**Midterm: Criminal Justice Statistics**

CRJS-3020-01 |100 Points

**Midterm Objectives**

To assess your knowledge of concepts covered in the class text and lectures (Chapters 1-6), as well as your practical knowledge using SPSS.

**Lecture/Text Assessment (50 points)**

This portion of the midterm should have typed answers. Please show all work where applicable on a scrap piece of paper and turn in a photograph or scan of that document (e.g. mean, standard deviation, standard error).

- (5 points). You are interviewing robbery victims for a research study and have developed five questions to ask them. For each of the below questions you ask, identify the appropriate scale of measurement – nominal, ordinal, continuous (i.e. interval or ratio).
- Question: What was the dollar value of the item(s) stolen from you?

Possible Responses: $0-$99, $100-$199, $200-$299, $300-$399, $400-$499, $500 or more

Scale of Measurement:

- Question: How severe were your injuries?

Possible Responses: No injuries, minor injuries, major injuries, severe injuries

Scale of Measurement:

- Question: What type of weapon was used?

Possible Responses: Bodily weapon (hands and/or feet), knife, gun, blunt object, other

Scale of Measurement:

- Question: How fearful are you of being robbed again in the future?

Possible Responses: Not fearful, a little fearful, moderately fearful, extremely fearful

Scale of Measurement:

- Question: How many days has it been since your robbed?

Possible Responses: 1, 2, 3, 4, 5, 6…

Scale of Measurement:

- (5 points). Imagine you are developing a survey to ask police officers about their health. Create five of your own questions that can broadly relate back to this topic and identify the appropriate scale of measurement, using each scale of measurement at least once (Nominal, Ordinal, Continuous). Be specific as to how the responses will be measured. Do not replicate any of the variables from Question 1.

Example: Question: How many hours of overtime do you work each week?

Possible Responses: Any numeric value between 0 and 100.

Scale of Measurement: Continuous.

- Question:

Possible Responses:

Scale of Measurement:

- Question:

Possible Responses:

Scale of Measurement:

- Question:

Possible Responses:

Scale of Measurement:

- Question:

Possible Responses:

Scale of Measurement:

- Question:

Possible Responses:

Scale of Measurement:

- (5 points). From the below distributions, please write which distributions fit each description.
- Normal Distribution:
- Platykurtic Distribution:
- Leptokurtic Distribution:
- Positively Skewed:
- Negatively Skewed:

DISTRIBUTION 1 DISTRIBUTION 2

DISTRIBUTION 3

DISTRIBUTION 4

DISTRIBUTION 5

For questions 4 through 9, please use the yearly robbery counts for a metropolitan area in the Midwest to answer the questions. These include the number of robberies, per year, from 2009 through 2018.

2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 |

590 | 423 | 426 | 445 | 603 | 579 | 543 | 582 | 539 | 680 |

- (5 points). Measures of Central Tendency. Please use the robbery data to calculate and report on the below.
- Mean:
- Median:
- Mode:
- (5 points). Measures of Variability. Please use the robbery data to calculate and report on the below (Hint: treat all distributions as populations).
- Range:
- Variance:
- Standard Deviation:
- (5 points). Z-scores. Please use the robbery data to calculate the Z-scores for the below values.
- 423:
- 603:
- 543:
- 582:
- 680:
- (10 points). Area under the curve. Identify what percentage of the distribution should be found under the curve using the below information. Although not graded, it may be helpful to draw the corresponding normal distribution where that percentage is located (either here if you know how or on a piece of scrap paper for your own reference). An example is provide below.

Example: What percentage of the distribution would we expect to fall between the Z-score for the value of 426 from the original distribution and a Z-score of 0? The Z-score associated with 1,416 is -1.25. We would expect 39.44% of the distribution to fall between the Z-scores of -1.25 and 0. | |

a. What percentage of the distribution would we expect to fall between the Z-score for the value of 423 from the original distribution and a Z-score of 0? | |

b. What percentage of the distribution would we expect to fall between the Z-score for the value of 603 from the original distribution and a Z-score of 0? | |

c. What percentage of the distribution would we expect to fall between the Z-score for the value of 543 and the rest of the distribution to the right of that value? | |

d. What percentage of the distribution would we expect to fall between the Z-score for the value of 582 and the rest of the distribution to the right of that value? | |

e. What percentage of the distribution would we expect to fall between the Z-score for the value of 423 from the original distribution and the Z-score for the value of 680 from the original distribution? |

- (5 points). Standard Error of the Mean. What is the standard error of the mean for the following values sampled from the population of Seattle robberies: 426, 445, 603, 579, 543. (Also treat these five numbers as a population when calculating their standard deviation)?
- (5 points). Standard Error Z-scores & Area under the curve.
- What is the Z-score associated with the standard error of the mean you calculated in question 8?
- What percentage of a normal distribution would we expect to fall between the Z-score for the standard error of the mean and a Z-score of 0?

**Dataset:** The dataset for this portion of the assignment is data from the Seattle Public Safety Survey and is labeled Safety_Survey_Midterm.sav. IMPORTANT: Use only the dataset linked from the Assignments page where the Midterm information is located and where you downloaded this document.

There are multiple variables that capture information about the respondents and their views on public safety related issues in the Seattle area. To be eligible to complete the survey, respondents need to live and/or work in Seattle. Please type your answers directly into this document and insert all graphs and tables requested into this document. In addition, save your output and submit it with this file.

- (5 points). Create two pie charts that compare the distribution of individuals who did not report their victimization (NO_REPORT) between whether the respondent identified as female or not (FEMALE). Edit the graph so that it is presentable and copy and paste it into this document. Explain what differences, if any, do you see between the two pie charts.
- (5 points). Create a scatterplot that explores the relationship between a respondent’s perception of social disorganization in their neighborhood (SOCIAL_DISORGANIZATION_SCALE) and their fear of crime (FEAR_CRIME_SCALE). Social disorganization measures a respondent’s perception of visible problems in their neighborhood, such as broken windows, graffiti, etc… Fear of crime measures how often they think about, or are fearful of, criminal victimization. Edit the graph so that it is presentable and copy and paste it into this document. What trends do you see in the data? Offer an explanation for why you think that might be.
- (5 points). Using the year the respondent completed the survey (SURVEY_YEAR) and whether the respondent was victimized or not (VCTM_YES), create a multiple line graph. Edit the graph so that it is presentable and copy and paste it into this document. Interpret your graph for me (i.e. explain the patterns you see in the data).
- (5 points). Using the variable for social cohesion (SOCIAL_COHESION_SCALE) request and report on the three main measures of central tendency we discussed in class as well as the three measures of variability/dispersion.
- (5 points). Request frequency tables for marital status (MARITAL_STATUS) and the age of the respondent (AGE). Answer the below questions.
- What is the mode for marital status?
- What % of respondents were single?
- For respondents who provided information about their age, what percent were younger than 60?
- What is the scale of measurement for age?
- (5 points). Recode age into the following categories: 29 and younger, 30-49, 50-69, 70 and older. Request a frequency table and bar chart for this new variable. Paste both below.
- (5 points). Request and report the mean for social cohesion (SOCIAL_COHESION_SCALE). Social cohesion measures how well one believes their neighborhood works together. Typically, neighborhoods with high social cohesion contain individuals who know each other, share similar values, and look out for each other. Now, filter your data so that you are only looking at respondents who reported they were retired (RETIRED). Request and report on the mean again. Explain what differences, if any, you see in the means for the social cohesion scale across the two groups (All respondents vs retired respondents).
- (15 points). Compute a new variable (POLICE_LEGITIMACY_SCALE) by summing the following variables: POLICE_LEGITIMACY_1
*through*POLICE_LEGITMACY_19. - Report all measures of central tendency and variability for this new variable.
- Now, ask SPSS to convert this new variable to Z-scores and report all measures of central tendency and variability for this new standardized variable.
- Create a histogram for both your new POLICE_LEGITIMACY_SCALE variable and the variable of Z-scores. Paste them below.