Analysis Of Variance Chapter 7 1st Edition Exam Prep

Chapter 7: Analysis of Variance

1. Let’s assume you randomly draw three samples of correction officers from a single facility (50 black/50 white/50 other). You aim to find whether they have ever been a victim of sexual assault or harassment within the correction facility (yes/no). Your friend tells you to run an ANOVA to determine whether there is a difference between white, black, and other correction officers. Will you follow your friends’ suggestion? Explain.
2. Although the social climate surrounding sexual identity is slowly changing toward more tolerance, individuals who are female or transsexual still experience stigma regarding their sexual identity. Assume you have a master list of students enrolled in a large public high school in Portland (OR) and the list also includes their sexual identity. You randomly select 10 students who self-identify as female, 10 who self-identify as male, and 10 who self-identify as transgender. You want to know how accepted they feel by their teachers (with 1 indicating feeling marginalized and 10 indicating a feeling of being 100% accepted). You select an alpha level of 0.05. The results are presented in the table below.
   1. What is the IV and what is the DV? Also indicate the level of measurement for each variable.
   2. State your null and alternative hypotheses.
   3. Compute:
      1. The group mean.
      2. Grand mean.
      3. Standard deviation for each group.
      4. Sum of squares.
      5. The degrees of freedom (within and between).
      6. F.
   4. State the decision rule.
   5. Make a decision and interpret your findings.
   6. Use the Scheffé test to determine which means (if any) significantly differ from each other.

1. We know from research that poverty is a criminogenic risk factor. You select a random sample of 50 adolescents (age 24 and younger) with a criminal record who are still living with their parents from a diverse neighborhood in Orlando (FL) (with known household income/year). You group them into four categories: poverty ($0–$23,000; low income ($23,001–$35,000); lower middle class ($35,000–$55,000); upper middle class ($55,001–$150,000), and high income ($150,001+). You are interested to find whether the average age of onset (understood as a conviction; FL has no minimum age for criminal responsibility) varies between individuals from different socioeconomic backgrounds. You select an alpha level of 0.05. The results are to be found in the table below.
   1. What is the IV and what is the DV? Also indicate the level of measurement for each variable.
   2. State your null and alternative hypotheses.
   3. Compute:
      1. The group mean.
      2. Grand mean.
      3. Standard deviation for each group.
      4. Sum of squares.
      5. The degrees of freedom (within and between).
      6. F.
   4. State the decision rule.
   5. Make a decision and interpret your findings.
   6. Use the Scheffé test to determine which means (if any) significantly differ from each other.

1. Building on Burgess’s (1925) concentric zone theory, Shaw and McKay (1930) developed social disorganization theory. Social disorganization of neighborhoods is, according to Shaw and McKay (1942), characterized by a combination of persistent poverty, racial/ethnical heterogeneity, transiency (rapid/frequent population turnover), and urbanism, which in turn is fueling the disruption of core social institutions, such as the family, the church community, and schools. It was hypothesized that crime is more likely to occur in the core of the city and the enclosing zone in transition, with crime decreasing with the distance from the center. In the contemporary United States, an invert trend can be witnessed. Urban revitalization appears to invert Burgess’s concentric zone theory and Shaw and McKay’s (1930) social disorganization theory, with more and more wealthy and educated individuals moving back into the core. You want to test this inverse trend by analyzing the levels of perceived neighborhood problems (using a scale of 1–15, where 15 represents the highest level of perceived neighborhood problems) of a random sample of 40 individuals living in Minneapolis and its suburbs. Although Burgess’s concentric zone theory entails five zones (central business district, zone in transition, working man, residential, and commuter), you decide to compare the mean levels of perceived neighborhood problems of residents from downtown, residential areas, and suburbs. You select an alpha level of 0.05. The descriptive information is presented in the table below.
   1. Indicate which variable is the IV and which is the DV. Also indicate the level of measurement for each variable.
   2. State your null and alternative hypotheses.
   3. Compute:
      1. The group mean.
      2. Grand mean.
      3. Standard deviation for each group.
      4. Sum of squares.
      5. The degrees of freedom (within and between).
      6. F.
   4. State the decision rule.
   5. Make a decision and interpret your findings.