HOMEWORK ANSWERS  MEASUREMENT & CENTRAL TENDENCY
HOMEWORK ANSWERS  VARIABILITY
HOMEWORK ANSWERS  CROSSTABULATION
Hypothesis: Rank causes cynicism Zeroorder table
We do not need to convert these cell frequencies into percentages. Why? When selecting the sample, I stratified (as usual) by the independent variable. By choosing 100 officers and 100 supervisors, the distributions along the dependent variable, at each value of the independent variable, are automatically percentages (PER 100).
Is there are relationship? You bet. Note that as we "switch" the independent variable RANK from officers to supervisors, the distribution of cases along the dependent variable changes, from 20 LOW and 80 HIGH to 50/50. Changes in the independent variable go along with changes in the dependent variable. So there is an association between the variables.
Firstorder partial tables: "replication"
Here we converted frequencies to percentages because the totals at each level of the independent variable are no longer 100. Inspecting the percent tables for both levels (male, female) of the control variable GENDER, we notice that each depicts a relationship between RANK and CYNICISM that resembles the relationship in the zeroorder table. We have "replicated" our original finding. GENDER, whether male or female, does not tell us anything new. It does not change our original opinion  changes in rank appear to cause changes in cynicism. BUT suppose the firstorder tables came out looking like this:
Firstorder partial tables: "specification"
Although there still seems to be a relationship between rank and cynicism for males, there does not seem to be a relationship between rank and cynicism for females. For females, when we "switch" the independent variable from officers to supervisors, the distributions of cases along dependent variable CYNICISM remain the same. There seems to be no connection  no relationship  between rank and cynicism.
When some values of a control variable are consistent with the zeroorder relationship, but others are not, we call the effect of the control variable "specification".
Firstorder partial tables: "explanation"
Above, there seems to be no relationship between rank and cynicism for females. IF there had been no relationship for males, then control variable GENDER would have completely "explained away" the relationship in the zeroorder table. We could then say that rank does not cause cynicism  gender does!
When an association between variables in a zeroorder table is rejected at every level of a control variable, we say that the control variable "explains away" the zeroorder relationship.
HOMEWORK ANSWERS  CORRELATION & REGRESSION
The scattergram depicts a very strong positive relationship between variables. Estimated r is + .80 or + .90
Below are the same variables rescaled as categorical. Note that the distribution of the dependent variable runs vertically at each value of the independent variable.
At the Short value of the independent variable (height), the distribution of the dependent variable (weight) is skewed completely to Low. But when we change the value of the independent variable to Tall, the distribution of the dependent variable flips, with most cases now High.
Adjusting the value of the independent variable does change the value of the dependent variable. Considering the magnitude of the change, their association seems strong even after they are rescaled from continuous to categorical.
HOMEWORK ANSWERS  STANDARD ERROR OF THE MEAN & CONFIDENCE INTERVAL
Standard deviation for sample 1: .99
Standard deviation for sample 2: .97
Standard error of the mean based on sample 1: .33
Standard error of the mean based on sample 2: .32
95% Confidence interval into which the population mean should fall, based on sample 1:
Left limit = 2.25 Right limit = 3.55
95% Confidence interval into which the population mean should fall, based on sample 2:
Left limit = 1.77 Right limit = 3.03
HOMEWORK ANSWERS  DIFFERENCE BETWEEN THE MEANS TEST
Pooled sample variance = .96
Standard error of the difference between means= .44
t test = 1.14
df ( n_{1} + n_{2} 2) = 18
Hypothesis one:
TWOtailed test (we did not predict which sample means would be significantly larger)
Minimum size t for significance (<.05) is 2.101
We CANNOT reject the null hypothesis. The probability that the difference between means is due to chance exceeds 5 in 100.
Hypothesis two:
ONEtailed test (we predicted that the male mean would be significantly larger)
Minimum size t for significance (<.05) is 1.734
We CANNOT reject the null hypothesis. The probability that the difference between means is due to chance exceeds 5 in 100.
HOMEWORK ANSWERS  CHISQUARE

Job Stress


Position on police force

Low

High

Total

Sergeant

52

38

90

Patrol officer

64

46

110

Total

116

84

200


df = 1 (r1)(c1)
Can we reject the null hypothesis? Yes, p <.001
HOMEWORK ANSWERS  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?
*  .05 level  less than 5 chances in onehundred that the null hypothesis is true  Adversity, Age at first arrest, Number of crime types, Access to potential cooffenders
**  .01 level  less than 1 chance in onehundred that the null hypothesis is true  White, Frequency of Offending
***  .001 level  less than 1 chance in onethousand that the null hypothesis is true  Excitement seeking
2. Interpret Exp(b) for "White" using percentage
41 percent less likely that Whites (as compared to nonwhites) instigate crime (Exp b less than 1, so subtract from 1.00: 1.00.59=41)
3. Interpret Exp(b) for "Number of crime types" using percentage
16 percent more likely that the more types of crime one commits, the more he/she will instigate others to commit crimes
4. Interpret Exp(b) for "Excitement seeking" using percentage
248 percent more likely that persons motivated by excitement will instigate others to commit crimes
