PSYCHOLOGY 210 Dr. Jennifer Kunz Module 8: One- Way ANOVA – Chapter 12 The Analysis of Variance (ANOVA) is a statistic that allows us to compare more than two samples by comparing the differences in...

...


PSYCHOLOGY 210 Dr. Jennifer Kunz Module 8: One- Way ANOVA – Chapter 12 The Analysis of Variance (ANOVA) is a statistic that allows us to compare more than two samples by comparing the differences in means between treatments, through a comparison of variances. In its simplest form, the one-way ANOVA looks at only one independent variable that has at least three levels. Here, two variances are computed and compared: the variability between the condition or levels and the average variability within the sample conditions, which is sometimes considered our error variance, or variability due to chance. In this module you will use run a one-way ANOVA by hand as in chapter 12. We have discussed these topics in lecture and in the textbook. Please review these ideas. Fill in the blanks to complete the sentences. (.5 points/question) 1. Using an ANOVA, we are determining if the variance ___________groups is greater than the variance _____________ groups. 2. The output of an ANOVA is the ____-ratio. If our ___-critical value is smaller than the calculated value, we would __________ the null hypothesis. 3. If the between variance is large compared to the _______ variance, will the F-ratio be large or small? 4. The ___________ hypothesis says that at least one of the sample __________ is different from another. Does the type of reward you are given for completing chores effect how many chores you complete? Parents told their children that they would either receive praise, candy, or money after completing chores around the house. Below you will find a table of the number of chores completed by 15 children in one week. In addition, you will find the Means, Totals, and Sum of Squares values below each column for each treatment. Is there enough evidence to show that the type of reward effects the number of chores completed? Compute a one-way ANOVA following the steps below. (1 point/question). Praise Candy Money 0 2 2 0 4 3 2 0 1 1 1 4 2 3 5 Treatment: M1= 1 M2= 2 M3= 3 T= 5 T=10 T= 15 SS1= 4 SS2=10 SS3=10 5. Compute the following values: N = # of total scores = G = ∑T= grand total of all scores= ∑X2= k = # of conditions = n = # per group = 6. For the data above in the table, calculate SSTotal: SStotal = ΣX2 – (G2/N)  7. Now, calculate SSwithin: SSwithin = ΣSSeach treatment = 8. Finally, calculate SSbetween:  SSbetween = Σ(T2/n) – G2/N OR SStotal – SSwithin =  9. Calculate the degrees of freedom: dftotal= N-1 = dfwithin= N- k = dfbetween= k-1 = 10. Calculate the between and within treatments variance: MSbetween= SSbetween/dfbetween = MSwithin= SSwithin/dfwithin= 11. Finally, calculate the F -statistic F = MSbetween/MSwithin= 12. Can we reject the null hypothesis at the alpha of .05 level? Find the F-critical value using the correct degrees of freedom, then compare your F-calcluated to the F-critical to make a statistical decision. Fcritical = Fcritical(dfbetween, dfwithin) = Originals prepared by Pamela M. Schaefer, Ph.D.