Research paper. One-way Analysis of Variance (ANOVA) Research paper. SPSS output. Learning objectives. Alcohol and driving ability

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1 Research paper Alcohol and driving ability One-way Analysis of Variance (ANOVA) Thirty-six people took part in an experiment to discover the effects of alcohol on drinking ability. They were randomly assigned to three conditions: placebo (no alcohol), low alcohol and high alcohol. The non-alcoholic drink looked and tasted exactly the same as the other drink. Participants were weighted and given the appropriate amount of drink. After half an hour of drinking, participants drove in a simulator for ten minutes, and the number of errors made was automatically registered by the computer. 1 2 Research paper SPSS output Results: A one-way ANOVA revealed a significant effect of the amount of alcohol on the error rate (F(2,33) = 9.91; p = 0.001). Degrees of Freedom ANOVA P-value SCORE One-way ANOVA?????? Sum of Squares df Mean Square F Sig. Between Groups F(2,33) = 9.91; p = 0.001???? Within Groups Total Learning objectives ANOVA Principles of ANOVA Null Hypothesis: The means of all groups are equal. Read research papers Experiment: Alcohol has no influence on driving ability Read SPSS s printouts Between-groups vs. Within-groups 5 6

2 Within-groups Within-groups Group 1 Group 2 Group 3 Sources: Individual differences Experimental error Alternative Names: within, error 7 8 Between-groups Between-groups Group 1 Group 2 Group 3 Sources: Treatment effects Individual differences Experimental error Alternative Names: treatment; between; systematic 9 10 Broadly: F is the ratio between Between-groups and Within-groups Small F: The larger F the more likely to reject the null hypothesis 11 12

3 Large F: Large F: P-value given by F-distribution: F(dfbetween, dfwithin) Degrees of Freedoms: df between = groups 1 df within = participants groups Research Paper p-value Important: Rejection of null hypothesis means at least one of the means is different from at least one other mean, but we do not know exactly which means are different from which other means! F(2,33) = 9.91; p = Degrees of freedom One-way = one factor = one independent variable 17 18

4 SPSS output ANOVA ~ Variance SCORE Between Groups Sum of Squares df 2 Mean Square F Sig One-way Analysis of Variance Part 2 Within Groups Total p-value Research paper Research paper Alcohol and driving ability Twelve people took part in an experiment to discover the effects of alcohol on drinking ability. The experiment included three conditions: placebo (no alcohol), low alcohol and high alcohol. The non-alcoholic drink looked and tasted exactly the same as the other drink. Participants were weighted and given the appropriate amount of drink. After half an hour of drinking, participants drove in a simulator for ten minutes, and the number of errors made was automatically registered by the computer. Each participant performed the task in all three conditions. Results: A repeated-measures ANOVA revealed a significant effect of the amount of alcohol on the error rate (F(2,22) = 10.83; p = 0.001). Repeated-measure???? 12 participants F(2,22) = 10.83; p = Repeated-measures ANOVA Learning objectives Between groups Degrees of freedom ~ Variance p-value Tests of Within-Subjects Effects Principles of repeated-measures ANOVA Measure: MEASURE_1 Type III Sum Source of Squares df Mean Square F Sig. ALCOHOL Sphericity Assumed Greenhouse-Geisser Error(ALCOHOL) Sphericity Assumed Greenhouse-Geisser Read research papers Read SPSS s printouts 23 24

5 Two experimental designs Total (between participants) Between-participants design: Experimental design in which different participants serve under the different treatment levels Within-participants design: Experimental designs in which each participants receives all levels if at least one independent variable Total Variance Partitioning (between participants) Total Betweengroups Withingroups Partitioning Total Error Betweengroups Individual diff Degrees of freedom Broadly: F is the ratio between Between-groups and Error (Within without individual differences) dftotal = participants * groups 1 dfindividual_differences = participants 1 dfwithin = dftotal dfindividual_differences dfbetween = groups 1 P-value given by F-distribution: F(dfbetween, dferror) dferror = df within - dfbetween 29 30

6 Repeated-measures ANOVA Advantages Tests of Within-Subjects Effects Measure: MEASURE_1 Type III Sum Source of Squares df Mean Square F Sig. ALCOHOL Sphericity Assumed Greenhouse-Geisse Error(ALCOHOL Sphericity Assumed Greenhouse-Geisse Avoidance of variability from participant to participant Require fewer participants than betweenparticipant designs Error (without individual differences) Report Greenhouse-Geisser Disadvantage Counterbalancing Order effects or carry-over (practice) effects An arrangement of treatment conditions design to balance practice effects Counter balancing for avoidance Example: Participant: Placebo; Low Alcohol; High Alcohol Participant: Placebo; High Alcohol; Low Alcohol Participant: Low Alcohol; Placebo; High Alcohol Participant: High Alcohol; Placebo; Low Alcohol Participant: Low Alcohol; High Alcohol; Placebo Participant: High Alcohol; Low Alcohol; Placebo Participant: like first participant 33 34