Research paper. Split-plot ANOVA. Split-plot design. Split-plot design. SPSS output: between effects. SPSS output: within effects

Transcription

1 Research paper Effects of alcohol and caffeine on driving ability Split-plot ANOVA conditions: No alcohol; no caffeine alcohol; no caffeine No alcohol; caffeine Alcohol; caffeine Driving in simulator Error rate Split-plot design 0 February 00 0 February 00 Split-plot design Split-plot design Alcohol as between-participants factor No Alcohol Participant No caffeine Caffeine Participant Alcohol No caffeine Caffeine Caffeine as within-participants factor 0 Meaning: participants in the no alcohol condition participants in the alcohol condition But all of them in the caffeine/no caffeine conditions 0 February 00 0 February 00 SPSS output: between effects SPSS output: within effects Main effect of caffeine Main effect of alcohol Tests of Between-Subjects Effects Measure: MEASURE_ Transformed Variable: Average Type III Sum Source of Squares df Mean Square F Sig. Intercept ALCGROUP Error.. Tests of Within-Subjects Effects Measure: MEASURE_ Type III Sum Source of Squares df Mean Square F Sig. CAFFEINE Sphericity Assumed Greenhouse-Geisse CAFFEINE * ALCGROUP Sphericity Assumed Greenhouse-Geisse Error(CAFFEINE) Sphericity Assumed.000. Greenhouse-Geisse Interaction between 0 February 00 caffeine and alcohol 0 February 00

2 SPSS output: cell plot Research paper of MEASURE_ CAFFEINE : The number of driving errors was analyzed with a split-plot ANOVA with alcohol as the betweenparticipants factor and caffeine as the withinparticipants factor. The test indicated a main effect of alcohol (F(, ) =., p < 0.00) and of caffeine (F(, ) =., p < 0.00). The interaction between alcohol and caffeine was significant as well (F(, ) =., p < 0.00). ALCGROUP 0 February 00 0 February 00 Comparison Between-participants design: Alcohol: (F(, ) =., p < 0.00) Caffeine: (F(,) =., p < 0.00) Alcohol x caffeine: F(,) =., p < Within-participants design: Alcohol (F(, ) =., p < 0.00) Caffeine (F(, ) =., p < 0.00). Alcohol x Caffeine: (F(, ) =., p < 0.00). Mixed design: Alcohol (F(, ) =., p < 0.00) Caffeine (F(, ) =., p < 0.00). Alcohol x Caffeine: (F(, ) =., p < 0.00).. Example Do and differ in the ability to perceive colours? The study assumed that will be better than at perceiving differences in colours from a very early age. They therefore tested two different age groups (-year-olds and -year-olds) on a standard colour perception test and compared the performance (marked out of 0) of and. 0 February February 00 Performance Cell plot -year-olds -year-olds of SCORE years-old GENDER -years-old AGE 0 February 00 0 February 00

3 . Example Age: F(,) = 0.; p = 0.00 Gender: F(,) =.; p < 0.00 Age x Gender: F(,) =.; p = 0.00 Has the academic ability fallen in the last 0 years? The study compared the A-level performance of a sample of students who the exams in and a sample who took them in. Each had taken an examination in both English and Mathematics. In order to ensure that the exams are marked to the same criteria the samples are re-marked by examiners. 0 February 00 0 February 00 New marks Cell plot Students from Mathematics English Students from Mathematics English 0 of MEASURE_ 0 0 SUBJECT Math English YEAR 0 February 00 0 February 00 More independent variables Subject: F(,) = 0.00; p = 0. So far: x factorial design x factorial design Year: F(,) =.; p = 0.0 Subject x Year: F(,) = 0.0; p = 0. Possible: arbitrary number of independent variables and levels Examples: x x factorial design (Three-way ANOVA) x x x x x x factorial design 0 February 00 However, more then independent variables does not make sense! 0 February 00

4 Example for xx design Typical Visual Search results Does advance information help in visual search? L Reaction time Chevron Number of items 0 February February 00 Experimental procedure Design Target: L, Chevron, absent (catch-trials) Advance Information (prime): Valid, Invalid, Neutral Number of items:, xx ANOVA repeated-measures 0 February 00 0 February 00 Mean Reaction Time (ms) Valid L Valid Chevron Neutral L Neutral Chevron Invalid L Invalid Chevron Validity: F(,)=0.,p < 0.00 Target: F(,)=., p < 0.00 Items: F(,)=0.0, p < 0.00 Validity x target: F(, ) =., p < 0.00 Validity x items: F(, ) = 0., p=0. Target x items: F(,) =.0, p=0.00 Number of Items Validity x target x items: F(,)=.,p= February 00 0 February 00

5 : Simple effect Power of test Target Chrevon: Validity : F(,)=., p < 0.00 Item: F(,)=., p < 0.00 Validity x items: F(,)=.,p = 0.0 Probability of correctly rejecting a false H 0 Or not making Type II error Target L: Validity: F(,)=., p=0. Item: F(,)=., p < Validity x items: F(,)=., p = 0.0 Decision Reject H 0 State of the world: H 0 true Type I error State of the world: H 0 false Correct decision Fail to reject H 0 Correct decision Type II error 0 February 00 0 February 00 Influences on power of test a-level (Probability of Type I error) Grand mean True difference between the null hypothesis and the alternative hypothesis Sample size Variance Properties of the test employed 0 February 00 0 February 00 Grand mean 0 February February 00