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Assignment/Problem Set #3 (Correlation on Chapter 5)

April 10, 2025

Assignment/Problem Set #3 (Correlation on Chapter 5)

Students must provide answers to each question beneath the question. Students must show all work including all SPSS outputs and interpret the outputs. This means that you cannot submit only answers. All variables must be labeled, you can abbreviate the names of the variables.

(1). Here is a set of 3 variables for each of 20 participants in a study on recovery from drug addiction. Create a simple matrix that shows the correlations between pairs of variables (use SPSS). Interpret the correlations coefficients between the variables. Label the variables.

Age at addiction (Age)	Level of treatment (level)	12-month Treatment Score (score
28	4	78
19	5	69
12	5	81
26	6	92
34	7	90
22	7	93
20	7	99
34	8	79
24	4	59
29	4	75
27	8	87
28	8	90
39	7	72
46	7	90
19	7	91
26	4	95
34	5	98
56	5	72
14	6	82
36	5	72

(2). The Pearson correlation coefficient between two variables (rehabilitation program and recidivism) is
–.854. Answer the following questions:

a. What type of correlation coefficient exist between the two variables above?

b. If rehabilitation program is variable X and recidivism is variable Y, what happens when rehabilitation program (X variable) increases.

c. What is the coefficient of determination?

d. State the meaningfulness of the relationship between the two variables.

e. Interpret the strength of the relationship using the general range of very weak to very strong?

(3). Sample Dataset: Crime Rate and Socioeconomic Factors

The dataset below contains crime rates per 100,000 people and socioeconomic factors (unemployment rate and median household income) across ten cities.

City	Violent Crime Rate (per 100,000)	Unemployment Rate (%)	Median Household Income ($)
City A A	450	7.2	50,000
City B	520	6.8	48,500
City C	610	8.1	45,200
City D	700	9.0	42,300
City E	800	10.2	40,100
City F	330	5.5	55,000
City G	400	6.0	52,700
City H	580	7.5	46,800
City I	750	9.5	41,200
City J	900	11.0	39,000

Using SPSS/Excel, compute Pearson’s
correlation coefficient (r) for the dataset above. Ensure to include your SPSS output. Analyze the SPSS/Excel output according to the following:

1. a. From the output, determine the correlation coefficient between Crime Rate vs. Unemployment Rate.

b. What type of relationship exist between these two variables?

c. Does crime increase as unemployment rises?

d. What is the strength of the relationship?

e. Determine the coefficient of determination

f. Determine the coefficient of non-determination

2. a. From the output, determine the correlation coefficient between Crime Rate vs. Median Household.

b. What type of relationship exist between these two variables?

c. Is there an inverse relationship between income and crime?

d. What is the strength of the relationship?

e. Determine the coefficient of determination

f. Determine the coefficient of non-determination

Reliability (on Chapter 6)

(4) You are in charge of the test development program for a police agency and you need at least two forms of the same test to administer on the same day.

(i). What kind of reliability will you want to establish?

(5). You are developing a test that will examine preferences for different types of rehabilitation programs. You may administer the test in January and re-administer the same test on the same people in August, and you have a measure of reliability.

a. What type of reliability is this?

b. Using SPSS/Excel, compute the reliability coefficient of the following scores from the test at Time 1 and Time 2.
Interpret the reliability coefficients

ID	Scores from Time 1	Scores from Time 2
1	56	58
2	67	77
3	68	88
4	85	87
5	87	88
6	88	90
7	86	89
8	88	90
9	96	97
10	67	78

(6). a. Manually, Compute the following interrater reliability coefficients of 2 raters. Show all your work.

b. Interpret the reliability coefficients

Time period	Rater 1 (Scott)	Rater 2 (Lizzy)
1	X	X
2	X	–
3	–	–
4	X	X
5	X	X
6	X	X
7	–	X
8	–	–
9	–	–
10	X	X
11	X	–
12	X	X
13	X	X
14	–	–
15	X	–
16	X	X

Notes for Inter-rater reliability

The note/textbook provides an easy step to computing interrater reliability coefficient when you are rating categorical values of Yes (X) and No (-).

Formula =

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