Math-Statistics-Quiz:Quantitative Methods in Public Admin
Math-Statistics: Quantitative Methods in Public Administration. Please show work. SEE ATTACHMENT(S) FOR ASSIGNMEN/QUESTIONS.
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Instructor’s Notes #6:
Observational Methods (continued)
1. Quasi-Experimental Designs (Quantitative)
Research outside the laboratory setting may not allow the required amount of control achieved in the classic experimental approach. However, one alternative is the use of so-called “quasi-experiments,” where the researcher constructs the best possible approximation of an experiment and controls for as many threats to validity as practical.
2. Experimental Options in the Absence of Randomization
Without randomization we now must deal with selection problems directly through either:
•Study Design. Find ways to match up the control and treatment groups before the research is conducted. This involves thinking through important dimensions of the treatment group that might be related to the results, and to find a control group that is similar.
•Statistical Methods. This involves collecting information about confounding factors that might affect the outcomes for both the control and treatment group. Multiple regression is the typical form of statistical analysis. We will cover multiple regression later in this course.
3. Key to Good Quasi-Experimental Design
Both strong study design and adequate data are keys to good quasi-experimental design because they make possible the use of powerful statistical tools. I will discuss design issues and analysis tools within the context of three “typical” types of quasi-experimental design.
•Pre- and Post-Design
•Time Series Design
4. Basic Non-equivalent Group Designs
Without randomization, the study design takes on even greater importance. The credibility of the study to the public, even if you use sophisticated statistical methods, will often hinge on whether you have a good study design. The key question to ask yourself in designing a study is: Are there alternative explanations for the results that you found in the study? If so, can you design a study that will rule-out alternative explanations? A key in quasi-experimental design is the selection of the control group.
5. Selecting the Control Group – Design Alternatives:
First you need to characterize your treatment group on important observable characteristics. Then, you will constrain your potential control group to fall within these ranges. The control group is artificially constrained to look as much like the treatment group as possible.
•Matched Pair Sampling If you keep adding control factors to the cluster sampling eventually you will get to the point where there is only one member of the control group. This is termed the “matched pair” sample. A profile for each treatment group member is developed and then a match is found for the control group with similar characteristics.
•Cell matching is a version of cluster sampling, except a separate cell is created for each treatment group member (or group of members) with certain characteristics. The control group is then divided into similar cells and equal numbers of control group members to the treatment group are selected from this cell.
•Distance function matching involves creating a composite measure for each treatment and control group member which is a combination of relevant characteristics. Treatment group members are then matched to the control group member that is the closest distance.
Sometimes the best comparison group is within the same organization itself, but at an earlier time.
Although seldom discussed, it is possible to actually do a random sample of the control group, even if the treatment group is self-selected. If you know the direction of the bias, then it is possible to use statistical methods to provide a rough estimate of the effects without the bias. The control group is used to fit a model of the true population. You then attach confidence intervals around this regression model, and see if the treatment group falls within the intervals. If not, then you can conclude with confidence that there is a significant difference.
MIDTERM EXAMINATION (Ch. 1-7)
Student’s name: __________________________________________
There are 5 parts to this 100-point exam; you are to answer each part. If problems need calculations and you use a calculator, please show explicitly all the computational steps you followed to obtain your results. [In case of a calculation mistake, you’ll get partial credit. Don’t miss this opportunity]! For other problems just type your answers. [You can use reasonably unlimited space]. Do well!
Part 1 (30 POINTS, one for each question)
1. A researcher is preparing a report and wants to select a measure of central tendency that shows the most commonly occurring score in a particular distribution. Which statistic should she select?
d. none of the above
2. Since computation of the standard deviation requires addition, division, and other mathematical operations, it should be used for
a. interval-ratio level variables
b. non-continuous variables at any level of measurement
c. nominal level variables
d. discrete variables only
3. When interval-ratio data are badly skewed, the appropriate measure of central tendency is the
d. first quartile
4. The Z score table gives the area between a score and the mean. For a Z score of -1.00 that area (in percentages) is
5. If the scores on a variable are 11, 18, 14, 25, and 20, the median is
6. The area between a negative Z score and a positive Z score can be found by a. subtracting the Z scores from each other
b. subtracting each Z score from the mean and adding the results
c. adding the Z scores and finding the area in the Z score table for the summed Z scores
d. adding the areas between each Z score and the mean
7. When constructing a frequency distribution, the number of class intervals, in general, should be
a. more than 20
b. about 10
c. only 2
d. the same as the number of cases
8. The sampling distribution links the ________ distribution to the __________ distribution. a. stratified, EPSEM
b. statistical, empirical
c. sample, population
d. empirical, real
9. The purpose of inferential statistics is to acquire knowledge of the ____________ from the ___________ by means of the _____________ distribution
a. population, sample, sampling
b. sample, sampling, population
c. inductive, empirical, stratified
d. theoretical, empirical, theoretical
10. The most commonly used confidence level is
11. In addition to saying that one case is different from another, the ordinal level of measurement allows us to
a. order categories from high to low
b. measure the distance between high and low
c. say that one case is more or less than another
d. both a and c
12. Which sample size will produce the confidence interval with the smallest width?
13. Which of the following is NOT a nominal level variable?
a. level of education
b. zip code
d. maker of auto
14. Computation of a mean is completely justified when a variable is measured at which level?
15. To obtain the area below a positive Z score or above a negative Z score you would a. subtract the value of the Z score from the mean
b. subtract the area in the “Area Beyond Z” column of the Z score table from 50%
c. add the value of the Z score to the area beyond the mean
d. add the area between the Z score and the mean to 50%
16. The average weight of a sample of women who attend aerobics classes at the YWCA is 130 pounds. We constructed a confidence interval (using an alpha of 0.05) of ± 3.45. The upper and lower limits of our estimate are
a. 130.00 and 133.45
b. 126.55 and 130.45
c. 126.55 and 133.45
d. unknown; these values will depend on the number of women who are truly serious about exercising
17. Below are some items from a population survey. For each survey item, identify the level of measurement.
a. In what region of the country were you born?
__ Far West
__ Born out of Country
b. How many siblings do you have? ______
c. How satisfied are you with the quality of instruction at this institution?
__ Very satisfied
__ Very Dissatisfied
d. How many miles per gallon does your car average?____
e. People convicted of first degree murder should be executed.
__ Strongly Agree
__ Neither Agree nor Disagree
__ Strongly Disagree
18. In Table 1, what percentage of Community A are Republicans?
a. (103/264) x 100 = 39.02
b. (103/17) x 100 = 605.88
c. (264/328) x 100 = 80.49
d. (103/135) x 100 = 76.30
|TABLE 1 POLITICAL PARTY MEMBERSHIP IN TWO COMMUNITIES|
|PARTY:||COMMUNITY A||COMMUNITY B|
19. In Table 1, what is the ratio of Socialists to Democrats in Community B?
20. As our confidence in an interval estimate increases, the width of the interval
c. remains the same
d. increases or decreases depending on the alpha level
21. A police department reports that the number of reported rapes in their jurisdiction increased by 100% over the past decade. This means that the number of reported rapes today is
a. double the number 10 years ago
b. actually about the same as 10 years ago
c. equal to the number 10 years ago plus 50%
d. triple the number 10 years ago
22. The chance of a randomly selected case having a score beyond ± 1.00 standard deviation of the mean is
d. 1/2 of the area of 1 standard deviation
23. Histograms and line charts or frequency polygons are used with data measured at the
a. nominal level
b. ordinal level
c. interval-ratio level
d. any level
24. In a two person race, if the Republican presidential candidate is projected to attract 44% ± 3% of the vote and the Democratic candidate is projected to attract 46%±3% of the vote, then
a. the Republican is the probable winner
b. the Democrat is the probable winner
c. neither candidate will win a majority of votes in the electoral college
d. the race is “too close to call”
25. In a positively skewed distribution the mean is
a. equal in value to the median
b. greater in value than the median
c. less in value than the median
d. either a or b, depending on the value of the mode
26. The most appropriate measure of central tendency for the variable age (measured in years) would be the
d. standard deviation
27. In any distribution, the mean and the median will have the same value when the distribution is a. symmetrical
b. positively skewed
c. negatively skewed
d. all of the above
28. The variable socioeconomic status ranges from upper class to lower class and is an example of the
a. nominal level of measurement
b. ordinal level of measurement
c. interval-ratio level of measurement
d. ratio level of measurement
29. If you subtracted the mean from each score in a distribution and added the results, the sum would be
b. less than zero
c. a minimum
d. the mode
30. If distribution A and distribution B have the same mean but A has a larger standard deviation, we may conclude that
a. the medians of both distributions would be the same
b. distribution B has a range of 0
c. A has a greater degree of dispersion
d. distribution B displays more variety
Part 2 (15 POINTS)
Read the following article from The New York Times (on page 7) and answer the following questions.
- What is the objective of Dr. Larry Kurdek’s research?
To determine how marital quality changes over time
- What is the population that he is studying?
- What is the sample size?
- What is the unit of analysis?
Rate of change in marital quality
- What is the dependent variable? (What level of measurement would you use for it? In other words, given what you know about measurement, how do you think the respondents were asked to reply to the questions?).
- What are the independent variables? (What level of measurement would you use for each variable? In other words, given what you know about measurement, how do you think the respondents were asked to reply to the questions?).
- Divorce history,
- Presence of children
- Personality variables
- Draw Kurdek’s theory (causes and effects) using boxes and arrows…
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