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v Debrieng What methods did we employ in this experiment? On each trial you rated the happiness evoked by an image of abstract art. There were no right or wrong answers; we were just interested in your interpretation of the art. You made yourjudgments under three different conditions. One condition was a normal condition, but the other two conditions might have seemed odd. In one condition you were asked to place (or pretend to place) a pen or pencil between your teeth. This is a special condition because the act of holding a pen in your teeth utilizes facial muscles in a way that is similarto when you smile. The experiment is investigating whether making a smilingtype face inuences yourjudgments of happiness in abstract art. Asecond condition is a kind of control condition where you held (or pretended to hold) a pen or pencil in your lips. This condition is just as odd as the teeth condition, but does not utilize muscles involved in smiling. The dependent variable is the happiness rating, with 0 indicating the piece of art does not evoke happiness at all and 100 indicating very much happiness. We will use a oneway analysis of variance (ANOVA) to explore whether the happiness ratings are equal or different across the three conditions. What do we predict participants will do? Why? The null hypothesis is that the population mean happiness rating is the same for all three conditions: 03 litre pen 2 \"Teeth Z lJLips. while the alternative hypothesis is that at least one of the means differs om the others 3: pi at pj for some i,j. fthe effect exists, you will reject the null hypothesis, and the mean for the pen in teeth condition will be larger than the other means. Formulas There are several ways to calculate the terms for an ANOVA. We will use formulas that make explicit the important parts of the approach. These formulas only apply to the case (as here} where there are equal sample sizes, n, for all groups. To calculate the ANOVA, you need to rst calculate the mean and variance of scores for each condition. This is done in the rst six questions. Now you compute two estimates of the population variance [ANOVA assumes that each condition has the same variance). The rst estimate is called Mean Square Between (WISE!) because it derived from the variance between groups. To compute it we rst calculate the variance of the means. For three groups the raw score formula is: : 21:1 I: _ (21:1 fate/3 32 B 2 This variance is then used to estimate the variance of the population with the following formula: M SB 2 nszg. where n is the number of scores in each group. The next step is to compute a second estimate of the population variance, which is called Mean Square Error {MSE}. (Sometimes this estimate is called Mean Square Within, because it is based on the variances within each condition.) This is done by pooling the variances within each group: MSE: Z:=' 5: The two estimates of population variance are then compared by computing the F ratio: MSB MSE' which has two degrees of freedom. The rst is for M83, dfnummmFK'1: where K is the number of groups. The second is for MSE, o'fdemmmm = NK where N is the total number of scores across all groups. F: Finally, you can calculate the pvalue for the F ratio. This is most easily done with an online calculator. Answer the questions using the data below. You will often nd it helpful to sort the data and calculate values using a spreadsheet such as Microsoft Excel, Sheets from Google apps, Open Ofce, or Numbers (Mac only). To import the data into a spreadsheet select and copy all the cells in the trialbytlial data table below and then paste them into an open page of the spreadsheet. Questions Use the trial-by-trial data to answer these questions. Question Answer Status Mean happiness for art with no pen: (The difference between your answer and the correct value must be less 53.272727272 Check Hint Correct than 0.01.) answer Mean happiness for art with the pen in your teeth: (The difference between your answer and the correct value must be less 40.090909090! Check Hint Correct than 0.01.) answer Mean happiness for art with the pen in your lips: (The difference between your answer and the correct value must be less 43.727272727: Check Hint |Correct than 0.01.) answer Variance of the means: (The difference between your answer and the correct value must be less Check Hint Not yet answered than 0.001.) answer correctly Mean Squared Between (MSB) variance: (The difference between your answer and the correct value must be less Check Not yet answered Hint than 0.001.) answer correctly Variance of happiness for art with no pen: (The difference between your answer and the correct value must be less Check Hint Not yet answered than 0.01.) answer correctly Variance of happiness for art with the pen in your teeth: (The difference between your answer and the correct value must be less Check Not yet answered than 0.01.) answer Hint correctly Variance of happiness for art with the pen in your lips: (The difference between your answer and the correct value must be less Check Not yet answered than 0.01.) answer Hint correctly Mean Squared Error (MSE) variance: (The difference between your answer and the correct value must be less Check Not yet answered Hint than 0.01.) answer correctly F value: (The difference between your answer and the correct value must be less Check Hint Not yet answered than 0.01.) answer correctly Of numerator. Check Not yet answered (Your answer must exactly equal the correct value.) answer Hint correctly of denominator Check Not yet answered (Your answer must exactly equal the correct value.) answer Hint correctly p-value: (The difference between your answer and the correct value must be less Check Not yet answered answer Hint than 0.001.) correctly Do you reject the null hypothesis?: No v Check Hint Correct answerv Your trial-bytrial data On each trial. you indicated the evoked happiness of an image of abstract art. Trials differed in how you held a pen in your mouth (or not at all). The nal column givesr the evoked happiness rating for the given image of art. Trial Condition Happiness rating 1 Pen in lips 33.0 2 Pen in lips 10.0 3 Pen in lips 100.0 4 Pen in lips 100.0 5 Pen in lips 100.0 6 Pen in lips 25.0 7 Pen in lips 0.0 8 Pen in lips 0.0 9 Pen in lips 0.0 10 Pen in lips 6?.0 11 Pen in lips 46.0 12 Pen in teeth 91.0 13 Pen in teeth 100.0 14 Pen in teeth 0.0 15 Pen in teeth 0.0 16 Pen in teeth 75.0 1? Pen in teeth 10.0 18 Pen in teeth 71.0 19 Pen in teeth 0.0 20 Pen in teeth 60.0 21 Pen in teeth 23.0 22 Pen in teeth 11.0 23 ho pen 100.0 24 ho pen 80.0 25 ho pen 100.0 26 ho pen 0.0 2? ho pen 0.0 28 ho pen 88.0 29 ho pen 2?.0 30 ho pen 89.0 31 ho pen ?4.0 32 ho pen 28.0 33 ho pen 0.0