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PPA 207: Quantitative Methods
Meeting 8, Spring 2004
1. Homework
Studenmund, Chapter 7, Number 13
a. The dependent variable (E) is the defined as the efficiency rate or total output
to goal output. The explanatory variables are total output (Q), absentee rate in
percentage (A), and incidents of violence (V). I hypothesize that Q should have a
positive influence on E. A and V should both have a negative influence on E. The
dof are 20 and using a 95 percent level of confidence the critical t in a one-tailed
test is 1.725; in a two-tailed test it is 2.086. The calculated t on Q is 4.0; on A it is
2.0 and on V it is 0.125.Therefore we can "accept" the alternative hypothesis that
Q has a positive influence on E using both the one-tailed and two-tailed test
(actual t > critical t). We can also "accept" the alternative hypothesis that A has a
negative influence on E if using one-tailed test, but not if using a two-tailed test.
We cannot "accept" the alternative hypothesis that V has a negative influence on
E using either a one or two tailed test.
b. The calculated effect of Q on E is done with both in log form. Thus the
regression coefficient of 0.16 represents the percentage change in E given a
one-percent change in Q. We have calculated an elasticity that is constant for all
values of E. With regards to A and V they are not in log form. The regression
coefficient of -0.020 on A and -0.0001 on V are not elasticities but need to
multiplied by a value of either A or V to transform them into an elasticity. Usually
this value is chosen as the mean. Thus the elasticity is not constant, but varies
by the chosen value for either A or V.
c. As stated in part a, we cannot reject the null hypothesis that V has a zero or
positive effect on E. Thus the court cannot conclude from this regression that
violence had a significant impact on efficiency rate.
d. There are obviously omitted variable problems. There are other important
variables that determine efficiency rate that have been left out of this regression.
This may be the reason for the finding that V has no effect on E. There is also a
problem with taking the log of E and the log of Q and creating a log-log functional
form. Since E equals Q over goal output, and in a given week goal output is
constant, a one unit increase in Q will result in a constant increase in E. For
example assume that goal output is 3. If Q equals 1, E equals 1/3; if Q equals 2,
E equals 2/3; if Q equals 3, E equals 3/3; etc. For each one unit increase in Q, E
increases by 1/3. This is a pure linear relationship and there is no reason to run a
regression that models it as a non-linear relationship. So the one thing that I
would change is drop taking the log of Q and just re-run as a left log-linear
regression.
Pollock, Chapter 5, Numbers 1 and 2
2. Midterm Exam
3. Pollock, Chapter 6, Making Inferences About Sample Means

Draw a sample that wish to make inferences about entire population on
Need to discuss “confidence” or “probability” of being correct

For example, calculate mean
How confident that it is representative of population

Load NES2000.sav
Descriptive statistics on SPEND13

How confident can you be in mean
Based upon calculated standard error
One-Sample T Test (95% confidence interval)
Analyze=>compare means=> one-sample T test
Lower and upper bounds reported
Can change it to represent a 90% confidence interval

Hypothesize that political science majors are more likely to favor gov’t
spending
The mean value of SPEND13 = 5.86 (total sample mean = 5.76)
Within confidence intervals calculated earlier
Run another one-sample T test, but enter 5.86 into test value box
Sig. in two tailed is 0.134 (or 0.067 in each tail)
Meaning that there is a 6.7% probability of observing this difference
if means of two groups are the same
We seek less than 5% probability

Compare the sample means of a dependent variable for two groups
Analyze=>compare means=>independent sample T tests
Need test variables, grouping variable (define groups)
Means reported for each variable, by male and female
Mean differences are reported below
Check Levene’s test for equality of variances
Value greater than or equal to 0.5, use equal
variances assumed
Look at sig. (2-tailed) and divide by two
15.9% of time we could observe difference
even if same
Cannot reject null hypothesis that same
Not the case for opinion on women’s
movement
5. Homework Due the Start of Meeting Nine
(1) Read all of the material under meeting nine in the syllabus; come prepared to
discuss.
(2) A typed and well developed question from reading assignment for week nine.
(3) Answer questions 1, 2 and 3 in Pollock, Chapter 6, handwritten on given
pages and turn in any requested SPSS output.