Discussion: Social Statistics

Discussion: Social Statistics ORDER NOW FOR CUSTOMIZED AND ORIGINAL ESSAY PAPERS ON Discussion: Social Statistics Name:_______________________ SOC 390: Social Statistics I Summer 2017 Homework 5 (ANOVAs, Correlation, Regression) Discussion: Social Statistics (Total points = 20) Instructions: Download and complete this word document. Read each question carefully and answer all parts of the question. Show your work! If you choose to handwrite your answers and scan your document, please make sure your answers are legible. You will not receive credit if you do not show your work (where applicable). This assignment will cover Chapters 12-16 and involves both hand calculations (Parts 1 and 2) and conceptual interpretations (Part 3). Part 1: One-way ANOVA (11 points) The following is a made-up data set that contains scores for 15 children. The children are in three groups. Five of the children are in group 1, five of the children are in group 2, and five of the children are in group 3. Children in group 1 were shown a funny cartoon, children in group 2 were shown a boring cartoon, and children in group 3 were shown a sad cartoon. Data are ratings of children’s joy. Joy was rated on a scale of 1 (no joy) to 10 (extremely high joy). Subject ID number Group Joy 1 1 8 2 1 6 3 1 9 4 1 4 5 1 6 6 2 3 7 2 5 8 2 4 9 2 2 10 2 3 11 3 4 12 3 3 13 3 1 14 3 2 15 3 2 1) Using the data set above, compute the three group means ( ) and compute the total mean ( ) to two decimal places. For full credit, be sure to show all of your work. (1.5 points) g1 = g2 = g3 = tot = 2. Now compute the three between-group deviations as well as the between-group deviations squared using two decimal places. (1.5 points) Formulas: and == = = = = 3. Compute the 15 within-group deviations as well as the 15 within-group deviations squared using two decimal places. (1.5 points) Formulas: x g1 x – g1 ?2 (x – g1)2 8 – ____ = ____ = ____ 6 – ____ = ____ = ____ 9 – ____ = ____ = ____ 4 – ____ = ____ = ____ 6 – ____ = ____ = ____ x g2 x – g2 ?2 (x – g2)2 3 – ____ = ____ = ____ 5 – ____ = ____ = ____ 4 – ____ = ____ = ____ 2 – ____ = ____ = ____ 3 – ____ = ____ = ____ x g3 x – g3 ?2 (x – g3)2 4 – ____ = ____ = ____ 3 – ____ = ____ = ____ 1 – ____ = ____ = ____ 2 – ____ = ____ = ____ 2 – ____ = ____ = ____ 4. Compute the 15 total deviations as well as the 15 total deviations squared using two decimal places. (1.5 points) Formulas: x tot x – tot ?2 (x – tot)2 8 – ____ = ____ = ____ 6 – ____ = ____ = ____ 9 – ____ = ____ = ____ 4 – ____ = ____ = ____ 6 – ____ = ____ = ____ x xbartot x – xbartot ?2 (x – xbartot)2 3 – ____ = ____ = ____ 5 – ____ = ____ = ____ 4 – ____ = ____ = ____ 2 – ____ = ____ = ____ 3 – ____ = ____ = ____ x xbartot x – xbartot ?2 (x – xbartot)2 4 – ____ = ____ = ____ 3 – ____ = ____ = ____ 1 – ____ = ____ = ____ 2 – ____ = ____ = ____ 2 – ____ = ____ = ____ 5. Now compute the sum of squares for the between-groups deviation, the within-groups deviation, and the total deviation. HINT: For SS between you must multiply your results for each group (there are three of them) by the n of each group (which is 5) before summing because we did not compute the deviation for each person. (1.5 points) Discussion: Social Statistics Formulas: SSbetween SSwithin SStotal SSbetween (Hint: you already calculated each of these in question 2 – just plug in the numbers and multiple by 5.): (g1 – tot)2 _____ x 5 = _____ (g2 – tot)2 _____ x 5 = _____ ( g3 – tot)2 _____ x 5 = +_____ SSbetween = ?(g – tot)2 ________ SSwithin = ?(x – g)2 = ____________ (Hint: you already calculated (x-g)2 in question 3… just add all 15!) SS total = ?(x – tot)2 = ___________ (you already calculated (x- tot)2 in question 4…. Just add all 15! 6. Compute the degrees of freedom within, degrees of freedom between, and degrees of freedom total. (1.5 points) Formulas: Within degrees of freedom: N-k Between degrees of freedom: k-1 Total degrees of freedom: N-1 Where k = number of groups and N = sample size dfwithin = _______ dfbetween = _______ dftotal = ______ 7. Compute the mean squares within and mean squares between using two decimal places. (.5 point) Formulas: MSwithin = SSwithin / dfwithinand MSbetween = SSbetween / dfbetween MSwithin = _______ MSbetween = ______ 8. Compute the observed F value using two decimal places. (.5 point) Discussion: Social Statistics Formulas: Fobs = MSbetween / MSwithin Fobs = _______ 9. UseTable B.3 with an ? = .05, the degrees of freedombetween, and degrees of freedomwithinto determine the F critical value needed to make a decision regarding the null hypothesis. What is the F critical value? (.5 point) Fcrit = ________ 10. What is your decision regarding the null hypothesis that group means are equal? (.5 point) Part 2: Correlations (4 points) The next two questions involve hand calculation of a correlation. You will use the following made-up data set that includes two variables: X and Y 11. Using the made-up data set above, compute the correlation between X and Y by hand. Use 3 decimal places. Be sure to show all of your work to receive full credit. (3 points) Discussion: Social Statistics Formula: 12. The criticalvalue of r associated with the answer to question 1 is .950 (? was set at .05, and there were 2 degrees of freedom [N-2 ? 4-2 = 2]). Using this knowledge and your answer from question 11, please interpret the correlation between X and Y. Specifically, you should report the direction of the correlation and whether the correlation is statistically significant from zero or not. (1 point) PART 3: Two-way ANOVAand Regression Concepts (5points) 13. Please describe what a main effect examines in factorial ANOVA, and describe what an interaction effect examines in factorial ANOVA. (1 point – .5 point main effect, .5 point interaction effect). A main effect… An interaction effect… 14. In factorial ANOVA, an F ratio is computed for each main effect and for each interaction effect. For example, if we have two factors –factor A and factor B–this gives us three F ratios. We would have an F ratio for the main effect of factor A, for the main effect of factor B, and for the interaction between A X B. How many F ratios would we get if we had three factors –A, B, and C—and we tested all main effects, all possible 2-way interactions, and the 3-way interaction? (1 point) You would have… Discussion: Social Statistics 15. Please write out the basic (i.e., single-predictor) regression equation (1 point) ? = 16. If the unstandardized regression coefficient (the slope of y on x) in a basic, single-predictor regression was found to be byx = +0.70, what is the interpretation of “byx= +0.70”? (1 point) 17. If the regression constant (the y intercept) in a basic, single-predictor regression was found to be a = .20, what is the interpretation of “a = .20”? (1 point) Get a 10 % discount on an order above $ 100 Use the following coupon code : NURSING10

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