetweenSubjectsEffects Va ri a b l e :H EIGH T Typelll Sumof Mean Source S orrare Souares df 9orrecreoMooel 215.0274 1U /.D 'tJ 2 lntercept 5.580 I 5.580 WEIGHT 1 1 9.964 1't9.964 1 SEX 66.367 66.367 1 Error 1 3.91 1 13 1.070 Total 7 1 9 1 9.000 16 CorrectedTotal 228.938 15 a. R Squared= .939(AdjustedR Squared= .930)
F
100.476 5.215 112.112 62.023
Siq.
.000 .040 .000 .000
PhrasingResultsThatAre Significant Theaboveexample obtained a significant result,sowecouldstatethefollowing: A onewaybetweensubjects ANCOVA wascalculatedto examinethe effect of sexon height,covaryingout theeffectof weight.Weightwassignificantly relatedto height(F(1,13): ll2.ll,p
events. .05).Flipsof a coinappearto be independent Practice Exercise wantsto knowwhetheror not individualsaremorelikely to helpin an A researcher emergencywhen they are indoorsthan when they are outdoors.Of 28 participantswho who wereindoors,8helpedand wereoutdoors,19helpedand9 did not.Of 23 participants 15 did not. Enterthesedata,and find out if helpingbehavioris affectedby the environment.The key to this problemis in the dataentry.(Hint: How many participantswere there,andwhatdo you knowabouteachparticipant?) Section7.3 MannWhitnev UTest Description t test. equivalentof the independent The MannWhitneyU testis thenonparametric It testswhetheror not two independent samplesarefrom thesamedistribution.The Mannweaker independent t test,and the / testshouldbe usedif you WhitneyU testis thanthe canmeetits assumptions. Assumptions The MannWhitneyU testusesthe rankingsof the data.Therefore,the datafor the aboutthe shapeof the distwo samplesmustbe at leastordinal. Thereareno assumptions tribution.
90
!il;tIFfFF".
Chapter7 NonparametricInferentialStatistics
,SPS,S Data Format This command requiresa singlevariablerepresenting thedependentvariableand a second variableindicating groupmembership. Running the Command This example will use a new data file. It representsl2 participantsin a series of races. There were long races, medium races, and short races. Participants either had a lot of experience (2), some experience(l), or no experience(0). Enter the data from the figure at right in a new file, and savethe data file as RACE.sav. The values for LONG. MEDIUM, and SHORT represent the results of the race, with I being first place and 12 being last. WMw I Andy* qaphr U*lx , R.po.ti Doroht*o1raru.r , t CdolaaMcrfE  6on ralthccl'lodd I ) C*ru*c j r Rooa!33hn )' cta*iry i j ) DatrRoddton i I
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I I
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To run the command,click Analyze, then Nonparametric Tests, then 2 Independent Samples. This willbring up the maindialog box. Enter the dependentvariable (LONG, for this example) in the Test Variable List blank. Enter the independentvariable (EXPERIENCE)as the Grouping Variable.Make surethat MannWhitneyU is checked. Click Define Groupsto selectwhich two groups you will compare.For this example,we will compare those runners with no experience(0) to those runners with a lot of experience(2). Click OK to run the analvsis.
lbb
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2:
O$squr.,.. thd*rl... Rur... 1sdTpbX5,.. rl@ttsstpht,., e Rlnand5{ndnr,,, KRdetcdsrmplo*.,,
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I_ Ko&nonsov'SrnirnovZ I l Mosasa significantdifferencewas founddg 0.049,p .05).The lengthof the racedid not significantly affecttheresultsof therace. Practice Exercise Usethedatain PracticeDataSet3 in AppendixB. If anxietyis measured on an ordinal scale,determineif anxietylevelschangedovertime.Phraseyour results.
98
Chapter8 $
't, s
TestConstruction
.fi i$
j Section 8.1 ltemTotal Analvsis Description Itemtotalanalysisis a way to assessthe internal consistencyof a data set. As such,it is one of many testsof reliability. Itemtotalanalysiscomprisesa numberof items that make up a scaleor testdesignedto measurea singleconstruct(e.g.,intelligence),and determinesthe degreeto which all of the items measurethe sameconstruct.It doesnot tell you if it is measuringthe correctconstruct(that is a questionof validity). Before a test can be valid, however,it must first be reliable. Assumptions All the itemsin the scaleshouldbe measuredon an interval or ratio scale.In addition, eachitem shouldbe normallydistributed.If your itemsare ordinal in nature,you can conduct the analysisusing the Spearmanrho correlationinsteadof the Pearsonr correlation. SP.SSData Forrnat SPSSrequiresone variablefor each item (or I Andyle Grrphs Ulilities Window Help question)in the scale.In addition,you must have a RPpo*s , Ds$rripllvoStatirlicc ) variablerepresentingthe total scorefor the scale.
iilrliililrr' Vuiabla*
.q ! l
I"1l J13l
F Ccmpar*Msans GtneralLinearMadel I
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)
:
Conducting the Test
analysisuses the . ry1 PearsonItemtotal Coruelation command.
, Condation Coalfubr*c l Kcndafsta* l7 P"as*
To conduct it, open the you crefile data l * *  * _ _ . _ ^ _ _ QUESTIONS.sav ,'. Tsd ot SlJnific&cs ated in Chapter 2. Click Analyze, f ona.{atud I rr r'oorxaa I then Coruelate, then Bivariate. Place all questionsand the 7 nag ris{icsitqorrcldimr total in the righthand window, and click OK. (For more help on conductingconelations,seeChapter5.) The total can be calculatedwith the techniquesdiscussedin Chapter2. f Spoamm
99
Chapter8 Test Construction
Readingthe Output The output consistsof a correlation matrix containingall questionsand the total. Use the column labeledTOTAL, and locate the correlationbetweenthe total scoreand each question.In the exampleat right, QuestionI hasa correlationof 0.873with the totalscore.Question2 hasa correlation of 0.130 with the total. Question3 has a correlationof 0.926with thetotal.
Correlatlons
o2
o1 l'oarson \,orrelallon Sig. (2tailed) N PearsonCorrelalion UZ Si9.(2tailed) N P€arsonCorrelation Q3 Sig.(2tailed) N TOTAL PearsonConelation Sig.(2tailed) N Lll
1.000
t to
.553 4 .447 .553 4
.718 .?82 4
.873 .127 4
TOTAL
Q3
cll
4
1.000 4
..229 .771 4 .130 .870 4
.282 4
.229 .771 4
1.000 4 .926 .074 4
o/J
.127 4
 .130 .870 4 .YZ O
.074 4 1 .000 4
Interpreting the Output Itemtotalcorrelations shouldalwaysbe positive.If you obtaina negativecorrelation, that questionshouldbe removedfrom the scale(or you may considerwhetherit shouldbe reversekeyed). Generally,itemtotalcorrelationsof greaterthan 0.7 are considereddesirable. Thoseof lessthan 0.3 are considered weak.Any questionswith correlationsof lessthan 0.3 shouldbe removedfrom thescale. After thetoNormally,theworstquestionis removed,thenthetotal is recalculated. tal is recalculated, the itemtotalanalysisis repeatedwithout the questionthat was removed.Then,if anyquestions havecorrelations of lessthan0.3,the worstoneis removed, andtheprocessis repeated. When all remainingcorrelationsare greaterthan 0.3, the remainingitems in the scaleareconsidered to be thosethatareinternallyconsistent. Section8.2 Cronbach's Alpha Description Cronbach's As such,it is oneof many alphais a measure of internalconsistency. testsof reliability. Cronbach'salphacomprisesa numberof itemsthat makeup a scale designedto measurea singleconstruct(e.g.,intelligence), the degreeto and determines whichall the itemsaremeasuring the sameconstruct.It doesnot tell you if it is measuring the correctconstruct(thatis a questionof validity). Beforea testcanbe valid,however,it mustfirst be reliable. Assumptions All the itemsin thescaleshouldbe measured on an interval or ratio scale.In addition, eachitem shouldbe normallydistributed.
100
Chapter8 Test Construction
Data Format ,SP,SS SPSSrequiresonevariablefor eachitem(or question)in the scale. Running the Command This example uses the QUESTIONS.savdatafile we first createdin Chapter 2. Click Analyze,thenScale,then Reliability Analysis. This will bring up the maindialogbox for Reliability Analysis.Transferthe questions from your scaleto the Itemsblank,and click OK. Do not transferany variablesrepre' sentingtotal scores.
Udtbr Wh&* tbb ) f:
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Notethatwhenyou changethe oPof tionsunderModel,additionalmeasures (e.9., can splithalf) internal consistency be calculated.
ql
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Readingthe Output In this example,the reliability coefficientis 0.407. Numberscloseto 1.00are very good,but numberscloseto poorinternal consistency. 0.00represent
RelLrltilityStntistics Cronbach's N of ltems Aloha 3 .407
Section8.3 TestRetestReliability Description Testretestreliabilityis a measureof temporal stability. As such,it is a measure thattell you theextentto whichall of internal consistency of reliability. Unlikemeasures of temporal of the questionsthat makeup a scalemeasurethe sameconstruct,measures overtime and/orovermultiple stability tell you whetheror not the instrumentis consistent administrations. Assumptions The total scorefor the scaleshouldbe an interval or ratio scale.The scalescores shouldbe normallydistributed.
l 0l
Chapter8 Test Construction
.SP,S,S Data Format SPSSrequiresa variablerepresenting thetotalscorefor the scaleat the timeof first administration. A secondvariablerepresenting at a thetotal scorefor the sameparticipants differenttime (normallytwo weekslater)is alsorequired. Running the Command The testretestreliabilitycoefficientis simplya Pearsoncorrelationcoefficientfor the relationship To computethe coefbetweenthetotal scoresfor the two administrations. ficient,follow the directionsfor computinga Pearsoncorrelationcoefficient(Chapter5, Section5.1).Usethetwo variablesrepresenting of thetest. thetwo administrations Readingthe Output The correlationbetweenthe two scoresis the testretestreliabilitycoeffrcient.It shouldbe positive.Strongreliability is indicatedby valuescloseto 1.00.Weakreliability is indicated by valuescloseto 0.00. Section 8.4 CriterionRelated Validitv Description Criterionrelated validity determines the extentto which the scaleyou are testing correlates with a criterion.For example,ACT scoresshouldcorrelatehighly with GPA. If theydo, thatis a measure of validity forACT scores.If theydo not,thatindicatesthatACT scoresmaynot be valid for theintendedpurpose. Assumptions All of the sameassumptions for the Pearson correlationcoefficientapplyto measuresof criterionrelated validity(intervalor ratio scales,normal distribution,etc.). .SP,S,S Data Format Two variablesarerequired.Onevariablerepresents thetotal scorefor the scaleyou aretesting.Theotherrepresents thecriterionyou aretestingit against. Running the Command Calculatingcriterionrelated validity involvesdeterminingthe Pearsoncorrelation valuebetweenthe scaleandthecriterion.SeeChapter5, Section5.1 for completeinformation. Readingthe Output The correlationbetweenthe two scoresis the criterionrelated validity coefficient. It shouldbe positive.Strongvalidity is indicatedby valuescloseto 1.00.Weakvalidity is indicated by valuescloseto 0.00.
102
AppendixA
Effect Size Many disciplines are placing increasedemphasison reporting effect size. While statisticalhypothesistestingprovidesa way to tell the odds that differencesare real, effect sizesprovide a way to judge the relative importanceof thosedifferences.That is, they tell us the size of the differenceor relationship.They are alsocritical if you would like to estimatenecessarysamplesizes,conducta power analysis,or conducta metaanalysis. Many professionalorganizations(e.g.,the AmericanPsychologicalAssociation)are now requiring or strongly suggestingthat effect sizesbe reportedin addition to the resultsof hypothesis tests. Becausethere are at least 4l different types of effect sizes,reach with somewhat different properties,the purposeof this Appendix is not to be a comprehensiveresourceon effect size, but ratherto show you how to calculatesomeof the most common measuresof effectsizeusingSPSS15.0. Co h e n ' s d One of the simplest and most popular measuresof effect size is Cohen's d. Cohen's d is a memberof a classof measurements called"standardized meandifferences." In essence, d is the differencebetweenthe two meansdivided by the overall standard deviation. It is not only a popularmeasureof effect size,but Cohenhasalso suggested a simple basisto interpretthe value obtained.Cohen'suggested that effect sizesof .2 aresmall, .5 are medium,and .8 are large. We will discussCohen's d as the preferredmeasureof effect size for I tests.Unfortunately,SPSSdoes not calculateCohen's d. However,this appendixwill cover how to calculateit from the output that SPSSdoesproduce.
EffectSizefor SingleSample t Tests Although SPSSdoesnot calculateeffect size for the singlesample / test,calculating Cohen's d is a simplematter.
' Kirk, R.E. (1996). Practicalsignificance:A conceptwhose time has come. Educational & Psychological Measurement,56, 7 467 59. ' Cohen,J. (1992). A power primer. PsychologicalBulletin, t t 2, 155159.
103
Appendix A Effect Size
TTest Om'S$da
sltb.tr
std xoan LENOIH
0
Cohen's d for a singlesampleI test is equal to the mean differenceover the standard deviation. If SPSSprovidesus with the following output,we calculated as indicatedhere:
Std Eror Ygan
Dflalon
16 qnnn
 9?2
o'r..Srt!
d
Iad
sD
TsstValuo= 35 95$ Conld6nca lhlld.t ottho d
71r'
slg (2lailsd) I
D
Igan Dill6f6nao
.90 t.t972 d = .752 d
uo00r
sooo
I l 5 5 F 0 7
In this example,using Cohen's guidelinesto judge effect size, we would have an effect size betweenmedium and large.
EffectSizefor IndependentSamples t Tests Calculating effectsizefromtheindependent t testoutputis a little morecomplex becauseSPSSdoesnot provideus with the pootedstandard deviation. The uppersection of the output, however, does provide us with the information we need to calculateit. The output presentedhere is the sameoutput we worked with in Chapter6. Group Statlltlcr
graoe
morntno No yes
S pooled =
N
z 2
Mean Std. Oeviation J.JJIDJ UZ.SUUU 7.07107 78.0000
Std.Error Mean Z,SUUUU
s.00000
(n ,1 )s , 2+ (n , l)s r2 n r+ n r2
 tlr.Sr552+ (2 t)7.07 (
rp o o te d\ /12
2+ 21 S pool"d
=
Spooted= 5'59
Once we have calculatedthe pooled standard deviation (spooud), we can calculate Cohen'sd.
, x ,x ,
Q= 
S pooled
 78.00 82.50 5.59 =.80 d , o =
104
Appendix A
Effect Size
So, in this example,using Cohen's guidelinesfor the interpretationof d, we would have obtaineda large effect size.
EffectSizefor PairedSamples t Tests As you have probably learned in your statisticsclass, a pairedsamplesI test is just really I test.Therefore,the procedurefor calculata specialcaseof the singlesample ing Cohen's d is also the same.The SPSSoutput,however,looks a little different,so you will be taking your valuesfrom different areas. Pair€dSamplosTest Paired Differences 95% Confidence Intervalof the
std. Mean YAlt 1
'KE ttss I . FINAL
f)eviatior
22.809s
A OTqA
Std.Error Mean
f)iffcrcnne
Lower
sig Upper
1.9586 26.8952 18.7239
(2tailed)
df 11.646
20
.000
,D
u 
JD
 22.8095 8.9756 d = 2.54 Notice that in this example,we representthe effect size (d; as a positive number eventhoughit is negative.Effect sizesare alwayspositivenumbers.In this example,using Cohen'sguidelinesfor the interpretationof d, we have found a very large effect size. 12(Coefficient of Determination) While Cohen's d is the appropriatemeasureof effect size for / tests, correlation and regressioneffect sizes should be determinedby squaringthe correlation coefficient. This squaredcorrelationis called the coefficient of determination. Cohen' suggestedhere that correlationsof .5, .3, and.l corresponded to large,moderate,and small relationships. Thosevaluessquaredyield coefficientsof determination of .25,.09, and .01 respectively. It would appear,therefore,that Cohen is suggestingthat accounting for 25o/oof the variability representsa large effbct, 9oha moderateeffect, and lo/oa small effect.
EffectSizefor Correlation Nowhere is the effect of sample size on statisticalpower (and therefore significance) more apparentthan with correlations.Given a large enoughsample,any correlation can becomesignificant.Thus, effect size becomescritically important in the interpretation of correlations.
'Cohen, J. (1988). Statisticalpower analysisfor the behavioral sciences(2"d ed). New Jersey:Lawrence Erlbaum.
105
Appendix A
Effect Size
The standardmeasureof effect size for correlationsis the coefficient of determination (r2) discussedabove. The coefficient should be interpretedas the proportion of variance in the dependent variable that can be accountedfor by the relationshipbetween the independentand dependentvariables.While Cohenprovidedsomeusefulguidelines for interpretation,each problem should be interpretedin terms of its true practical significance. For example,if a treatmentis very expensiveto implement,or has significant side effects,then a larger correlationshould be required before the relationshipbecomes"important." For treatmentsthat are very inexpensive,a much smaller correlationcan be considered"important." To calculatethe coefficientof determination, simply take the r value that SPSS providesand squareit.
EffectSizefor Regression TheModelSummary section of the output reports R2 for you. The example output here shows a coefficient of determination of .649, meaningthat almost 65% (.649\ of the variability in the dependentvariable is accountedfor by the relationship betweenthe dependent and independentvariables.
ModelSummary Adjusted R R Souare R Souare .8064 .649 .624
Model
Std. Error of the Estimate 16.1 480
a. Predictors: (Constant), HEIGHT
Eta SquaredQtz) A third measureof effect size is Eta Squared (ry2).Eta Squared is usedfor Analysis of Variancemodels.The GLM (GeneralLinear Model) functionin SPSS(the function that runs the proceduresunderAnalyzeGeneral Linear Model) will provide Eta Squared (tt'). Eta Squared has an interpretationsimilar to a squaredcorSS"ik", relationcoefficient1l1.lt represents the proportionof the variance tt n, accountedfor by the effect.Unlike ,2, ho*euer, which represents Sqr," . SS* onlylinearrelationships,,72canrepresentanytypeofrelationship.
Effect Sizefor Analysis of Variance For mostAnalysisof Varianceproblems,you shouldelectto reportEta Squared asyour effectsizemeasure. SPSSprovidesthis calculationfor you as part of the General LinearModel(GLIrl)command. To obtainEta Squared,you simplyclick on theOptionsbox in the maindialog box for the GLM commandyou arerunning(this worksfor Univariate,Multivariate,and RepeatedMeasuresversionsof the commandeventhoughonly the Univariateoption is presented here).
106
Appendix A Effect Size
Onceyou haveselectedOptions,a new dialog box will appear.One of the optionsin that box will be Estimatesof ffict sze. When you select that box, SPSSwill provide Eta Squaredvaluesaspartofyour output.
l[qoral*  $FdYrdg f A!.it?ld
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Dependenl Variable: score TypelllSum nf Sdila!es df tean Souare Source u0rrecleo M00el 1 0 .4 5 0 r 5.225 2 4 Inlercepl I s't.622 91.622 1 gr0up 5.225 1 0 .4 5 0 Enor 12 .27 4 3 .2 8 3 Total 15 1 0 5 .0 0 0 't4 Corrected Total 1 3 .7 3 3 a. R Squared = .761(Adiusied = .721) R Squared
PadialEta F
19.096 331.862 1S .096
si q, .000 .000 .000
Souared
761 965 761
In the examplehere,we obtainedan Eta Squaredof .761for our main effectfor groupmembership. Because we interpretEta Squaredusingthe sameguidelinesas,', we wouldconcludethatthisrepresents alargeeffectsizefor groupmembership.
107
Appendix B PracticeExerciseData Sets
PracticeData Set2 A survey of employeesis conducted.Each employeeprovides the following information: Salary (SALARY), Years of Service (YOS), Sex (SEX), Job Classification (CLASSIFY), and EducationLevel (EDUC). Note that you will haveto code SEX (Male: : 3). l, Female: 2) and CLASSIFY (Clerical: l, Technical: 2, Professional
ll*t:g  Jrs$q Numsric lNumedc
SALARY 35,000 18,000 20,000 50,000 38,000 20,000 75,000 40,000 30,000 22,000 23,000 45,000
YOS 8 4 I 20 6 6 17 4 8 l5 16 2
SEX Male Female Male Female Male Female Male Female Male Female Male Female
CLASSIFY EDUC 14 Technical l0 Clerical Professional l6 Professional l6 20 Professional 12 Clerical 20 Professional 12 Technical 14 Technical 12 Clerical 12 Clerical Professional l6
PracticeData Set3 Participants who havephobiasare given one of threetreatments(CONDITION). Their anxietylevel (1 to l0) is measured at threeintervalsbeforetreatment(ANXPRE), one hour after treatment(ANXIHR), and againfour hoursafter treatment(ANX4HR). Notethatyou will haveto codethevariableCONDITION.
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,Numeric i''* '"
ll0
Appendix B Practice Exercise Data Sets
ANXPRE 8
t0 9 7 7 9 l0 9 8 6 8 6 9 l0 7
ANXIHR 7 l0 7 6 7 4 6 5 3 3 5 5 8 9 6
ANX4HR 7 l0 8 6 7 5 I 5 5 4 3 2 4 4 3
lll
CONDITION Placebo Placebo Placebo Placebo Placebo ValiumrM ValiumrM ValiumrM ValiumrM ValiumrM ExperimentalDrug ExperimentalDrug ExperimentalDrug ExperimentalDrug ExperimentalDrug
AppendixC
Glossary everypossibleoutcome. All Inclusive.A set of eventsthat encompasses Alternative Hypothesis. The oppositeof the null hypothesis,normally showing that there is a true difference. Generallv. this is the statementthat the researcherwould like to support. Case ProcessingSummary. A sectionof SPSSoutput that lists the number of subjects usedin the analysis. Coefficient of Determination. The value of the correlation, squared. It provides the proportionof varianceaccountedfor by the relationship. Cohen's d. A common and simple measureof effect size that standardizesthe difference betweengroups. Correlation Matrix. A section of SPSS output in which correlationcoefficientsare reportedfor allpairs of variables. Covariate. A variable known to be relatedto the dependentvariable,but not treatedas an independentvariable.Used in ANCOVA as a statisticalcontrol technique. Data Window. The SPSSwindow that containsthe data in a spreadsheetformat. This is the window usedfor running most commands. Dependent Variable. An outcome or response variable. The dependent variable is normally dependenton the independentvariable. Descriptive Statistics. Statisticalproceduresthat organizeand summarizedata. $ $
nialog Box. A window that allows you to enter information that SPSS will use in a command.
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Oichotomous with onlytwo levels(e.g.,gender). Variables.Variables
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DiscreteVariable. A variablethat can have only certainvalues(i.e., valuesbetween *hich thereis no score,like A, B, C, D, F).
I'
i .
Effect Size. A measurethat allows one to judge the relative importanceof a differenceor relationshipby reportingthe size of a difference. Eta Squared (q2).A measureof effectsizeusedin Analysisof Variancemodels.
I 13
AppendixC Glossary
Grouping Variable. In SPSS,the variableusedto representgroup membership.SPSS often refersto independent variablesas groupingvariables;SPSSsometimesrefersto groupingvariablesasindependent variables. IndependentEvents.Two eventsareindependent if informationaboutoneeventgivesno informationaboutthe secondevent(e.g.,two flips of a coin). IndependentVariable.Thevariablewhoselevels(values)determinethe groupto whicha subjectbelongs.A true independentvariable is manipulatedby the researcher.See GroupingVariable. Inferential Statistics.Statisticalproceduresdesignedto allow the researcherto draw inferences abouta populationon thebasisof a sample. Interaction.With morethanone independent variable,an interactionoccurswhena level of oneindependent variableaffectstheinfluenceof anotherindependent variable. Internal Consistency.A reliabilitymeasurethat assesses the extentto which all of the itemsin an instrumentmeasure thesameconstruct. Interval Scale. A measurement scale where items are placed in mutually exclusive categories,with equal intervalsbetweenvalues.Appropriatetransformationsinclude counting,sorting,andaddition/subtraction. Levels.The valuesthata variablecanhave.A variablewith threelevelshasthreepossible values. Mean.A measure of centraltendencywherethesumof thedeviationscoresequalszero. Median.A measureof centraltendencyrepresenting the middleof a distributionwhenthe dataaresortedfrom low to high.Fifty percentof thecasesarebelowthe median. Mode. A measureof centraltendencyrepresenting the value (or values)with the most subjects(thescorewith thegreatestfrequency). Mutually Exclusive. Two events are mutually exclusivewhen they cannot occur simultaneously. Nominal Scale. A measurement scalewhere items are placed in mutually exclusive categories. Differentiationis by nameonly (e.g.,race,sex).Appropriatecategories include "same"or "different." Appropriatetransformations includecounting. NormalDistribution.A symmetric, unimodal, bellshaped curve. Null Hypothesis.The hypothesisto be tested,normally in which there is no tnre difference.It is mutuallyexclusiveof thealternative hypothesis.
n4
Appendix C Glossary Ordinal Scale. A measurementscale where items are placed in mutually exclusive categories, in order. Appropriate categories include "same," "less," and "more." Appropriatetransformationsinclude countingand sorting. Outliers. Extreme scoresin a distribution. Scoresthat are very distant from the mean and the rest of the scoresin the distribution. Output Window. The SPSSwindow that containsthe resultsof an analysis.The left side summarizesthe resultsin an outline. The right side containsthe actual results. Percentiles(Percentile Ranks). A relative scorethat gives the percentageof subjectswho scoredat the samevalue or lower. Pooled Standard Deviation. A single value that representsthe standarddeviation of two groupsofscores. Protected Dependent / Tests. To preventthe inflation of a Type I error, the level needed to be significantis reducedwhen multipletestsare conducted. Quartiles. The points that define a distribution into four equal parts. The scoresat the 25th,50th,and 75th percentileranks. Random Assignment. A procedurefor assigningsubjectsto conditionsin which each subjecthasan equalchanceofbeing assignedto any condition. Range. A measureof dispersionrepresentingthe number of points from the highestscore through the lowest score. Ratio Scale. A measurementscale where items are placed in mutually exclusive categories, with equal intervals between values, and a true zero. Appropriate transformationsinclude counting,sorting,additiott/subtraction, and multiplication/division. Reliability. An indication of the consistencyof a scale. A reliable scale is intemally consistentand stableover time. Robust. A test is said to be robust if it continuesto provide accurateresultseven after the violationof someassumptions. Significance. A difference is said to be significant if the probability of making a Type I error is less than the acceptedlimit (normally 5%). If a difference is significant, the null hypothesisis rejected. Skew. The extent to which a distribution is not symmetrical.Positive skew has outliers on the positive(right) sideof the distribution.Negativeskew hasoutlierson the negative(left) sideof the distribution. Standard Deviation. A measureof dispersion representinga special type of average deviation from the mean.
I 15
AppendixC Glossary
Standard Error of Estimate.The equivalentof the standarddeviationfor a regression line with a standard line.The datapointswill be normallydistributedaroundthe regression deviationequalto the standarderrorof the estimate. StandardNormal Distribution. A normaldistributionwith a meanof 0.0 anda standard deviation of 1.0. String Variable. A stringvariablecancontainlettersandnumbers.Numericvariablescan containonly numbers.Most SPSScommands will not functionwith stringvariables. Temporal Stability. This is achievedwhen reliability measureshave determinedthat scoresremainstableovermultipleadministrations of the instrument. Tukey's HSD. A posthoccomparisonpurportedto reveal an "honestly significant difference"(HSD). erroneouslyrejectsthe null Type I Error. A Type I error occurswhen the researcher hypothesis. fails to rejectthe erroneously Type II Error. A Type II erroroccurswhenthe researcher null hypothesis. Valid Data.DatathatSPSSwill usein its analyses. Validity. An indicationof theaccuracyof a scale. Variance.A measure deviation. of dispersion equalto thesquaredstandard
l16
AppendixD
SampleDataFilesUsedin Text A varietyof smalldatafiles areusedin examplesthroughoutthis text. Hereis a list of whereeachappears. COINS.sav Variables:
COINI COIN2
Enteredin Chapter7 GRADES.sav Variables:
PRETEST MIDTERM FINAL INSTRUCT REQUIRED
Enteredin Chapter6 HEIGHT.sav Variables:
HEIGHT WEIGHT SEX
Enteredin Chapter4 QUESTIONS.Sav Variables: Ql Q2 (recodedin Chapter2) Q3 TOTAL (addedin Chapter2) GROUP(addedin Chapter2) Enteredin Chapter2 Modifiedin Chapter2
tt7
AppendixD SampleDataFilesUsedin Text
RACE.sav Variables:
SHORT MEDIUM LONG EXPERIENCE
Enteredin Chapter7 SAMPLE.sav Variables:
ID DAY TIME MORNING GRADE WORK TRAINING (addedin Chapter1)
Enteredin ChapterI Modifiedin ChapterI SAT.sav Variables:
SAT GRE GROUP
Enteredin Chapter6 Other Files For somepracticeexercises, seeAppendixB for neededdatasetsthatarenot usedin any otherexamplesin thetext.
l18
AppendixE
Informationfor Users of EarlierVersionsof SPSS
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Thereare a numberof differences betweenSPSS15.0and earlierversionsof the software.Fortunately,mostof themhavevery little impacton usersof this text. In fact, mostusersof earlierversionswill be ableto successfully usethis text withoutneedingto reference this appendix. Variable nameswere limited to eight characters. Versionsof SPSSolderthan 12.0arelimitedto eightcharacter variablenames.The othervariablenamerulesstill apply.If you areusingan olderversionof SPSS,you needto makesureyou useeightor fewerlettersfor yourvariablenames. The Data menu will look different. The screenshotsin the text where the Data menu is shown will look slightly different if you are using an older version of SPSS.These missing or renamedcommandsdo not have any effect on this text, but the menusmay look slightly different. If you are using a version of SPSS earlier than 10.0,the Analyzemenu will be called Statistics instead.
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Graphing functions. Prior to SPSS12.0,the graphingfunctionsof SPSSwerevery limited.If you are using a version of SPSSolder than version 12.0, thirdpartysoftwarelike Excel or of graphs.If you areusingVersion14.0of for theconstruction SigmaPlotis recommended graphing. to Chapter4, whichdiscusses thesoftware,useAppendixF asan alternative
l 19
Appendix E Information for Usersof Earlier Versionsof SPSS
Variableiconsindicatemeasurement type. In versions of SPSS earlier than 14.0,variableswere represented in dialog boxes with their variable label and an icon that represented whether the variable was string or numeric (the examplehere shows all variablesthat were numeric). Starting with Version 14.0, SPSS shows additional information about each variable. Icons now representnot only whether a variable is numeric or not, but also what type of measurementscale it is. Nominal variables are representedby the & icon. Ordinal variables are representedby the dfl i.on. Interval and ratio variables(SPSSrefers to them as scale variables) are represented bv the d i"on.
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sqFr*u., 4*r.rl qql{.,I SeveralSPSSdata filescan now be openat once. Versionsof SPSSolder than 14.0 could have only one data file open at a time. Copying data from one file to another entailed a tedious process of copying/opening files/pastingletc.Starting with version 14.0, multiple data files can be open at the same time. When multiple files are open,you can selectthe one you want to work with using the Windowcommand.
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AppendixF
GraphingDatawithSPSS13.0and14.0 This appendixshouldbe usedas an alternativeto Chapter4 whenyou are using SPSS13.0or 14.0.Theseproceduresmay alsobe usedin SPSS15.0,if desired,by selectingLegacyDialogsinsteadof ChortBuilder. GraphingBasics In addition to the frequency distributions,the measuresof central tendency and measuresof dispersiondiscussedin Chapter3, graphing is a useful way to summarize,organize,and reduceyour data. It has been said that a picture is worth a thousandwords. In the caseof complicateddatasets,that is certainlytrue. With SPSSVersion 13.0 and later,it is now possibleto make publicationquality graphsusing only SPSS.One importantadvantageof using SPSSinsteadof other software to createyour graphs(e.9., Excel or SigmaPlot)is that the data have alreadybeen entered. Thus, duplicationis eliminated,and the chanceof making a transcriptionerror is reduced. Editing SP,S,SGraphs Whatever command you use to create your graph, you will probably want to do some editing to make it look exactly the way you want. In SPSS,you do this in much the sameway that you edit graphsin other software programs (e.9., Excel). In the output window, select your graph (thus creating handles around the outside of the entire object) and righrclick. Then, click SPSSChart Object, then click Open. Alternatively, you can doubleclick on the graph to open it for editing.
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AppendixF GraphingDatawith SPSS13.0and 14.0
Whenyou openthe graphfor editing,theChartEditor HSGlHffry;'
window and the correspondingProperties window will appear.
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OnceChartEditoris open,you caneasilyedit eachelementof the graph.To select just click on therelevantspoton the graph.For example,to selectthe element an element, representing the title of the graph,click somewhere on the title (the word "Histogram"in theexamplebelow).
Once you have selectedan element,you can tell that the correctelementis selected becauseit will havehandlesaroundit. If the item you have selectedis a text element(e.g.,the title of the graph),a cursor will be presentand you can edit the text as you would in word processingprograms.If you would like to changeanotherattributeof the element(e.g., the color or font size), use the Propertiesbox (Text propertiesare shownabove).
t22
AppendixF GraphingDatawith SPSS13.0and 14.0
With a little practice,you can makeexcellentgraphs usingSPSS.Onceyour graphis formattedthe way you want it, simplyselectFile,thenClose. Data Set For the graphingexamples,we will usea new set of data.Enterthe databelowand savethe file as HEIGHT.sav. The data representparticipants' HEIGHT (in inches), WEIGHT(in pounds), andSEX(l : male,2= female). HEIGHT 66 69 73 72 68 63 74 70 66 64 60 67 64 63 67 65
WEIGHT 150 155 160 160 150 140 165 150 110 100 9 52 ll0 105 100 ll0 105
SEX r I I I l l I I 2 2 2 2 2 2 2
Checkthat you haveenteredthe datacorrectlyby calculatinga mean for eachof the threevariables(click Analyze,thenDescriptiveStatistics,thenDescriptives).Compare yourresultswith thosein thetablebelow. Descrlptlve Statlstlcs
std. Minimum Maximum
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95.00 1.00
Valid N (listwise)
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Deviation Mean I1.U U oo.YJ/0 J .9U O/ 165.00 129.0625 26.3451 2.00 .5164 1.s000
AppendixF GraphingDatawith SPSS13.0and 14.0
Bar Charts,PieCharts,and Histograms Description Bar charts,pie charts,and histogramsrepresentthe number of times each scoreoccurs by varying the height of a bar or the size of a pie piece.They are graphicalrepresentations of the frequencydistributionsdiscussedin Chapter3. Drawing Conclusions The Frequenciescommandproducesoutput that indicatesboth the number of cases in the sample with a particular value and the percentageof caseswith that value. Thus, conclusionsdrawn should relate only to describing the numbers or percentagesfor the sample.If the dataare at leastordinal in nature,conclusionsregardingthe cumulativepercentages and/orpercentilescan alsobe drawn. SPSS Data Format You needonlv one variableto usethis command. Running the Command The Frequenciescommand will produce I gnahao Qr4hs $$ities graphical frequency distributions.Click Analyze, Regorts then Descriptive Statistics,then Frequencies.You @ will be presentedwith the main dialog box for the : lauor Comps?U6ar1s Frequenciescommand, where you can enter the ' Eener.lllnEarlrlodsl variables for which you would like to create r'txedModds Qorrelate graphsor charts.(SeeChapter3 for other options availablewith this command.)
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Click the Chartsbuttonat the bottom to produce frequencydistributions. Charts This will give you the Frequencies: dialogbox.
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r llrroclu* ,' There are three types of charts under this command: Bar charts, Pie charts, andHistograms.For each type, the f axis can be either a frequency count or a percentage(selectedthrough the Chart Valuesoption). You will receivethe chartsfor any variablesselectedin the main Frequenciescommanddialog box. 124
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AppendixF GraphingDatawith SPSS13.0and 14.0
Output The bar chart consistsof a Y axis, representing the frequency, and an X axis, representing each score. Note that the only values representedon the X axis are those with nonzero frequencies(61, 62, and 7l are not represented).
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The pie chart shows the percentageof the whole that is representedby eachvalue.
The Histogramcommandcreatesa groupedfrequencydistribution.The range of scores is split into evenly spaced groups.The midpoint of each group is plotted on the X axis, and the I axis represents the numberof scoresfor each group. If you selectLl/ithNormal Curve,a normal curve will be superimposed over the distribution.This is very useful for helping you determineif the distribution you haveis approximately normal.
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Practice Exercise Use PracticeData Set I in Appendix B. After you have enteredthe data,constructa histogramthat representsthe mathematicsskills scoresand displaysa normal curve, and a bar chart that representsthe frequenciesfor the variableAGE.
t25
AppendixF GraphingDatawith SPSS13.0and 14.0
Scatterplots Description Scatterplots(also called scattergramsor scatterdiagrams)display two values for eachcasewith a mark on the graph.The Xaxis representsthe value for one variable.The / axis representsthe value for the secondvariable. Assumptions Both variablesshouldbe interval or ratio scales.If nominal or ordinal data are used,be cautiousaboutyour interpretationof the scattergram. .SP,t^tData Format You needtwo variablesto perform this command. Running the Command
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You can produce scatterplotsby clicking Graphs, then I Scatter/Dot.This will give you the first Scatterplotdialog box. i Selectthe desiredscatterplot(normally,you will select Simple ! Scatter),then click Define.
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3*J qej *fl This will give you the main Scatterplot dialog box. Enter one of your variablesas the I axis and the secondas the X axis. For example, using the HEIGHT.sav data set, enter HEIGHT as the f axis and WEIGHT as the X axis. Click
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126
AppendixF GraphingDatawith SPSS13.0and 14.0
Output X andI levels. Theoutputwill consistof a markfor eachsubjectat theappropriate 74.00
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Adding a Third Variable Even though the scatterplotis a twodimensionalgraph,it canplot a third variable. To makeit do so,enterthethird variablein the SetMarkers by field.In our example,we will enterthe variable SEX in the ^SelMarkers by space. Now our outputwill havetwo different sets of marks. One set representsthe male participants, the and the secondset represents femaleparticipants. Thesetwo setswill appear in differentcolorson your screen.You canuse the SPSSchart editor to make them different shapes, asin thegraphthatfollows.
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AppendixF GraphingDatawith SPSS13.0and 14.0
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Practice Exercise UsePracticeDataSet2 in AppendixB. Constructa scatterplot to examinethe relationshipbetweenSALARY andEDUCATION. Advanced Bar Charts Description You canproducebar chartswith theFrequencies command(seeChapter4, Section 4.3). Sometimes, however,we are interested in a bar chartwherethe I axis is not a frequency.To producesucha chart,we needto usetheBar Chartscommand. SPS,SData Format At leasttwo variablesare neededto performthis command.Thereare two basic kinds of bar chartsthosefor betweensubjects designsand thosefor repeatedmeasures designs.Usethe betweensubjects methodif onevariableis the independentvariableand the otheris the dependentvariable.Use the repeatedmeasures methodif you havea dependentvariable for eachvalueof the G"dr tJt$ths Mdsns €pkrv independentvariable(e.g.,you wouldhavethreevariablesfor a IrfCr$We designwith three valuesof the independentvariable). This ) Map normallyoccurswhenyou takemultipleobservations overtime.
128
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AppendixF GraphingDatawith SPSS13.0and 14.0
Running the Command Click Graphs,thenBar for eithertypeof bar chart. This will openthe Bar Chartsdialog box. If you haveone independentvariable, selectSimple.If you have more thanone,selectClustered. design,select If you are usinga betweensubjects Summariesfor groups of cases.If you are using a repeatedmeasures design, select Summariesof separate variables. graph,you If you are creatinga repeatedmeasures will seethe dialog box below.Move eachvariableoverto theBars Representarea,and SPSSwill placeit insideparentheses followingMean.This will give you a graphlike the one below at right. Note that this exampleusesthe dataenteredin Section6.4 (Chapter6). GRADES.sav
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Practice Exercise Use PracticeDataSet I in AppendixB. Constructa bar graphexaminingthe relaskills scoresandmaritalstatus.Hint: In the BarsRepresent tionshipbetweenmathematics area.enterSKILL asthevariable.
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