Computational Formulas for One-Way and Two-Way ANOVA in Psychology, Cheat Sheet of Psychology

Download Computational Formulas for One-Way and Two-Way ANOVA in Psychology and more Cheat Sheet Psychology in PDF only on Docsity! PSYCHOLOGY 315 DR. MCFATTER Computational Formulas for ANOVA One-Way ANOVA Let a = # of levels of the independent variable = # of groups N = total # of observations in the experiment n1 = # of observations in group 1, etc. H0: µ1 = µ2 = µ3 = . . . = µa ΑNOVA analyzes sample variances to draw inferences about population means. Sample variances can always be calculated as SS/df and these sample variances are called mean squares (MS): SST = 92 + 82 + . . . + 12 + 52 - (80)2/15 = 93.333 SSB = (402 + 252 + 152)/5 - 802/15 = 63.333 SSW = 93.333 - 63.333 = 30.000 An alternative computational approach emphasizing the conceptual basis of ANOVA is given below. This is the variance of all scores in the experiment = 6.667. This is the average of the variances within the groups = 2.50. (1.222 + 1.872 + 1.582)/3 = 2.50. This is n times the variance of the means = 5(6.333) = 31.667. Multiple Comparisons: tCrit is the critical value from a t-table using the df of the error term from the ANOVA table. The error term is always the denominator of the F-ratio. Thus, in the above example, the error df would be 12. The MSError would be 2.50; n is always the number of observations each mean you’re comparing is based on. Example. X1 X2 X3 Placebo Drug A Drug B 9 5 2 8 4 4 8 5 3 6 8 1 9 3 5 Sum 40 25 15 80 M 8 5 3 5.333 s 1.224745 1.870829 1.581139 ANOVA Summary Table Source SS df MS F p Between 63.333 2 31.667 12.67 0.0011 Within 30.000 12 2.500 Total 93.333 14 6.667 SSTotal SSBetween SSWithin s SS df MS2 = = ( ) SS X X NTotal = − ∑∑ 2 2 ( ) ( ) ( ) ( ) SS X n X n X n X NBetween a a = + + + − ∑ ∑ ∑ ∑1 2 1 2 2 2 2 2 K SS SS SSWithin Total Between= − df aBetween = −1 df N aWithin = −F MS MS Between Within = df NTotal = −1 ( ) $σ T Total X X N N MS2 2 2 1 = − − = ∑∑ $σW a Within s s s a MS2 1 2 2 2 2 = + + + = K $ $σ σB M Betweenn MS2 2 = = LSD t MS nCrit Error= 2