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2 x 2 Analysis of Variance (Ch. 14) Study Description Hyperactivity in children can be treated by counseling, by medication, or both. The following data are from an experiment designed to evaluate the e'ectiveness of these two treatments. The dependent variable is a measure of attention span (how long each child was able to concentrate on a specic task, higher scores indicate better per- formance). Conduct a 2 x 2 Analysis of Variance with alpha = .05 to evaluate the e'ectiveness of each treatment. Descriptive Statistics Factor B: Medication Factor A: Counseling Level 1: No Level 2: Yes Leve11:No 11:6 n=6 T:12 T:24 TR0w1236 33:4 35210 Level 2: Yes 91 : 6 n : 6 T227 T254 TROW2=81 SS = 5.5 SS = 4 TCOLI : 39 TCOLZ : 78 G: 117;N = 24;EX2 =972 2 x 2 Means Factor B: Medication Factor A: Counseling Level 1: No Level 2: Yes Mean Level 1: No 2 4 3 Level 2: Yes 4.5 9 6.75 Mean 3.25 6.5 2 x 2 Graph 13 _ Factor A - Level 1'. 8 Factor A - Level 2: 7 _ O 6 _ E 5 5' 4 3 2 1 _ |. (Level 1) (Level 2) Factor B: Summary Table Source SS df MS Between Treatments Factor A F = Factor B = F = A X B Within Treatments Total Sum of Squares (SS) . SStotal = EX2 _ G2 . S'S within treatments = L SS inside each treatment . Sbetween treatments = total -within treatments . SSA = ROW nROW . SSB = Z nCOL . SS AXB = between treatments - SSA - SSB Degrees of Freedom (df) . d ftotal = N - 1 . dof within treatments = _ defeach treatment . df between treatments = number of cells (or treatments) - 1 . df A = number of rows - 1 . dfB = number of columns - 1 . dfAXB = df between treatments - df A - df B Variances (MS) . MS within treatments SS within treatments dof within treatments . MSA SSA df A SS B . MSB = dfB SS AXB . MSAXB df AXB F-ratios (F) MSA . FA = MSwithin treatments MS B . FB = MSwithin treatments MS AXB . FAXB = MSwithin treatments 2Critical Value (Table p. 705) . df Numerator = df Denominator Critical Value of F = Simple Main Effects (One-Way ANOVAs) Simple Main Effect of Factor B at each level of Factor A . Describe the Simple Main Effect of Factor B at Level 1 of Factor A. . Describe the Simple Main Effect of Factor B at Level 2 of Factor A. Conclusion Report and describe the Main Effect for Factor A, the Main Effect for Factor B, and the Interaction between Factor A and Factor B (including a description of the simple Main Effects). Main Effect for Factor A: Main Effect for Factor B: Interaction between Factor A and Factor B: 3