Using SPSS: One-way Repeated-Measures ANOVAUSING SPSS: ONE-WAY REPEATED-MEASURES ANOVA1. ENTERING THE DATA:To do a repeated-measures ANOVA (also called a within-subjects ANOVA), youhave to enter the data in a different format from that used for independent-measuresANOVA's (between-subjects ANOVAs). The scores for each of the experimentalconditions that the subjects do are entered in separate columns.Take the following example. Imagine we were interested in the effects of practiceon doing statistics with computers. Suppose we tested eight people three times ontheir ability to perform a one-way repeated-measures ANOVA using SPSS. Let's callthese three tests "test1", "test2" and "test3". Here's how we would enter the data(which consists of times to complete the task, in minutes). As you can see, each rowprovides all of a single subject's data in the experiment: the row tells SPSS whichsubject the data come from, and the column tells SPSS which condition each scorebelongs to.2. PERFORMING THE RM-ANOVA:(a) Click on "Analyze" on the SPSS controls. On the menu that appears, click on"General Linear Model". On the menu that this produces, click on "RepeatedMeasures". This will produce a dialog box that looks like this:(b) In the box labelled "Within-Subject Factor Name", enter a name for yourrepeated-measures variable. In this case, I will replace the suggested title("Factor1") with something more meaningful to me: "testtime". You don't have to dothis; SPSS would quite happily proceed with your repeated-measures IV called"factor1", but a more meaningful label will help in the future, when we have morethan one IV.(c) Now move the cursor down to the box that says "number of levels". You needto tell SPSS how many "levels" (occasions or conditions) there are of your repeated-measures variable – for the current ANOVA design, this simply corresponds to tellingSPSS how many conditions you have in this experiment. We have three tests, so theanswer is "3". Type 3 in this box, and then click on "Add". The box to the right of the"Add" button will now show the name that you have chosen for your repeated-measures IV, with the number of levels behind it in brackets. In this case, you wouldsee "testtime(3)", for example.RM ANOVAPage 2(d) Now click on the button labelled "Define..." A dialog box will pop up, like thisone:The left-hand box contains the names of the columns in your SPSS data-window.Highlight the names of the various columns that represent different levels of theindependent variable, and press on the arrow-button to move them into the slotscontaining question marks in the right-hand box. In this case, "test1", "test2" and"test3" are the three levels of our independent variable (that we have just called"testtime"), and so we move them into the right-hand box.(e) At the bottom of the dialog box, there is a button labelled "Options..." Click onthis, and a new dialog box pops up. On the left, you will see a box entitled"Descriptive statistics". Click on this, and then "continue" to return to the previousdialog box.(f) Click on "Contrasts…". In the "Change Contrast" section use the arrow to findthe "Repeated" contrast, and then click on "Change", and then "Continue" (this is toproduce a type of post hoc tests). This function is optional – and should only be usedif the produced output will be meaningful.RM ANOVAPage 3(g) Now click on the button labelled "OK" to perform the ANOVA. You shouldhave output that looks like this. (The bracketed comments in italics explain whateach bit of the output means).3. THE SPSS OUTPUT:General Linear ModelWithin-Subjects FactorsMeasure: MEASURE_1TEST1TEST2TEST3TESTTIME123DependentVariableDescriptive Statistics178.1250 72.7980 899.6250 38.2172 888.7500 35.1273 8TEST1TEST2TEST3Mean Std. Deviation N[Unfortunately SPSS produces output you do not need for this example. Ignore thefollowing "Multivariate Tests" table for now - we will briefly review this process.]Multivariate Testsb.821 13.782a2.000 6.000 .006.179 13.782a2.000 6.000 .0064.594 13.782a2.000 6.000 .0064.594 13.782a2.000 6.000 .006Pillai's TraceWilks' LambdaHotelling's TraceRoy's Largest RootEffectTESTTIMEValue F Hypothesis df Error df Sig.Exact statistica. Design: Intercept Within Subjects Design: TESTTIMEb. [The following section gives the results of a test that SPSS does to see if your datasatisfy one of the requirements for doing a repeated-measures ANOVA – the so-called“sphericity assumption”. Imagine creating a new variable (test1-test2). Now find thevariance of this new variable. Then imagine you create a variable (test2-test3), and findits variance, and finally you find the variance of (test1-test3). The sphericity assumptionis that the variances of these three new variables are equal – it is the equivalent of thehomogeneity of variance assumption you previously checked in the between subjectscase. Happily, you do not need to create all these variables and compare theirRM ANOVAPage 4variances because SPSS tests the sphericity assumption for you automatically. If thetest produces a significant result, the sphericity assumption has been violated. Thismeans the p-value for the test of the within-subjects factor needs to be adjusted, whichSPSS does for you – see below, the p associated with the Huynh-Feldt correction. Inthis example, the Mauchly Sphericity test is not significant (p = 0.178, which is greaterthan .05), so there's no problem.][Further note for the curious: Just for your information, the multivariate tests in the tableabove are another way of testing the main effect of testtime that are valid whether ornot sphericity is satisfied. However, we will rely on the Huynh-Feldt solution whensphericity is violated, not the multivariate solution, that's why you can ignore themultivariate tests.] As a general rule, if the Epsilon value is < .75 – we would use theGreenhouse-Geisser adjustment, and if the Epsilon value is > .75 – we would use theHuynh-Feldt adjustment. Either way is acceptable – and can be supported through solidreferences.Mauchly's Test of SphericitybMeasure: MEASURE_1.565 3.427 2 .178 .697 .816 .500Within Subjects EffectTESTTIMEMauchly's WApprox.Chi-Square df Sig.Greenhouse-Geisser Huynh-Feldt Lower-boundEpsilonaTests the null hypothesis