Teaching Introductory Statistics Roger Woodard

ST311 Introductory Statistics Sections 700 students per semester Majors from social and biological sciences Many other majors Not for business or engineering Sections 10 to 12 per semester 65 students per section Most taught by graduate students

GAISE Guidelines Assessment and Instruction in Statistics Education

GAISE Recommendations Stress conceptual understanding rather than mere knowledge of procedures; Emphasize statistical literacy and thinking Use real data; Foster active learning in the classroom; Use assessments to improve and evaluate student learning; Use technology for developing conceptual understanding and analyzing data;

GAISE in the course? Emphasis on literacy, thinking and conceptual course Detailed learning objectives=> spell out content for instructors and students. Order of topics to maximize conceptual links Discussion of big picture during initial workshop Ongoing discussion of connections during weekly meetings Emphasis on big ideas (6 months after the course)

Conceptual approach Stress conceptual understanding rather than mere knowledge of procedures; Reduce total content Improve retention Emphasis on big ideas (6 months after the course)

Big ideas: How data are collected or generated is important if we want to make inference from it. In both experiments and surveys, randomization is necessary to insure appropriate inference.

Big ideas: Statistical inference is possible because statistics have a predictable distribution called a sampling distribution. The sampling distribution allows us to quantify the variability in sample statistics. including how they differ from the parameter and what type of variability would not be expected to happen by random chance.

Topics and order built around big ideas Detailed learning objectives Over 100 task level items Spell out exact content for instructors and students. Order of topics to maximize conceptual links Not textbook order Arrange the topics to maximize connections

Order of Topics Traditional Summaries and graphics Regression Surveys and sampling Experiments Normal distribution Sampling distribution Confidence intervals Hypothesis testing Regression inference

Order of Topics Traditional Revised Summaries and graphics Regression Surveys and sampling Experiments Normal distribution Sampling distribution Confidence intervals Hypothesis testing Regression inference Surveys and sampling Summaries and graphics Normal distribution

Order of Topics Traditional Revised Summaries and graphics Regression Surveys and sampling Experiments Normal distribution Sampling distribution Confidence intervals Hypothesis testing Regression inference Surveys and sampling Summaries and graphics Normal distribution Sampling distribution Confidence intervals Hypothesis testing

Order of Topics Traditional Revised Summaries and graphics Regression Surveys and sampling Experiments Normal distribution Sampling distribution Confidence intervals Hypothesis testing Regression inference Surveys and sampling Summaries and graphics Normal distribution Sampling distribution Confidence intervals Hypothesis testing Regression Regression inference Experiments

Order of topics

Order of topics

Order of topics

Order of topics

Order of topics

Order of topics

Foster Active Learning Active learning as a constant theme Get students involved in the course Many activities specifically designed to get students involved M&Ms for confidence intervals, grip meters, etc Learn by discovery, “what happens if?” Points specifically set aside for activities Each instructor can design their own

Foster Active Learning Where do we get the time? Reduce lecture time with guided note outlines Cut out minor topics that don’t relate to the big ideas.

Use real data Many data sets available Incorporate real data Home prices Car characteristics NBA and NFL rosters Price of textbooks Incorporate real data Not as easy as we thought Just using real data in a meaningless way does not help

BAC Data Study conducted at Ohio State by intro stat students 16 student volunteers Randomly assigned number of beers BAC was recorded

A question for you.

BAC Example

Use Technology Software Online software (Statcrunch) Allows analysis and exploration of data. Avoid extensive overhead Free, installation issues, difficult programming Online software (Statcrunch) Incorporated in homework Problems that require data exploration Incorporated in classes activities Written instructions don’t work but video does

Use Technology Applets and simulations Many concepts are hard to grasp Applets and simulations can demonstrate concepts Students need real world connection Black box simulations are not meaningful Concentrate on the connections with physical simulations

Distribution of the sample mean http://www.courses.ncsu.edu/st311/common/CoinDates.html

Assessment Homework Electronic, timely feedback Feedback linked to textbook sections and practice problems. Common across sections =>universal support, well tested Incorporates data analysis problems

Assessment In class activities Midterm exams More challenging and thought provoking Get at deeper levels of thought Midterm exams Specific time in the class set aside to return and review exams Instructors hand out learning objective key

Statistical thinking Emphasize statistical literacy and develop statistical thinking; Carpenter example Capstone activity Whole process from start to finish Design and carry out experiment, analyze the data, interpret the results Also acts as a review

Questions?

Web links GAISE report: Statcrunch: http://www.amstat.org/education/gaise/ Statcrunch: www.statcrunch.com Course page with learning objectives http://www.stat.ncsu.edu/courses/st311/

Learning Objectives Given a study, identify population, sample, parameter, sampling frame and statistic. Given a study, recognize typical forms of biases such as potential undercoverage, nonresponse, and response bias. Given side-by-side boxplots, contrast key features of the groups represented by the boxplots. Given a study, interpret the results of a test of significance in context.

Data exploration problem John is a new college graduate working at his first job. After years of living in an apartment he has decided to purchase a home. He has found a great neighborhood from which he can walk to work. Before buying a home in the area he has decided to collect some data on the homes in this neighborhood. A data set has been compiled that represents a sample of 100 homes in the neighborhood he is considering. The variables included in this data set include: Value: the current value of the home as determined by the county tax assessor. Size: the size of the home in square feet. Year: the year the homes were built. Basement: does the home have a basement (y=yes, n=no). Fireplace: does the home have a fireplace (y=yes, n=no). Type: the structure a single family house or a townhouse. (house or townhouse). Create histograms for each of the numeric variables and create bar charts for each of the categorical variables. Use these variables to explore the data and determine which of the following best fits this situation.

Data exploration problem

Data exploration problem The histogram for value is clearly bimodal. The reason it is bimodal appears to be because the homes in the neighborhood have higher priced single family houses and lower priced town homes. The histogram for value is clearly bimodal. The reason it is bimodal appears to be because the neighborhood was built in two phases, the newer phase consists of larger more expensive homes and the older phase consists of smaller less expensive homes. The histogram for value is clearly bimodal. The reason it is bimodal appears to be because the neighborhood was built in two phases, the older phase consists of larger more expensive homes and the newer phase consists of smaller less expensive homes. The histogram for value is clearly bimodal. The reason it is bimodal appears to be because the neighborhood has some homes that have basements that tend to be larger in size with another group of homes that do not have basements and tend to be smaller.

Homes Data