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Carleton University
PSYC 2002
Donna Mailloux

Analysis of VarianceANOVA Anovas test only twotailed hypotheses Independent samples between subjects dependent samples within subjects ANOVA statistic is F Kof levels Conditionslevels xT TG N totalof subjects nsno significant difference sigsignificant difference nof subjects for each level Oneway Between Subjects ANOVA Notations IVs are called factors each condition of factor is called level oneway ANOVA uses conditions from 1 IV Why do ANOVAs researchers more often have more than two levels to study more accurately describes the relationship linear nonlinear maximum information for cost and effort Why not use seperate tests experimentwise error rate would bealpha015 if three separate ANOVAs keep the experimentwise error at the alpha you selected by simultaneously different alphas Assumptions DV measured on intervalratio scale scores are normally distributed independence observations homogeneity of variance will not be testing Post Hoc Tukeys HSD test done when you reject the null hypothesis and k3 difference is significant always use at the 005 alpha not sure how large the difference between the means need to be in order to say the 2 groups are significantly different from each other when fishing around in the data you increase the probability of a type 1 error for each pairwise comparison you make HSD answer is the minimum absolute difference required to conclude that 2 means differ significantly from eachother if no significant difference then dont do post hoc if significant then must do post hoc to determine which means are different therefore account for significant finding Ttest VS Ftest ttestdifference between two meanserror ftestdifference in variance between the conditionserror Variance Portions Betweentreatment variance variance due to treatment effectsvariance due to error Withintreatment variance variance due to error such as experimental error or individual differences F distribution Fvariance for effecterrorvariance for error When H0 is true F0errorerror1 When H0 is false Ftreatmenterrorerror 1 positively skewed cant be less than 0 mean of 1 alpha 005 388 alpha 001 693 Effect Size n2 used to represent effect sizes with ANOVAs Step 1 Create Hypothesis Eg H0u1u2u3 H1 at least one mean is different from the others Step 2 Determine the alpha and critical regions K1 and NK Eg at alpha 005 3 levels and 15 subjects2 12388 Step 3 check assumptions Step 4 calculate F obtained and do chart Eg a each level calculate x b calculate average for each level xn c calculate x2 for each level and a total d calculate SS for each level and then the SStotal e compute SS withinsubjects SS for each level f compute SS between groups SStotalSSwn g computer MS for bn and wn h compute F obtained Step 5 if appropriate calculate post hoc if reject the null a find QK in chart need to know DFwn and K b compute HSD Eg 446 c determine the differences between all means mean1mean2m2m3m1m3 d compare each difference to the HSD Eg mean1 VS mean 2 2 446 ns mean1 VS mean3 5 446 sig Step 6 Graph level means Step 7 calculate n2 effect size Step 8 report the results Eg F obtained exceeds Fcriticaltherefore reject the null hypothesis and conclude that there is a relationship between the participants depression and amount of light but only for the low and high conditions OR does not exceed F critical so fail to reject the null and say there is not relationship betweenTwoway Between Subjects ANOVA Assumptions perform this ANOVA if it is a 2way design and a all cells contain independent samples of participants b the dependent variable measures interval or ratio scores that are approx normally distributed c there is homogeneity of variance Remember when looking at the interaction compare the cell means and when looking at a main effect compare the level means Variance Portions Betweentreatment variance factor AB interaction variance Withintreatment variance variance due to error such as experimental error or individual differences Interpretations consider the effect sizes when trying to detrermine what significant effect to focus on in interpretation those with highest effects are most important If interaction effect size is significant interpret this and NOT main effects but if not significant interpret main effects Step 1 State the hypotheses for all three effects determine the alpha and critical values for each effect Step 2 follow the example and fill in everything as you see below Step 3 compute SS total Step 4 compute SS bw groups for A main e
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