Two Factor Completely Between Subjects Analysis of Variance /1/1 Two-Factor AOVA, Between Subjects 1
ypothetical alertness data from a x completely between subjects factorial experiment Lighted room Darkened room B 1 B Day person 3 1 A 1 3 1 3 1 ight person 1 3 A 1 3 1 3 Dependent variable: Alertness = 1 /1/1 Two-Factor AOVA, Between Subjects
Mean alertness scores in the x completely between subjects factorial experiment Lighted room Darkened room B 1 B Row mean Day person A 1 3 1 ight person A 1 3 Column mean /1/1 Two-Factor AOVA, Between Subjects 3
Sources of Information in a x Completely Between Subjects Factorial Design Lighted room Darkened room B 1 B Row mean Day person A 1 3 1 ight person A 1 3 Column mean Main effect of A Main effect of B A x B interaction Sampling error: estimated by pooled within-group variance Main effect of treatment A: estimated using variance of mean values of Factor A collapsed (i.e., averaged) over factor B Main effect of treatment B: estimated using variance of mean values of Factor B collapsed over factor A A x B interaction -- estimated by variance of mean values of all cells minus Treatment A minus Treatment B /1/1 Two-Factor AOVA, Between Subjects 4
ypotheses Tested in a x completely between subjects AOVA Main effect of A (day/night person) : a : µ = µ 1 : µ µ 1 Treatment A + error F = error A x B Interaction a : The two variables do not interact. : The two variables interact. A x B interaction + error F = error Main effect of B (lighting) : a : µ = µ 1 : µ µ 1 Treatment B + error F = error Lighted room Darkened room B 1 B Row mean Day person A 1 3 1 ight person A 1 3 Column mean /1/1 Two-Factor AOVA, Between Subjects 5
Exercise 7.1 A researcher tests the influence of different dosages of a drug on the detection of targets flashed briefly in the visual field. Target location is also manipulated: For some participants targets flash on the periphery of the visual field whereas, for other participants, targets flash toward the center of the visual field. Scores represent the number of targets identified in 1 trials. 18 participants are assigned randomly to conditions. Dosage Location Low Medium igh Peripheral 4 3 3 3 3 1 Central 4 6 3 5 5 4 3 4 (a) Does the evidence indicate that performance differs according to target location? (α =.5) (b) Does the evidence indicate that drug dosage and target location interact? (α =.5) /1/1 Two-Factor AOVA, Between Subjects 6
Mean Alertness Scores as a Function of Target Location and Drug Dosage 5 4 Detection 3 1 Low Medium igh Peripheral 3.33.67 1 Central 3 4 5 Collapsed.33 4. Drug Dosage /1/1 Two-Factor AOVA, Between Subjects 7
Preliminary Calculations Low Med. igh B 1 B B 3 ΣA i B 1 B B 3 Peripheral A 1 4 16 4 4 3 3 9 9 3 3 1 9 9 1 ΣB ij 1 8 3 1 Central A 4 6 4 16 36 3 5 5 9 5 5 4 3 4 16 9 16 ΣB ij 9 1 15 36 ΣB j 19 18 ΣX= 57 ΣX =17 ( ΣX ) CM = SS = ΣX total T SSA = Σ A T SSB = Σ B T SSAB = Σ i i j j AB 57 = = 18.5 18 CM = 17 18.5 = 36.5 CM CM ij ij T Σ 1 = 9 19 = 6 A i i 36 + 9 + 6 T Σ B j j 18.5 = 1.5 18 + 6 CM 18.5 =.333 1 = 3 8 3 9 1 + + + + 3 3 3 3 15 + 3 SSE = SS = 36.5 1.5.333 14.334 = 9.333 MSA = = 1 = 18 1 = 17 = = = ( MSB = MSAB = 1 = 1 = 1 1 = 3 1 = = Σ( SSE MSE = F F A total A B AB error AB i j total i SSA SSB SSA SSB SSAB 1)( A B ij = = SSAB error AB 1) = (1)() = 1) = (6) = 1 1.5 = 1.5 1.333 =.167 = 14.334 = 7.167 9.333 = =.778 1 MSA 1.5 = = = 16.67 MSE.778 MSAB 7.167 = = = 9.14 MSE.778 1.5.333 18.5 = 14.334 j /1/1 Two-Factor AOVA, Between Subjects 8
Summary Table and ypothesis Tests Source SS MS F A 1 1.5 1.5 16.7 B.333.167.14 AB 14.334 7.167 9.15 Error 1 9.333.778 Total 17 36.5 a : µ 1 Reject F = 16.7. Reject = µ : At least two of the population means differ.. if F.5;1,1 > 4.75. a : Variables A and B do not interact. : Variables A and B interact. Reject F = 9.15 Reject. if F.5;,1 > 3.89. /1/1 Two-Factor AOVA, Between Subjects 9
SPSS Output Levene's Test of Equality of Error Variances a Dependent Variable: CORRECT Dependent Variable: CORRECT Source Corrected Model Intercept LOCATIO DOSAGE LOCATIO * DOSAGE Error Total Corrected Total F 1 Sig..168 5 1.969 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept+LOCATIO+DOSAGE+LOCATIO * DOSAGE Tests of Between-Subjects Effects Type III Sum of Mean Squares Square F Sig. 7.167 a 5 5.433 6.986.3 18.5 1 18.5 3.71. 1.5 1 1.5 16.71..333.167.14.81 14.333 7.167 9.14.4 9.333 1.778 17. 18 36.5 17 a. R Squared =.744 (Adjusted R Squared =.638) /1/1 Two-Factor AOVA, Between Subjects 1
ildebrand-saints, L. & Weary, G. (1989). Depression and social information gathering. Personality and Social Psychology Bulletin, 15, 15-16. Depressed persons are thought to feel a lack of control They feel chronically deprived of information and, therefore, have a heightened tendency to seek information, including social information e.g., what other people are like /1/1 Two-Factor AOVA, Between Subjects 11
Method 345 undergraduates Screened using the Beck Depression Inventory (BDI) Final sample -- 4 depressed and 4 not depressed participants Cover story interview another participant (confederate) as part of a film for another study Task select 1 prepared questions from a set of 3 to ask the interviewee questions varied in how much revealing information they would elicit - 8 were highly diagnostic participants were also informed that they would be quizzed about the interview afterward (high informational utility) or that they would be free to leave (low informational utility) Independent variables informational utility high (quizzed) low (free to leave) depression depressed not depressed x completely between subjects factorial design ypotheses nondepressed participants will ask diagnostic questions only when information utility is high depressed participants will ask diagnostic questions whether information utility is high or low /1/1 Two-Factor AOVA, Between Subjects 1
Mean number of high diagnostic questions selected by level of depression and utility condition Informational Utility Mood igh Low Depressed 3. 4.7 ondepressed 3.4.75 Only difference to exceed chance ote: Mood x utility interaction, p <.5. /1/1 Two-Factor AOVA, Between Subjects 13
Mean number of high diagnostic questions selected by depression level and utility condition 4.5 4.1 umber Selected (-8) 4 3.5 3.5 3. 3..8 Depressed ondepressed igh Low Informational Utility /1/1 Two-Factor AOVA, Between Subjects 14