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
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EXERCISE 1 - MEASURES OF DISPERSION
Assignment: compute each measure of dispersion
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EXERCISE 2 - COMPUTING Z-SCORES
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1. Obtain the z-score for each case.
2. Estimate how many arrests fall beyond each z-score.
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 sample? Why? (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.
RELATIONSHIP BETWEEN CONTINUOUS VARIABLES (CORRELATION)
Hypothesis: Changes in height causes changes in weight
1. Create a scattergram from this data
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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?
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 ______
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)
Sample 1 scores: 3 3 3 3 3 3 3 1 2 5 -- Variance = .99
Sample 2 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) ________
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.
CHI-SQUARE
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