Spring 2017 Statistics Assessment

We offer four statistics classes across the campus, one each in psychology, sociology, SPEA and math/education. In the spring of 2017, two courses (Sociology and SPEA) assessed the three general education requirements for this course:

IU Northwest students will:1. Use mathematical models such as formulas, graphs, tables to draw inference2. Represent mathematical information symbolically, visually, numerically, and verbally.3. Demonstrate the ability to effectively use arithmetic, algebraic, geometric, logical and/or statistical methods to model and solve real world problems.

The two courses assessed the same outcomes using different instruments and methods:

1. Sociology S262 used the same questions we assessed learning with the last time we assessed these outcomes in 2015 (see Appendix for the questions). The questions were presented as pop-quizzes in class as the students were in the part of the course where the knowledge applied.

2. SPEA used multiple instruments and a decaying average in Canvas to assess the learning over four assignments, with the last assignment counting 70% weight and the other three accounting for 30% total. This was done in the form of application quizzes where students had to make calculations (descriptive statistics, three t-tests, chi-square, analysis of variance, correlation and regression) and then apply them to the real-world problems they represent (see Appendix for the quizzes and rubrics).

Sociology Results

Outcome 1: Use mathematical models such as formulas, graphs, tables to draw inference.

90% of the class successfully drew inferences from scatterplot graphs.

Outcome 2: Represent mathematical information symbolically, visually, numerically, and verbally.This outcome was measured with two questions.

60% of the class correctly interpreted statistical information.50% of the class correctly represented statistical information visually and interpreted this information.

Outcome 3: Demonstrate the ability to effectively use arithmetic, algebraic, geometric, logical and/or statistical methods to model and solve real world problems.

70% of the class were able to choose and interpret the appropriate test statistic for the problem presented.

SPEA Results (N =78 students; each measured 4 times with decaying average)

Outcome 1: Overall, 65 of 78 students (83%) were rated as 70% or higher on this outcome. Outcome 2: Overall, 73 of 78 students (94%) were rated as 70% or higher on this outcome.Outcome 3: Overall, 32 of 78 students (41%) were rated as 70% or higher on this outcome.

Appendix 1-Sociology Questions

IU Northwest students can use the following formulae, calculators/computer software, and/or statistical tables to solve the following problems:

Confidence interval for means: x± t ∙ SE; standard error SE=s

√n

Hypothesis testing for means: t= x−μ

s√n

;

Outcome 1 (ask students to make inferences from charts or graphs)1. Three scatterplots are shown below. The calculated correlations are 0.9889 , 0.6667, and −0.9351. Determine which correlation goes with which graph.

A B C

Graph A has a correlation r=¿___________.

Graph B has a correlation r=¿___________.

Graph C has a correlation r=¿___________.

Outcome 2 (represent mathematical information)2. A political scientist is tracking support for Proposition B, a state-wide ballot initiative for the upcoming election. She carefully collects data from a sample of the population (n=1300) of state residents and finds that 73% her sample supports Proposition B. Her sample data has a margin of error equal to ± 2.3% (p = .05). In a sentence or two, please help our political scientist interpret her findings for a report in the local newspaper.

3. For the following numerical summaries of data, determine what the distribution looks like (i.e. shape). Explain your reason for each conclusion.

a. M = 50; median = 40, mode = 30

b. M = 50, median = 50, mode = 50

c. M = 50, median = 60, mode = 70

Outcome 3 (use methods to solve problems)

4. Twenty GPAs from a randomly selected sample of statistics students at a college are given below. 2.85, 3.36, 3.13, 2.57, 3.48, 2.77, 3.08, 3.51, 2.61, 3.98, 2.82, 2.65, 3.55, 3.01, 2.76, 3.42, 2.48, 3.13, 3.45, 3.16

Summary statistics:

Column n Mean Variance

Std. Dev. Std. Err. Media

nRang

eMin

Max Q1 Q3

GPA 20 3.0885 0.161392 0.401737 0.089831 3.105 1.5 2.48 3.98 2.765 3.435

Assume that the population distribution is approximately normal. The population mean GPA for the whole college is 2.85.

a) What is the sample mean?__________

Is it higher or lower than the population mean of 2.85? __________________

b) The chair of the statistics department claims that statistics students typically have higher GPAs than a typical college student. State the H0 (Null Hypothesis) and H1 (Hypothesis), choose

a test statistic, find the p-value, reject or do not reject the null hypothesis. Does his claim hold true at significance level of 0.05?

H0: Test statistic: _______

H1: p-value: ______

Conclusion:____________________________________________________________________

Appendix 2: SPEA Instrument and Rubrics

Application Quiz 2: Two Questions (one per student chosen at random)

Please review the tables and graphs below and determine which city was the LEAST effective in reducing homicide over the entire time frame. Not all the data provided is applicable here so you have to understand what is pertinent and what is not. Also, you must cite the data you used to make your decision. (HINT: remember that things happen over time which can impact the statistics, such as 9/11 or Hurricane Katrina, so keep that in mind).

Please take a look at the graphs below and determine whether or not stop and frisk worked in New York City in reducing crime over time. Cite all supporting data points you used to make your decision. Based upon your findings, determine if New York City should cease or continue to use stop and frisk.

Application Quiz 3: Each of three tests (students randomly assigned one)

Application Quiz 4: One chi-square and one analysis of variance question (each student randomly assigned one)

Application Quiz 5: Correlation and Regression (students are randomly given one question)

Rubric Used for All Four SPEA Assessment Instruments