Stats & Criminology 1. Supposed that there is a relationship

Stats & Criminology

1. Supposed that there is a relationship between an individual’s level of Self Control as measured by the Grasmick Self Control Scale (Self_Con) and his or her Number of Adult Arrests (ARR). Theory postulates that low self control is associated with higher number of arrests. Use the definitions of the variables contained in the Week One Dataset, reprinted below.

State your null and research hypotheses.

Variables are defined as follows: SELF_CON Grasmick Self-Control Scale Treated as interval-ratio level. A scale measuring self-control developed by Richard Grasmick. Scores may range from 24 to 96, with low scores indicating low self-control. 99 = No data in Record

ARR Number of adult arrests as recorded in court records. An interval-ratio level variable. Since all members of the population have (by definition) been arrested at least once, values will range from 1 to nn 99 = No data

Explain the following results from the SPSS output that can be found in this linked file called "Regression Data":

1. Mean and standard deviation for each variable.

2. The interpretation of the Pearson Correlation

3. R square

4. Unstandardized coefficients : (Constant and Self_Con)

5. Calculate the number of arrests for a person with a Self-Con score of 50.

“Regression Data”

Hypothetical data on the relationship of an inmate’s Grasmick Self Control Score to Adult Arrest History. Selected output from SPSS.

Descriptive Statistics

Mean

Std. Deviation

N

ARR

4.51

2.567

300

SELF_CON

43.37

16.953

300

Correlations

ARR

SELF_CON

Pearson Correlation

ARR

1.000

-.362

SELF_CON

-.362

1.000

Sig. (1-tailed)

ARR

.

.000

SELF_CON

.000

.

N

ARR

300

300

SELF_CON

300

300

Variables Entered/Removed^a

Model

Variables Entered

Variables Removed

Method

1

SELF_CON^b

.

Enter

a. Dependent Variable: ARR

b. All requested variables entered.

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.362^a

.131

.128

2.397

a. Predictors: (Constant), SELF_CON

Coefficients^a

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

95.0% Confidence Interval for B

B

Std. Error

Beta

Lower Bound

Upper Bound

1

(Constant)

6.893

.381

18.108

.000

6.144

7.642

SELF_CON

-.055

.008

-.362

-6.711

.000

-.071

-.039

a. Dependent Variable: ARR

2. Flip a coin 60 times. Record the outcome of each of the 60 flips in order from 1 to 60, using the Tally number of heads and the number of tails and calculate the proportion of heads in your sample.  The number of heads are 33 and the number of tails are 27.  Calculate a 95% Confidence Interval for the true population value. Calculate a 95% Confidence Interval for the proportion of heads.

3. Explain the difference between the information given by the tests of statistical significance t and Chi Square, and measures of association Cramer’s V, Gamma and Pearson’s correlation coefficient, r.

Can a test of significance show a statistically significant relationship while a measure of association shows a weak relationship between the variables?

If yes, present an example illustrating how such a situation might occur.

4. To locate treatment programs for heroin addicts, the mayor wants to conduct a study of persons arrested for possession in your city.

He suggests looking at data on location of arrest and residence of arrestees for the past month. This will yield a sample of at least eighty cases. From his statistics course, he says that with a sample size greater than 50, the central limit theorem will apply and you can to make a reasonable estimate of the numbers of people needing treatment with a level of confidence of 95%.

Is the mayor correct? From your knowledge of criminal justice and statistical analysis would you suggest a different sampling plan? If yes, what would you suggest?

5. A researcher conducts a study of white and black attitudes toward the police in her community.

The percentage of a random sample of white respondents (N = 250) who say they have a favorable attitude toward the police is 51%. The percentage of a random sample of black respondents (N = 300) who say they have a favorable attitude toward the police is 47%.

You are asked if there is a real difference between the percentage of whites and blacks who have a positive attitude toward the police in the larger population, or is this sample difference likely to have occurred by random chance or sampling error.

How do you respond? Explain your answer.

Construct a 95% confidence interval for the proportion of Blacks in the population who have a favorable attitude toward the police.