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Computing our example Step 1: compute sums of squares Recall our data KNR 445 Statistics ANOVA (1w) Slide 1 TV MovieSoap OperaInfomercial 1610 3813 4105 549 2128 n = 5 = 3= 8= 9 N = 15 1 2

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Computing our example Step 1: compute sums of squares SS total = [10 2 + 13 2 + 5 2 + 9 2 + 8 2 + 6 2 + 8 2 + 10 2 + 4 2 +12 2 + 1 2 + 3 2 + 4 2 + 5 2 + 2 2 ] - = 854 666.67 = 187.33 KNR 445 Statistics ANOVA (1w) Slide 2 1

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Computing our example Step 1: compute sums of squares SS group = 27.14 + 8.84 + 67.34= 103.32 KNR 445 Statistics ANOVA (1w) Slide 3 1 2

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Computing our example Step 1: compute sums of squares SS error =SS total -SS group = 187.33 103.32 = 84.01 So SS group = 103.32 SS error = 84.01 Ss total = 187.33 KNR 445 Statistics ANOVA (1w) Slide 4 1

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Computing our example Step 2: Compute df df group = k 1 = 3 1 = 2 df error = N k = 15 3 = 12 df total = N 1 = 15 1 = 14 KNR 445 Statistics ANOVA (1w) Slide 5 1

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Computing our example Step 3: Compute Mean Squares (MS) KNR 445 Statistics ANOVA (1w) Slide 6 1

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Computing our example Step 4: Put all the info in the ANOVA table: KNR 445 Statistics ANOVA (1w) Slide 7 Source Sum of Squares DFMSFsig. Between Groups 103.32251.66 MS B /MS W =51.66/7 =7.38 p-value Within Groups 84.01127 Total187.3314 1

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Computing our example Step 5: Compare F obs to F critical : F obs = 7.38 F critical = need to obtain F crit from tables for F df will be (numerator, denominator) in F-ratio df = 2, 12 F (2,12, =.05) = 3.89 Reject H 0 (F obs > F critical ) KNR 445 Statistics ANOVA (1w) Slide 8 1 2

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KNR 445 Statistics ANOVA (1w) Slide 9 1-way ANOVA in SPSS Data: One column for the grouping variable (IV: group in this case), one for the measure (DV: fitness in this case) Data: Note grouping variable has 3 levels (goes from 1 to 3) 1

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KNR 445 Statistics ANOVA (1w) Slide 10 1-way ANOVA in SPSS Procedure: Choose the appropriate procedure, and 1

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KNR 445 Statistics ANOVA (1w) Slide 11 1-way ANOVA in SPSS Dialog box: slide the variables into the appropriate places 1

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KNR 445 Statistics ANOVA (1w) Slide 12 1-way ANOVA in SPSS Here we see the between and within sources of variance Here are the SDs (here expressed as the mean square thats the average sum of squares, which is after all a standardized deviation) k-1 = 3-1 = 2n k = 15 - 3 = 12n-1 = 15-1 = 14 Result! 1

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KNR 445 Statistics ANOVA (1w) Slide 13 Significant resultnow what? Follow-up tests ONLY compute after a significant ANOVA Like a collection of little t-tests But they control overall type 1 error comparatively well They do not have as much power as the omnibus test (the ANOVA) so you might get a significant ANOVA & no sig. Follow-up Purpose is to identify the locus of the effect (what means are different, exactly?) 1 2

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KNR 445 Statistics ANOVA (1w) Slide 14 Significant resultnow what? Follow-up tests most common Tukeys HSD (honestly sig. diff.) Formula: But its easier to use SPSS 1

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KNR 445 Statistics ANOVA (1w) Slide 15 Follow-ups to ANOVA in SPSS Choose post-hoc test (meaning after this) 1 2 Check the appropriate box for the HSD (Tukey, not Tukeys b)

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KNR 445 Statistics ANOVA (1w) Slide 16 Follow-ups to ANOVA in SPSS Sig. levels between pairs of groups Groups that do not differ And one that does (from the other 2) 1 2 3

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KNR 445 Statistics ANOVA (1w) Slide 17 Follow-ups to ANOVA in SPSS 1 So TV Movie differs from both Soap Opera and infomercial, significantly Soap Operas and infomercials do not differ significantly

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KNR 445 Statistics ANOVA (1w) Slide 18 Assumptions to test in One-Way 1. Samples should be independent (as with independent t- test does not mean perfectly uncorrelated) 2. Each of the k populations should be normal (important only when samples are smallif theres a problem, can use Kruskal-Wallis test) 3. The k samples should have equal variances (this is the homogeneity of variance assumption, and well look at it shortlyviolations are important mostly with small samples and unequal ns) 1

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KNR 445 Statistics ANOVA (1w) Slide 19 Homogeneity of variance - SPSS 1. Click on the options button 2. Choose homogeneity of variance 3. Click continue

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KNR 445 Statistics ANOVA (1w) Slide 20 Homogeneity of variance - SPSS Homogeneity test output As you can see, no problems here. The test has to be significant for there to be a violation

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Interpret output The amount of aggression arising from watching TV changed according to the type of program watched, F(2,12) = 7.38, p .05. Tukeys HSD follow-up tests showed that those watching violent movies (M = 3) experienced less aggression than those watching soap operas (M = 8) or infomercials (M = 9). There was no difference in aggression level between those who watched soap operas and those who watched infomercials. KNR 445 Statistics ANOVA (1w) Slide 21 1