Provisionally approved June 6, 2002
STATISTICAL REASONING
Level III
RATIONALE: Statistical reasoning informs decision making in all public domains. It is essential to the understanding of existing policies and practices in public and private domains. It also provides powerful tools to substantiate advocacy for the improvement of public policies and practices.
A statistic is a number that summarizes information from a collection of data. Like all summaries, a statistic provides a general idea at the expense of a lot of details. Statistical reasoning is the process of using statistics to be informed about important issues. It is a two-fold process: It uses the summary statistic to search for information on particulars, and it extends the statistic to apply to a larger population. For example if the median cost of a single-family house in Boston is $245,000, one may want to look at the range of prices from cheapest to most expensive and how this range is spread, hence figuring out more of the details missed by the summary statistic, i.e. the median. Equally important is the process of generalizing from a single statistic. For example, if an opinion poll that was conducted using a sample of urban dwellers indicated a preference for government spending on public transportation, one can generalize this information to apply to all urban dwellers if the sample was well chosen. This competency requires students to use statistical reasoning to make sense out of data by making inferences and predictions from statistics as well as scrutinizing statistics for information on particulars.
Acquiring the concepts and skills in this competency will empower a student to select and use appropriate methods to analyze data; and to develop and evaluate inferences and predictions based on data. The concepts and skills can facilitate and deepen the acquisition and understanding of several other competencies, such as Social Research: Consumption and Design and the Doing Social Research capstone.
COMPETENCY: Can understand and use statistical data in order to inform
decisions about public and community issues.
CRITERIA:
Please note that all criteria assume the use of computer-based statistical software or the statistical capabilities of a graphic calculator.
1. Search for and collect appropriate data to answer critical questions about public and community issues.
2. Understand and utilize Normal, Binomial, and Sampling distributions.
3. Evaluate published reports that are based on data.
PORTFOLIO LINKS: You are expected to use the Writing Portfolio criteria
and standards as guidelines for the written products required by this competency.
Papers written for this competency may be considered for submission to the
Writing Portfolio.
STANDARDS:
1. For Criterion 1, you must engage in two activities and provide an oral presentation on each. The oral report must be substantiated by graphical displays either through a computer-based presentation tool such as a Power Point or through other appropriate visual aids.
a. In one activity, you must collect a simple set of data from a convenience sample aiming at answering a question that pertains to issues of public and community service. You must organize and display the data, produce the appropriate statistics, and attempt to answer the question asked.
b. In the second activity, you must take the same steps, using raw data that are found in a primary source such as the U.S. Census.
c. The total of the two activities must include both univariate and bivariate measures. This necessitates the following:
· For one set of data, apply a univariate measure: display a frequency distribution using appropriate graphical and tabular representations; describe the shape of the distribution; select and calculate summary statistics such as measures of central tendency and of variability.
· For two sets of data from the same population apply bivariate measures: display a scatterplot, describe its shape, determine if it fits a linear model (linear regression), and determine the strength of the association (correlation coefficient).
2. For Criterion 2, you will respond to a series of written questions and exercises provided by the evaluator to verify knowledge of concepts a-e below. Alternatively, you may negotiate with the instructor to provide other material that verifies the acquisition of concepts in a-e below.
a. Compare frequency distributions of actual data to theoretical distributions such as the Normal and Binomial distributions.
b. Use Normal and Binomial distributions to make inferences from sample statistics.
c. Use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions.
d. Show how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inferences.
e. Utilize sampling distributions to understand margins of errors and incorporate this understanding in the interpretations of inferences made.
3. For Criterion 3, you must either request a published report from the evaluator, or choose one, subject to the approval of the evaluator. You must write an evaluation of at least 5 pages addressing the following:
a. the type of samples used;
b. the appropriateness of data analysis;
c. the appropriateness of inferences and predictions made; and
d. the validity of conclusions made.
EXAMPLES OF DEMONSTRATION:
1. Prior Learning: You have worked with an organization in which you were part of a team conducting research on violence in public schools and its impact on student performance. You prepare a written outline or summary of your role and work; identifying which competency criteria you feel you have demonstrated. You submit written material, audiotapes, videotapes, or any other evidence documenting work done and skills demonstrated through your work. For any criterion not fully covered by prior learning, you negotiate with the evaluator(s) for additional work to be done independently or through the organization you are working with.
2. Independent Learning: You have good math and computer skills and have already demonstrated the Quantitative Reasoning competency. You feel that you can learn the concepts on your own. You meet with an evaluator to discuss the possibility. You go over the competency criteria and standards together, identify possible sources of information and materials you might read, and emerge from the meeting agreeing to put together a written timeline for your work. When your timeline has been finalized and the evaluator has signed off on it, you undertake your study, meeting periodically with the evaluator to go over what you have done and get feedback. Your final products are the same as stated in the requirements in the “Standards” section above. Your products are evaluated based on the same quality standards that other students taking an instructional activity are expected to meet.
3. Course: Complete a CPCS course addressing the competency or an appropriate transfer.
4. Field Project: You are part of a team of CPCS students and faculty working with an advocacy group concerned about how former welfare recipients are faring economically since the onset of welfare reform time limits in Massachusetts. The project will involve surveys, interviews, Census data, and a search of public records on relevant data. You are in charge of organizing data and identifying what other data are needed to answer the questions the team is interested in. You have strong quantitative and computer skills. You read about statistical methods and apply your understanding to analyze the data and reach conclusions based on them. Your final product is a written report, along with evidence of work done to collect and analyze information.