Choosing Statistical Tests, conducting those tests and interpreting the results of those tests

We noted on the midterm that an important skill necessary for conducting applied social science research is to be able to translate a research question into the correct choice of a statistical test.  It is just as important to be able to subsequently conduct the statistical test and interpret the results of that test.

For the research question below, you will not only choose the appropriate statistical hypothesis testing procedure, but you will also run the test using data that we provide and interpret the results.  Consider each of the research questions below and answer the questions that follow:

1) Among people who have been incarcerated at least once as a juvenile or young adult, are there differences among racial/ethnic groups in lengths of jail/prison sentences, after holding the following variables constant:  the frequency of crimes committed (as measured by whether a participant has been arrested once or more than once), the severity of crimes committed (as measured by whether they are classified as violent or non-violent offenses), whether the inmate was a juvenile or adult at the time of arrest, age and gender?

There is a data file on the CCLE course website named FINAL_Q5 containing data from a longitudinal study of adolescents who completed baseline questionnaires and were contacted to complete follow-up questionnaires measuring numerous variables every four years until age 30.  You will use this file to conduct the statistical test that you choose.  The following variables are in the file:

MONTHSINCAR - length of time served in months

RACEETHNICITY - race/ethnicity of respondent 1=white 2=black 3=Latino 4=Asian 5=Native American 6=Other

ARRESTFREQUENCY - arrested once or more than once (0=once 1=more than once)

VIOLENTCRIME - whether offense was violent or non-violent (0=non-violent 1=violent)

JUVORADULT - juvenile or adult at time of arrest (0=adult 1=juvenile)

AGEATINTERVIEW - age in years

GENDER - gender of the respondent (0=male 1=female )

a) identify the EV

b) identify the RV

c) identify the CV(s)

d) state a hypothesis about the direction of the expected association between the EV and the RV that you identified in a and b above.  You are not being asked to state null and alternative hypotheses here.  Just state the hypothesis that you would as the researcher conducting this study

e) identify the statistical test that will appropriately test whether or not the EV and RV are associated in the population after controlling for the CV(s), and explain why you chose this particular test

f) state the null and alternative hypotheses for the expected association between the EV and RV you identified in a and b above, after holding all CVs constant that you identified in part c above (either words or symbols is fine-no need to state the hypotheses both ways).

g) before you can conduct the statistical test of your choice, it will be necessary to create g-1 dummy variables from the RACEETHNICITY variable in order to test for race/ethnic group differences.  Run a TAB or TAB1 program on the RACEETHNICITY variable to observe its distribution and paste your output below.  Also, paste your code for creating these dummy variables below, and submit the code in your Stata session so that the dummy variables are ready to use.

h) conduct the statistical test you chose in part e above in STATA using the data provided on the CCLE course website.  Paste the output below

i) write a short summary of the results in which you state your decision to reject or retain the null hypothesis you stated in f above.  In your summary, identify and interpret the values the association between all EVs/CVs combined and the RV and its test statistic/p-value.  Also identify and interpret the values of the individual adjusted EV/RV associations, the adjusted CV/RV associations, their test statistics and p-values

j) what is your main conclusion about the presence or lack of presence of an EV/RV association in the population after holding the CV(s) constant?  You should state your answer to the research question above and comment on whether evidence of race/ethnic disparities exist.