Question

Assignment 4: ANOVA and Crosstabs/Chi-Square Tum in your computer printout for any Stata output that is requested, your hand calculations, and your typed answers to the fo lowing questions. BE SURE TO SHOW ALL OF YOUR WORK. Make sure that the ages are stapled, paper clipped, or otherwise attached together. Put your name on each page incl ding the computer priptout. Finally, always make a copy of your assignment before you turn in. 1. You are currently conduc search on the association between social network composition and depression among adolescents in the United States. You randomly select 15 adolescents and ask them about the individuals who comprise their friendship networks. You then divide the sample into three groups based on network characteristics: adolescents whose friends are of the same gender as the respondent, adolescents whose friends are of a different gender as the respondent, and adolescents who have friendship networks that are comprised of both men and women. You expect these three groups of adolescents to experience different levels of depression. Thus, you also measure depression among this sample using a scale that has a minimum value of 1 (least depressed) and a maximum value of 20 (most depressed). Their depression scores are as follows: Primarily Same Gender 15.0 19.2 8.4 12.8 10.2 Primarily Different Gender 10.8 13.6 6.2 7.4 9.8 Mixed Gender 8.6 10.4 6.4 5.6 6.6 Perform the appropriate hypothesis test to determine whether there is an gender composition of one's social network and depression. Set your alpha level at 0.05. Be sure to follow ali the steps discussed in lecture (Hint: There are five steps) and show any calculations you perform. Also, clearly state which variable is the independent variable and the dependent variable. Describe your conclusion in 1-2 complete sentences. association between the which one is

Answer 1

independent variable - social network composition

dependent variable - depression among adolescents

Anova one way

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ha: Not all means are equal The above hypotheses will be tested using an F-ratio for a One-Way ANOVA (2) Rejection Region Based on the information provided, the significance level is α-0.05, and the degrees of freedom are dfi-2 and df2-2, therefore, the rejection region for this F-test is R-{F : F > Fc-3.885} (3) Test Statistics F=Ms,etween 40.163 MSwithin 10.044 3.999 4) Decision about the null hypothesis Since it is observed that F- 3.999 > Fe-3.885, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p 0.0467, and since p-0.04670.05, it is concluded that the null hypothesis is rejected. 5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that not all 3 population means are equal, at the a0.05 significance level.