1) Explain how one should decide between ANOVA and crosstabulation procedures for examining relationships between two variables. Provide examples of two research questions that would require the use of ANOVA or crosstabulation, respectively.
2) Answer the following questions regarding degrees of freedom and Chi-Square critical values
in a crosstabulation procedure.
a) What is the formula for determining df inanyA x B crosstabulation?
b) A sample of UP faculty contains respondents from 15 departments. These subjects were
asked which of the following modes of transportation they use to commute to campus: Bus; Automobile; Bike; Walk; Other. How many degrees of freedom would the crosstabulation have? (Show your work.)
c) A sample of male and female adolescents are asked whether they have ever had sex. How many degrees of freedom would the crosstabulation have? (Show your work.)
d) A student in SOC 215 has conducted a 4 x 3 crosstabulation. Assuming a 0.05 test of significance is requested, what is the critical Chi-Square value to which the student’s computed Chi-Square statistic will be compared?
e) A student in SOC 215 has conducted a 3 x 3 crosstabulation. Assuming a 0.01 test of significance is requested, what is the critical Chi-Square value to which the student’s computed Chi-Square statistic will be compared?
3) A group of UP psychology students in Dr. Julka’s senior capstone course will conduct public health research. Their literature review on adolescent smoking has revealed an interesting pattern: large racial and ethnic differences in the proportions of youths who smoke cigarettes. They also have read studies that suggest peer pressure plays a strong role in whether youths take up smoking. Drawing on these findings, the students decide to explore whether there may be a statistical relationship between adolescent race and the number of a youth’s three closest friends who smoke cigarettes.
Using our AddHealth data, please engage their research question by conductinga cross- tabulation and chi-square testto evaluate the following null hypothesis: the proportional distribution of responses to the “number of close friends who smoke” question does not vary by race of respondent. Let alpha = 0.05. (NOTE: Use the 6-category race variable as
defined in our course syntax; you will need to clean and prepare the relevant peer smoking variable from section 28 of the in-home survey before performing the test.)
Copy and paste your output and explain your results. Your output should include a cross- tabulation table with observed counts, row and column percentages, and the chi-square test. Your discussion of the output should be sufficient to convince a reader that you understand the meaning of these statistics. (This could be accomplished by discussing the contents of two different cells of the crosstabulation; the chi-square statistic; the df; and the significance level reported by SPSS.)
4) Your research team has speculated that there is a statistical relationship between adolescent race and whether youths believe they will contract HIV/AIDS. Using our AddHealth data, please evaluate this hypothesis by conductinga cross-tabulation and chi- square testto evaluate the following null hypothesis: the proportional distribution of responses to the HIV/AIDS question does not vary by race of respondent (use the In-Home version of the HIV/AIDS question, not the In-School version). Let alpha = 0.05. (NOTE: Use the race variable as defined in our course syntax; you will need to clean and prepare the in- home version of the HIV/AIDS variable before analysis.)
Copy and paste your output and explain your results. Your output should include a cross- tabulation table with observed counts, row and column percentages, and the chi-square test. Your discussion of the output should be sufficient to convince a reader that you understand the meaning of these statistics. (This could be accomplished by discussing the contents of two different cells of the crosstabulation; the chi-square statistic; the df; and the significance level reported by SPSS.)
5) Answer the following questions regarding bivariate correlation statistics and significance tests.
a) What are the range of possible correlation values that are possible with this procedure?
b) Consider a correlation value of .123. Write the following sentence, filling in the blanks
with correct answers:As one variable increases in value by ___ standard deviation units,
the other variable ____ in value by .123 ____________ units.
c) Consider a correlation value of -.008. Write the following sentence, filling in the blanks with correct answers:As one variable increases in value by one ___ units, the other variable ____ in value by .008 ____________ units.
d) What if you encountered a correlation value of zero? How would you interpret that statistic?
e) In a correlation, what is the null hypothesis that is being evaluated?
6) In 2009 your instructor co-authored a paper that examined the possible effect of a sex education curriculum on reducing homophobia among college students. Part of the analysis reported in the paper included a correlation matrix for all variables used in the study. The paper is posted on our course website; please see the correlation matrix (Table 2, on page 219) to answer the following questions.
a) Which two variables have the highest positive and significant correlation?
b) Which two variables have the smallest and non-significant correlation?
c) Pick any two variables in the table (that were not referenced in parts a or b of this
question) and interpret their correlation and test of statistical significance.