HOMEWORK ANSWERS - MEASUREMENT & CENTRAL TENDENCY

PE answer 3

PE answers 1,2

PE answer 4


HOMEWORK ANSWERS -- VARIABILITY

Variability homework1 answers


HOMEWORK ANSWERS - CROSSTABULATION

Hypothesis:  Rank causes cynicism
Zero-order table

Picture1

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. 

First-order 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 zero-order 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 first-order tables came out looking like this:

First-order 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 zero-order relationship, but others are not, we call the effect of the control variable "specification".

First-order 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 zero-order table.  We could then say that rank does not cause cynicism - gender does!

When an association between variables in a zero-order table is rejected at every level of a control variable, we say that the control variable "explains away" the zero-order relationship.


HOMEWORK ANSWERS - CORRELATION & REGRESSION

Answer1

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.  

Answer2


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 ( n1 + n2 -2) = 18

Hypothesis one:

TWO-tailed 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:

ONE-tailed 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 - CHI-SQUARE

 

Job Stress

 

Position on police force

Low

High

Total

Sergeant

52

38

90

Patrol officer

64

46

110

Total

116

84

200

 

df = 1 (r-1)(c-1)

PE answer ChiSquare

 

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 one-hundred that the null hypothesis is true - Adversity, Age at first arrest, Number of crime types, Access to potential co-offenders

** - .01 level - less than 1 chance in one-hundred that the null hypothesis is true - White, Frequency of Offending

*** - .001 level - less than 1 chance in one-thousand 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 non-whites) 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