Psych 610 Handout #21, p. 1Prof. MooreTHREE-WAY BETWEEN-SUBJECT FACTORIALHoursHours61224726122472Visual10(100)90(900)70(700)50(500)10(100)50(500)70(700)60(600)Audio-Visual40(400)140(1400)130(1300)100(1000)20(200)70(700)170(1700)130(1300)Rhode Island RedsPlymouth RocksExperiment is on imprinting of chicks to wooden decoy, Row factor (Cue) is whether the decoy“clucks” (audio-visual) or not (visual). Column factor (Period) is hours of age (6, 12, 24, or 72) attime of first exposure to cue. Panel factor is Breed of chick (Rhode Island Red versus PlymouthRock). Data are minutes out of 180 spent following the decoy. Ten chicks are assigned a random toeach CPB combination. The table gives the cell means with cell totals in parentheses.I. Computing the ANOVAA. If needed, get pooled means and totals for various 2-way and 1-way matrices. Notice thatthese matrices show the means we need to graph various effects.Grand75.625(12100)6122472Period20(800)87.5(3500)110(4400)85(3400)VA-VCue51.25(4100)100(8000)RIRPRBreed78.75(6300)72.5(5800)6122472Period by CueV10(200)70(1400)70(1400)55(1100)A-V30(600)105(2100)150(3000)115(2300)6122472Period byBreedRIR25(500)115(2300)100(2000)75(1500)PR15(300)60(1200)120(2400)95(1900)RIRPRCue by BreedV55(2200)47.5(1900)A-V102.50(4100)97.5(3900)B. Compute the basic ratios[T] = 121002 = 915062.5 160[C] = 41002 + 80002 = 1010125 80[B] = 63002 + 58002 = 916625 80[P] = 8002 + 35002 + 44002 + 34002 = 109525040[CB] = 22002 + 19002 + 41002 + 39002 = 101175040[CP] = 2002 + 14002 … + 30002 + 23002 = 121150020[BP] = 5002 + 23002 … + 24002 + 19002 = 113450020[CBP] = 1002 + 9002 … + 17002 + 13002 = 125900010[Y] = (given) 1334000C. Compute the various SSSSM = 915062.5SSC = 1010125 – 915062.5 = 95062.5SSB = 916625 – 915062.5 = 1562.5SystematicSources SSP = 1095250 – 915062.5 = 180187.5SSCB = 1011750 – 1010125 – 916625 + 915062.5 = 62.5SSPB = 1134500 – 10952.50 – 916625 + 915062.5 = 37687.5SSPC = 1211500 – 1095250 – 1010125 + 915062.5 = 21187.5SSCPB = 1259000 – 1011750 – 1211500 – 1134500 + 1010125+ 916625 + 1095250 – 915062.5 = 8187.5(Note: The sum of the various SS for systematic sources equals 1259000. This is equalto [CPB] or the sum of the squared cell totals.]Error Source SSS/CPB = 1334000 – 1259000 = 75000D. Compute MS values and enter in tableSource df SS MS F pMean 1 915062.50 915062.5 1756.93 < .01Cue 1 95062.50 95062.5 182.52 < .01Period 3 180187.50 60062.5 115.32 < .01Breed 1 1562.50 1562.5 3.00 nsC x P 3 21187.50 7062.5 13.56 < .01C x B 1 62.50 62.5 .12 nsP x B 3 37687.50 12562.5 24.12 < .01C x P x B 3 8187.50 2729.17 5.24 < .01S/CPB 144 75000.00 520.83160 1334000.00Checks: ∑df = # of observations = 10 S/cell x 16 cells∑SS = [Y] = 1334000.00F*(1, 120) = 3.92 (no value available for dferror = 144)F*(3, 120) = 2.68 (no value available for dferror = 144)20406080100120140160180Mean Minutes FollowingRhode Island RedsPlymouth Rocks6122472 6 12247220406080100120140160180Mean Minutes FollowingTime PeriodTime Period6122472612247220406080100120140RhodeIslandRedsPlymouthRocksA-VVA-VVPRRIRA-VVA-VVHandout #21, p. 4Cell MeansTime Period x CueTime Period x BreedCue x BreedTime PeriodTime Period20406080100120140160180Mean Minutes FollowingHoursRIRPR6,000 12,000 24,00072,000Breed x TimeHandout #21, p.