Psych 610 Handout #7, p. 1Prof. MooreTREND ANALYSISBetween-groups experiment to test a method of teaching English spelling to adults who are learningEnglish. Dependent variable is the number of errors on a standardized spelling test. Independentvariable is the number of learning sessions using the method before the test. n = 10.# of sessions 1 2 3 4 5 6YT=JY # of errors 17.8 19.5 16.3 12.7 10.7 8.8 14.3Source SS df MS FMean 12269.4 1 12269.4 1740.34Between 890.6 5 178.12 25.27Within 380.7 54 7.05Graph of the cell means:Handout #7, p. 2I. Is there a linear trend?cjL = -5 -3 -1 +1 +3 +5SSLinear = 10[-5(17.8) + -3(19.5) + -1(16.3) + 1(12.7) + 3(10.7) + 5(8.8)]2(70)= 10(75)2 = 803.57 70MSLin = 803.57 = 803.57 1Flin = 803.57 = 113.98 p < .05 Yes.7.05Is there anything left over?SSResidual = 890.60 - 803.57 = 87.03 MSRes = 87.03 = 21.76 4Fres = 21.76 = 3.09 p < .05 Yes. 7.05II. Is there a quadratic trend?cjQ = 5 -1 -4 -4 -1 5SSQuadratic = 10[5(17.8) + (-1)(19.5) + (-4)(16.3) + -4(12.7) + -1(10.7) + 5(8.8)]2(84) = 10(-13.2)2 = 20.7484MSQuad = 20.74 1Fquad = 20.74 = 2.94 n.s. No. 7.05Is there anything left over?Handout #7, p. 3SSRes = 87.03 - 20.74 = 66.29 MSRes = 66.29 = 22.10 3Fres = 22.10 = 3.13 p < .05 Yes. 7.05III. Is there a cubic trend?cj cubic = -5 7 4 -4 -7 5SSCubic = 10[-5(17.8) + 7 (19.5) + 4(16.3) + -4(12.7) + -7(10.7) + 5(8.8)]2(180)= 10(-31.0)2 = 53.39 180MSCub = 53.39 1Fcub = 53.39 = 7.57 p < .05 Yes.7.05Is there anything left over?SSRes = 66.29 - 53.39 = 12.90 MSRes = 12.90 = 6.45 2Fres = 6.45 = .91 n.s. 7.05Stop extracting trends here unless you have planned comparisons (that is, questions of a prioritheoretical importance) which involve the higher order trends.IV. Examining the pattern of trend coefficients tells us what they test, but in the effects (alpha j), not inthe raw means.Handout #7, p.
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