Problem Set 5
Part 1 - In the first question, interpret the results and answer the related questions.
A police department is interested to see if their officers do better as a result of a new trauma-informed training course. They administer a skills test to 60 officers, 30 of whom took the new course and 30 the old.
Test Scores Customary Course New Course
Excellent 7 13 20
Good 15 15 30
Unsatisfactory 8 2 10
30 30 60
Step 1: What is the independent variable, dependent variable, null hypothesis and alternative (research) hypothesis in this example?
Independent Variable:
Dependent Variable:
Null Hypothesis (H0):
Alternative Hypothesis (H1):
Step 2: Identify the distribution and compute the df.
Degrees of Freedom = (r – 1)(c – 1) =
Step 3: Using the Chi Square Distribution Table (page 760 of your textbook), identify the critical value of the test statistic and state the decision rule.
Significance Level =
Critical value =
Step 4: The test statistic is computed below. The Chi Square value is 5.4
Expected Values
Customary Course New Course Row Marginal
Excellent Observed = 7
Expected = 10 Observed = 13
Expected = 10 20
Good Observed = 15
Expected = 15 Observed = 15
Expected = 15 30
Unsatisfactory Observed = 8
Expected = 5 Observed = 2
Expected = 5 10
Column Marginal 30 30 N = 60
Chi Squared value = 5.4
Step 5: Make a decision about the null and state the substantive conclusion.
What decision will we make about the null hypothesis and why?
Substantively, what do the results mean? SPSS Problem 6 on Page 233
For the SPSS problem, use the file called “pcs_98_modified for student use.sav,” which is available on Canvas. The original file (pcs_98.sav) has multi-category variables that I modified in the version you should use.
The SPSS problem asks you to list each step required in a test of statistical significance for each of the four relationships listed. However, to avoid having to list the same assumptions over and over, you may list any assumptions that pertain to all four parts of the question just once (e.g. level of measurement, if it’s the same for all four). List them under the title “Common Assumptions.” Make sure you read the question carefully to determine what the sampling frame is. Also, make sure that you are using the correct variables for each test you run (e.g. “method of conviction” is measured by the variable called “disp,” which stands for “type of disposition”).
To determine the degrees of freedom and thus the critical value for each relationship for the SPSS problem, you will have to first look at the categories of the two variables involved to see how many rows and columns the table will have. Do that by looking at the “values” of each variable. The chi-square critical value table is on Page 760 of your textbook.
For the “decision” step of each test, make sure you state whether you reject or fail to reject the null hypothesis as well as the substantive conclusion that you reach based on the results of the test. Also, make sure you refer to the actual chi-square value generated by SPSS and compare it to your critical value. SPSS will generate an actual p value associated with the test statistic. Therefore, you will be able to refer to that value, rather than simply saying “p< .05.” Note that the SPSS output refers to the p value as “asymptotic significance (2-sided).”
Here’s an example:
Based on the results of the chi-square test (Χ2 = 10.804, 3 df, p = .013), we conclude that the type of pre-release housing where formerly incarcerated individuals resided is statistically significantly related to the likelihood of re-arrest within 6 months of their release. People released from maximum and medium security facilities have much higher rates of re-arrest than people released from lower security level facilities.