HOMEWORK EXERCISE - MEASUREMENT AND CENTRAL TENDENCY

      SUMMARIZING DISTRIBUTIONS

1.  Calculate all appropriate summary statistics for each distribution

2.  Pictorially depict the distribution of arrests

3.  Pictorially depict the distribution of gender

PE Distributions

 HOMEWORK EXERCISE - VARIABILITY

MEASURES OF DISPERSION

Assignment:  compute each measure of dispersion

Variability homework1


HOMEWORK EXERCISE – CROSSTABULATION

                                         RELATIONSHIP BETWEEN CATEGORICAL VARIABLES

You are a Captain in the Research and Planning Unit of the Big Deal Police Department.  There are 4000 sworn personnel.

PART I.  The Chief wants you to measure cynicism of patrol officers and sergeants.  He is interested in
(a) how cynical each group is, and (b) whether rank is related to cynicism.  He is NOT interested in degrees
of cynicism – he only wants to distinguish between cynical and not cynical.

    1.  What is the unit of analysis?
    2.  How would you select the sampleWhy?  (include its size)
    3.  What statistic would you use to summarize the results?
    4.  Make up data that demonstrates a strong relationship between rank and cynicism
    5.  Provide summary statistics for each group
    6.  Prepare a table that displays the above relationship

PART II.  When you provide results, the Chief surprises you with another question.  Now he wants
to know whether gender might be a factor. (This was NOT anticipated when you received
your original assignment.)

Your assignment:  Using the above data, prepare tables that demonstrate a strong relationship
between RANK and CYNICISM, holding GENDER constant.


HOMEWORK EXERCISE - CORRELATION

Hypothesis:  Changes in height causes changes in weight

1.  Create a scattergram from this data

Height

Weight

71

185

70

210

71

178

68

135

64

123

65

141

72

220

68

137

67

140

67

170

70

130

70

180

68

192

64

145

72

195

62

100

61

110

69

185

68

134

70

235

73

195

2.  Does there seem to be a relationship between variables?  Is it positive or negative?
3.  Provide an estimate of the r statistic
4.  Rescale each variable as categorical
5.  Use the normal procedure to evaluate an association between categorical variables.  Does there
     still seem to be a relationship?


HOMEWORK - STANDARD ERROR OF THE MEAN & CONFIDENCE INTERVAL

Homework: two random samples of 10 patrol officers from the XYZ Police Department, each officer tested for cynicism (continuous variable, scale 1-5)

Sample 1 scores: 3 3 3 3 3 3 3 1 2 5

Sample 2 scores: 2 1 1 2 3 3 3 3 4 2

CALCULATE:

Standard deviation for sample 1: _________ (small sample, use n-1)

Standard deviation for sample 2: _________ (small sample, use n-1)

Standard error of the mean based on sample 1: __________

Standard error of the mean based on sample 2: __________

95% Confidence interval into which the population mean should fall, based on sample 1:

Left limit _____  Right limit ______

95% Confidence interval into which the population mean should fall, based on sample 2:

Left limit _____  Right limit ______


HOMEWORK - DIFFERENCE BETWEEN THE MEANS TEST

Homework: two random samples of 10 patrol officers from the XYZ Police Department, each officer tested for cynicism (continuous variable, scale 1-5)

Hypothesis 1:  Gender determines cynicism

Hypothesis 2:  Males are more cynical than females

Sample 1 (males) scores: 3 3 3 3 3 3 3 1 2 5  -- Variance = .99

Sample 2 (females) scores: 2 1 1 2 3 3 3 3 4 2  -- Variance = .93

CALCULATE:

Pooled sample variance _______

Standard error of the difference between means _______

t statistic _______

df (degrees of freedom) ________

Hypothesis 1:  Would you use a ONE-tailed t-test ____ OR a TWO-tailed t-test ____ (check ONE only)?

Can you reject the NULL hypothesis?  YES ____  NO ____

Hyothesis 2:  Would you use a ONE-tailed t-test ____ OR a TWO-tailed t-test ____ (check ONE only)?

Can you reject the NULL hypothesis?  YES ____  NO ____

Instructions for doing a t-test are in the book.  The t-test tables are in the appendix.


HOMEWORK - CHI-SQUARE

 

Job Stress

 

Position on police force

Low

High

Total

Sergeant

30

60

90

Patrol officer

86

24

110

Total

116

84

200

    1. Calculate expected cell frequencies (null hypothesis of no relationship
    is true)

    2. Compute Chi Square

    3. Use table in Appendix E to determine your Chi Square's probability level

    4. Can we reject the NULL hypothesis? (As usual, cannot take no more than 5 chances in 100 of being wrong)


HOMEWORK - LOGISTIC REGRESSION

Column b: Logistic regression coefficient reporting relationship between each IV and DV (instigating crime)

Column Exp b: Odds ratio

1. Which independent variable(s) have a statistically significant relationship with the dependent variable? At what level?

2. Interpret Exp(b) for "White" using percentage

3. Interpret Exp(b) for "Number of crime types" using percentage

4. Interpret Exp(b) for "Excitement seeking" using percentage