Student name: SOCI 420 Advanced Methods of Social Research Fall 2017

Transcription

1 SOCI 420 Advanced Methods of Social Research Fall 2017 EXAM 1 RUBRIC Instructor: Ernesto F. L. Amaral, Assistant Professor, Department of Sociology Date: October 12, 2017 (Thursday) Section 903: 9:35 10:50am Percent of final grade: 20% Write your name on the top of all pages of this exam. Return all pages to the professor. Multiple choice questions Answer the following 30 multiple choice questions. Each question is worth 0.4 points for a total of 12 points. Mark your responses on a grey and white 8.5 x11 Scantron testing form. Only No.2 pencils can be used to bubble in answers (not ink). The correct answers are underlined. 1. In social research the purpose of statistics is to a. prove that the research theory is correct. b. validate the research project design. c. manipulate and analyze data. d. ensure acceptance by the scientific community. 2. According to the "Wheel of Science," research projects begin a. with theory. b. with data. c. with a hypothesis. d. at any stage on the Wheel. 3. In the research process, theory a. is unnecessary. b. is always fully developed before any data is gathered. c. is developed only after the data have been completely analyzed. d. attempts to explain the relationship between phenomenon. 4. A hypothesis states, in part, that "income increases as education increases". In this statement, education is a. the dependent variable. b. the independent variable. c. the hypothetical variable. d. the secondary variable. 5. The statement "Eight out of ten elderly residents fear victimization" is an example of a. univariate descriptive statistics. b. multivariate descriptive statistics. c. inferential statistics. d. inductive statistics. 6. The data reduction process of descriptive statistics a. allows a few meaningful numbers to summarize a large amount of data. b. eliminates incorrect data. c. simply lists all available information in order. d. is rarely used. 1

2 7. A researcher wants to know if there is a relationship between region of birth and political party affiliation. She should calculate a a. univariate descriptive statistic like the mean. b. qualitative measure of influence. c. measure of association. d. statistic that measures the non-relational differentiation between the two variables. 8. A survey administered to a sample drawn from a local community finds that a person's political party affiliation is related to whether or not they favor an increase in local sales tax (the headline of a newspaper story based on this poll reads: "Republicans support proposed tax increase"). This is an example of the use of a. univariate descriptive statistics. b. multivariate descriptive statistics. c. inferential statistics. d. reductionist statistics. 9. Which of the following survey items would generate a discrete variable? a. How old are you? b. How long does it take you to commute to work? c. How much did you pay in taxes last year? d. How many cars do you own right now? 10. A researcher has calculated the mean for a variable that is ordinal in level of measurement. a. This operation is a violation of level of measurement criterion and the results should be disregarded. b. This violation of level of measurement criterion is common and results should be treated with caution. c. No violation has occurred, this is a perfectly acceptable application of statistics. d. This is a mistake: means should never be calculated for ordinal variables because they are always continuous. 11. To find the ratio of smokers to non-smokers, you would a. divide the number of non-smokers by the number of smokers. b. add them together and divide by the number of smokers. c. divide the number of smokers by the number of non-smokers. d. multiply the number of smokers by the total number of people. 12. In Table 1, what percentage of Community A are Republicans? a. (103/264) x 100 = b. (103/17) x 100 = c. (264/328) x 100 = d. (103/135) x 100 = Table 1. Political party membership in two communities Party Community A Community B Total Republicans Democrats Independents Socialists Total Source: Fictitious data. 13. To calculate a proportion, the number of cases in any category (f) is divided by a. the total number of categories (k). b. the number of cases in all categories (N). c. the cases in that category (f). d. the number of cases in adjacent categories (k-1). 2

3 14. The midpoints of intervals for frequency distributions constructed with interval-ratio variables are found by a. adding the upper and lower class limits for each interval and then dividing by 2. b. multiplying the upper and lower class limits for each interval. c. dividing the range by 10. d. None of the above. Class intervals for interval-ratio variables do not have midpoints. 15. Cumulative frequencies and cumulative percentages allow a researcher to a. be sure the column totals are correct. b. tell at a glance how many cases fall above or below a given category. c. show the accuracy of his or her findings. d. All of the above 16. A frequency distribution should reflect a balance of a. detail and conciseness. b. time and money. c. questions and answers. d. elegance and symmetry. 17. The crude birth rate of a city that has 250 births in a year and a population of 7500 would be found by using which of the following? a. crude birth rate = (250/7500) x 1000 b. crude birth rate = 7500/250 c. crude birth rate = (1000/7500) x 250 d. crude birth rate = (250/1000) x A small town of 1,709 residents had one homicide in the past year. The homicide rate for this town a. cannot be determined from the information given. b. is (1/1709) x 100,000. c. is rising. d. is (1709:1) x 1, When examining a single categorical variable with emphasis on the differences between two or more categories, it is best to use a a. histogram. b. column chart. c. line chart. d. none of these choices are correct. 20. 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. 21. A line chart or frequency polygon is based on a. the upper limits of each interval. b. the lower limits of each interval. c. the midpoint of each interval. d. any limit which the researcher selects. 22. The purpose of measures of central tendency is to describe what value of a distribution of scores is a. the most typical or representative. b. the most surprising or unexpected. c. the most significant or important. d. all of the above. 3

4 23. If the scores of an even number of cases are arranged from high to low, the median is a. the middle score. b. exactly halfway between the two middle values. c. the average of the highest and lowest scores. d. the same as the mode. 24. For ordinal level variables, the most appropriate measure of central tendency is generally a. the mode. b. the median. c. the mean. d. None of the above 25. If you subtracted the mean from each score in a distribution, squared the differences, and then added the squared differences, the sum would be a. zero. b. less than zero. c. a minimum. d. a maximum. 26. A distribution of income for a sample of 45 people that included the presidents of the five largest corporations in the United States and 40 assembly line workers would be a. unskewed. b. negatively skewed. c. positively skewed. d. symmetrical. 27. Measures of dispersion provide information about the a. typical or most common score. b. variety within the distribution of scores. c. size of the sample. d. adequacy of the selection criteria for the sample. 28. One problem with the range (R) as a measure of dispersion is that it a. is very difficult to calculate. b. ignores the most extreme scores. c. can be used only for nominal level variables. d. is based on only the most extreme scores. 29. Your score on the test is the same as the third quartile (Q3). You may conclude that a. the distribution of the scores is skewed. b. you scored higher than 75% of the people who took the test. c. your score is 'typical' since it is the same value as the median. d. you scored higher than 25% of the people who took the test. 30. The income of a sample has been measured in dollars per year. Which of the following would be the preferred measure of the dispersion for this variable? a. The index of qualitative variation b. The average deviation c. The quartile deviation d. The standard deviation 4

5 Essay questions Please answer the following 4 essay questions. Each question is worth 2 points for a total of 8 points. Answer these questions on the back of the pages of this exam. You should number your answers. Use a black ink pen or a blue ink pen to answer these questions (not pencil). 31. Explain the purpose of inferential statistics. Include in your essay the concepts of sample, population, statistic, parameter, representativeness, the principle of EPSEM, and the sampling distribution. Make sure that you define each of these terms as you develop your answer. Explain the two theorems that define the characteristics of the sampling distribution. 10 items at.2 points each 1. Inferential statistics definition 2. Sample definition 3. Population definition 4. Statistic definition 5. Parameter definition 6. Representativeness definition 7. EPSEM definition 8. Sampling distribution definition 9. Theorem Theorem 2 5

6 32. Explain and distinguish between simple random sampling, systematic random sampling, stratified random sampling, and cluster sampling. How these techniques are designed to guarantee representativeness? Why did the professor mention his research project about visitors of street markets when he was explaining sampling techniques? 7 items at.286 each 1. Simple random definition 2. Systematic random definition 3. Stratified random definition 4. Cluster definition 5. Difference between these sampling techniques 6. How do techniques guarantee representativeness? 7. Why the street market example? It was an example of a nonprobability sampling 6

7 33. Write and explain each component of the formulas for: (1) Z score; and (2) confidence interval for sample proportions with large samples (N>100). Explain what happens to the alpha, Z score, and width of the confidence interval when the confidence level increases. Give an example with fictitious sample proportion, population proportion, and sample size. Explain what happens to the confidence interval when the sample size increases. 9 items at.222 points each 1. Formula: Z score 2. Description of components 3. Formula: Confidence interval for sample proportions 4. Description of components 5. Confidence level increases, alpha decreases 6. Confidence level increases, Z score increases 7. Confidence level increases, width of confidence interval increases 8. Example includes proportion, standard deviation, sample size 9. Sample size increases, confidence interval is narrower 7

8 34. Explain in detail each of the following outputs from Stata. These tables are about the respondent income in constant dollars (conrinc) from the 2016 General Social Survey. Write and explain the formulas for the mean, standard error, and confidence interval. Explain the reasons of different estimations in each output.. svyset [weight=wtssall], strata(vstrat) psu(vpsu) singleunit(scaled). mean conrinc Mean estimation Number of obs = 1,632 Mean Std. Err. [95% Conf. Interval] conrinc mean conrinc [aweight=wtssall] Mean estimation Number of obs = 1,632 Mean Std. Err. [95% Conf. Interval] conrinc svy: mean conrinc (running mean on estimation sample) Survey: Mean estimation Number of strata = 65 Number of obs = 1,632 Number of PSUs = 130 Population size = 1, Design df = 65 Linearized Mean Std. Err. [95% Conf. Interval] conrinc items at.182 points each 1. What is the first command doing? Complex survey design takes into account stratum (vstrat variable), primary sampling unit (vpsu variable), and weight (wtssall variable). 2. What is the second command doing? Interpret results. Mean estimation with no weight, no complex survey design. The second command generates information that is valid only for the sample. It is not representative to the population. 3. What is the third command doing? Interpret results. Mean estimation with weight, no complex survey design. This command corrects the estimation of the mean. The point estimate (mean) is representative to the population. 4. What is the fourth command doing? Interpret results. Mean estimation with complex survey design (which also takes into account the weight). This command corrects the estimation of the mean, standard error, and confidence interval. The point estimate (mean) and the interval estimate (confidence interval) are representative to the population. 5. Formula for mean 6. Explanation 7. Formula for standard error 8. Explanation 9. Formula for confidence interval 10. Explanation 11. What is different about the estimations in the three outputs? First estimation (no weight, no complex survey design) relates only to the sample. Second estimation (weight, no complex survey design) has a point estimate (mean) that is representative to the population. Third estimation (complex survey design, which also informs weight) has a point estimate (mean) and interval estimate (confidence interval) that are representative to the population. 8