Four Steps to compute the F-Test: STEP #1 2 Compute the sums and means X X for each level. Then add together thes from all the levels to get the total. Add together the Xs S get the total to from all levels to STEP #2 Computing the Total Sum of Squares 1. Compute the total sum of squares (SS tot) SS = EX (EX tot) 2 tot tot N SO and SS tot 629 SS (85) 15 7225 tot 629 15 SS tot 629 481.67 = 147.33 - STEP #3: Computing Sum of Squares Between 2. Compute the sum of squares between groups (SSbn) SSon bn = (Sumof scores in thecolumn n of scores in thecolumn (EX tot) (or) 2 N SO and SSbp = ((40) (30) (15)) (85)) + 5 + - 15 SS bn = (320 + 180 +45) - 481.67 SSb = 545 - 481.67 = 63.33 bn STEP #4: Computing the Sum of Squares Within 3. Compute the sum of squares within groups (SSwn) SSwn = SS tot - SSbn In the example, SS tot is 147.33 and SSb is 63.33, so SSwn = 147.33 - 63.33 = 84.00 Filling in the first column of the ANOVA summary table, we have Source Sum of Squares df Mean Square F Between 63.33 dfon MS bn Fobt Within 84.00 dfwn MSwn Total 147.33 dftot STEP #5: Computing Degrees of Freedom 4. Compute the degrees of freedom 1. The degrees of freedom between groups equals k 1 - 2. The degrees of freedom within groups. equals N - k 3. The degrees of freedom total equals N - 1 ANOVA table, almost complete Sum of Squares df Mean Square Source Between 63.33 Within 84.00 Total 147.33 14 221 F Fobt MSbn MSwn STEP #6: Computing the Mean Squares 5. Compute the mean squares MS SS bn bn df bn 63.33 MSbn 31.67 2 MS wn SS wn df wn 84 MS wn 7.00 12 STEP #7Computing Fobt (finally!) 6. Compute F MS obt Fobt bn = MS wn Source Sum of Squares df Mean Square F Between 63.33 2 31.67 Fobt Within 84.00 12 Total 147.33 21 7.00 14 MSbn 31.67 = 4.52 Fobt = MSwn 7.00 Now the completed ANOVA summary table is Source Sum of Squares df Mean Square F Between 63.33 Within 84.00 12 Total 147.33 14 221 31.67 4.52 7.00 MSbn 31.67 = = 4.52 Fobt MSwn 7.00 Now the completed ANOVA summary table is Source Sum of Squares df Mean Square F Between 63.33 Within 84.00 12 Total 147.33 14 227 31.67 4.52 7.00 Page < 12 > of 26 - ZOOM + ANOVA EXAMPLE & Step #1, cont'd... Factor A: Perceived Difficulty TABLE 13.4 Data from Perceived Difficulty Experiment Level A: Easy Level A: Medium Level A: Difficult 9 4 1 12 6 3 4 8 8 2 5 7 10 2 Totals EX = 40 = 30 = 15 EX = 85 ? = 354 X = 220 EX = 55 EX = 629 n = 5 n = 5 n = 5 N = 15 X = 8 X = 6 X = 3 k = 3