Comprison Procedures Single Fctor, Between-Subects Cse /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects
Two Comprison Strtegies post hoc (fter-the-fct) pproch You re interested in discovering which popultion mens differ. Perform the ANOVA. If is not reected, no popultion mens differ; so stop. If is reected, perform the Tukey SD procedure to test ll pirwise comprisons of popultion mens. priori (plnned) pproch Before conducting the experiment, you mke specific predictions bout which popultion mens differ. Perform plnned comprison t-tests, one per prediction, to determine which of the hypothesized differences between popultion mens exceeds chnce. /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects
The post hoc pproch 5. A resercher bkes smll cookies with icing of one of three different colors (green, red, or blue). The resercher offers cookies to subects while they re performing boring tsk. Ech subect is run individully under the sme conditions, except for the color of icing on the cookies. Six subects re rndomly ssigned to ech color. The number of cookies consumed by ech subect during the 3-minute session is shown here: Green Red Blue 3... 7. 4. 7. 4. 8.. 4. 6. 3. 9. 8... 6.. () Does the evidence indicte tht color of cookie influences mount eten? (lph =.5) (b) If n effect is found, determine which pir(s) of popultion mens differ? (lph =.5) /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects 3
ANOVA: Cookie Dt Test of omogeneity of Vrinces NUMBER Levene Sttistic df df Sig.. 5.38 ANOVA NUMBER Between Groups Within Groups Totl Sum of Men Squres df Squre F Sig. 78.778 39.389 5.45. 4.833 5 7.656 93.6 7 NUMBER green red blue Totl N Descriptives 95% Confidence Intervl for Men Std. Lower Upper Men Devition Std. Error Bound Bound Minimum Mximum 6 6.5 3.57.438.895.85 3.. 6 7..976.8563 4.7987 9.3 4.. 6.3333.533. -.938 4.964. 7. 8 5.778 3.3747.7954 3.5996 6.956.. /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects 4
ypothesis Test : µ = µ = µ Reect F = 5.45 Reect : At lest two of. if F 3.5;,5 the popultion mens differ. > 3.68. If is reected: It is then pproprite to perform test tht compres prticulr popultion mens. Commonly, investigtors mke ll pirwise comprisons while keeping experiment-wise error t pproximtely lph =.5. If is not reected, stop. /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects 5
Preliminry clcultions rmonic n Studentized Rnge Sttistic Tukey s SD post hoc test Clculte w, the criticl difference : MSE w = qα ; k, ν n~ α = significnce level used in the ANOVA =.5 k = number of mens = 3 ν = degree of freedom ssocited with MSE = 5 MSE = men squre error from the ANOVA = 7.656 ~ k 3 n = = = 6 + +... + + + n n n 6 6 6 From Studentized Rnge Sttistic tbles : q.5;3,5 w = 3.67 = 3.67 7.656 6 k = 3.67.3 = 4.46 /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects 6
Tukey s SD post hoc test: Expressing ll Pirwise ypothesis Tests t Once : µ : µ Reect µ µ if = W > 4.46. x 3 =.333 x =6.5 x =7. x 3 =.333 -- 4.67* 4.667* x =6.5 --.5 x =7. -- *Reect. /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects 7
The priori pproch Ex. 5. One study experimented with the order of cognitive orgnizers tht structure the mteril for the lerner. A group of thirty persons ws rndomly split into three groups of ten ech. Group received orgnizing mteril before studying instructionl mterils on mthemtics; Group received the orgnizer fter studying the mthemtics; nd group 3 received the mth mterils but no orgnizing mteril. On -item test over the mthemtics covered, the following scores were erned: Before After None 5 4 5 4 5 4 4 3 6 7 6 8 6 7 3 6 3 6 4 4 4 4 4 3 7 5 Use plnned contrsts to test () the difference between the two orgnizer groups nd (b) whether the mens of the two orgnizer groups differ from the no orgnizer group. /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects 8
Dt Anlysis Report Mth test score Orgnizer Men N before 5.6 fter 4. none 3.9 Totl 4.5 3 Test of omogeneity of Vrinces SCORE Levene Sttistic df df Sig..847 7.44 ANOVA SCORE Between Groups Within Groups Totl Sum of Men Squres df Squre F Sig. 8. 9. 4.8.3 6.3 7.7 79.5 9 /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects 9
= weight ssigned to the th group = the men of the th group MSE( N Contrst : where Σ = ()5.6 + ( )4. =.6 Preliminry Clcultions Compute L, liner combintion, for ech hypothesis test : L = Σ X = And compute the estimted stndrd error of the contrst : s ψˆ L = Σ L = Σ ψˆ = = + sψˆ =.7( + ) = Contrst : s X X X N +... + N.454 =.674 = ( )5.6 + ( )4. + ( )3.9 =.9 c.5.5 ( ).7( + + ) = c ).34 =.584 /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects
ypothesis Tests Contrst : Reect t = : µ µ L s ψˆ : µ µ Reect. if = t <.5 or t.6 = =.374.674 <.5. Contrst : µ µ : µ 3 = µ µ : µ 3 Reect if t <.5 or t = L s ψˆ.9 = =.54.584 Do not reect. t <.5. Use df for MSE : df = Σ( N ) /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects
SPSS Output Contrst Coefficients Contrst Orgnizer before fter none -.5.5 - Contrst Tests Mth test score Assume equl vrinces Does not ssume equl vrinces Contrst Vlue of Sig. Contrst Std. Error t df (-tiled).6.6739.374 7.5.9.5836.54 7.35.6.653.449 7.54.5.9.69.498 6.66.53 /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects