# Economics: Student Thought Processes For Choosing Appropriate Statistical Methods

Title: Developing Students’ Thought Processes for Choosing Appropriate Statistical Methods
Discipline(s) or Field(s): Research Methods, Statistics
Authors: Elizabeth Knowles and James Murray, Department of Economics, University of Wisconsin – La Crosse
Submission Date: August 23, 2012

Abstract: Introductory statistics classes typically emphasize computation and implementation procedures for a number of statistical tests. While it is essential to build these skills before achieving higher-order critical thinking skills, students often struggle in subsequent research methods courses when expected to select appropriate statistical tests to answer research questions. This requires an understanding of how statistical methods are related to one another; and to achieve this, students must develop a more advanced organization of knowledge. We designed a lesson to help students build a knowledge organization to achieve this outcome, and observed students to better understand their thought processes. We share our thought process map for selecting a statistical test, report on the impact it had for our students, and offer suggestions for improving the lesson. In addition, we describe the thought processes students used, both before and after being exposed to the thought process map, and identify sources of confusion revealed through the lesson study process. These include: when to apply an independent-samples test versus a paired-samples test, how the identification of scale of measurement led students to choose the wrong statistical method, the difficulty students had recognizing or defining what the variables in a problem were, and the lack of understanding of the difference between statistical language and colloquial language.

Economics Lesson Study: Student Thought Processes for Choosing Appropriate Statistical Methods (Final Report)

# Statistics: Interpretation of Confidence Intervals

Title: Interpretation of Confidence Levels
Discipline(s) or Field(s): Mathematics, Statistics
Authors: Jeff Baggett, Brooke Fridley, David Reineke, University of Wisconsin – La Crosse
Submission Date: June 9, 2006

Report Excerpts:

Our group decided to address the topic of confidence intervals and the interpretation and use of confidence intervals, in particular focusing on the interpretation of confidence intervals (i.e. what intervals say and what they do not say). We chose this topic after having noticed students having difficulty with the interpretation and use of the confidence interval and not so much the computation of the confidence interval.

Based on the results of the pre and post quiz, the misconception regarding the interpretation of a confidence interval by applying it to individuals rather than means seems to have been adequately addressed by the lesson.  However, students still do not have a clear understanding of the interpretation of a confidence interval for the mean as it relates to the subtle difference between probability and confidence.

Full Report Below:

# Mathematics: Statistical Inference of Means

Title: It depends on what “mean” means: a lesson study on sampling distributions
Discipline(s) or Field(s): Statistics
Authors: Abdulaziz Elfessi, Heather Hulett, Dan Nordman, University of Wisconsin – La Crosse
Submission Date: August 29, 2006

Executive Summary: In this activity, we hope to help students differentiate and explain three statistical terms at the heart of statistical inference: the mean of a population, the mean of a sample of observations, and the mean of the sample means.

Past experience indicates that term “mean” can be very confusing for students in an Elementary Statistics class, especially when the same word choice may be applied in all three situations above, with different meanings in each case. Understanding the differences, as well as the connection, between the three types of means above is important for the most basic hypothesis tests in statistics: testing if the population mean equals a certain value by looking at just one random sample. The idea that data from a small sample can be used to estimate the mean of an entire population, which cannot be obtained directly, is critical to statistical applications in many, many fields.

The specific learning goals of the lesson are as follows:

• Students will practice applying statistical techniques to data collected from samples.
• Students will see and explain sample variability and how sample size decreases the variability of sample means.
• Students will see graphically that the “typical/central/mean/expected” value of a sample mean is the same as the population mean.

In this lesson students will take random samples of different sizes and calculate their averages. They will then put their averages on Post-It notes and place them in the correct spot on the chalkboard to make histograms that will represent the sampling distributions. By comparing their sample means, the mean of the histogram (the mean of all the samples), and the population mean (which will be revealed at the right moment), they will hopefully get a fuller appreciation of the three different uses of the word “mean”.

The activity was successful in several ways. Students enjoyed the short exercise in drawing random samples and were surprised by some of the sample means obtained. As the histograms were formed, they saw clearly how the variability decreased as sample size increased. Finally, they got to see how most sample means gave close approximations to the true population mean.

# Computer Science: Discovering Inheritance through a Popular Video Game

Topic: Discovering Inheritance through a Popular Video Game
Department(s) or Field(s): Computer Science, Mathematics, Statistics
Authors: Terry Mason, Diane Christie, Radi Teleb, Bruce Johnson, University of Wisconsin – Stout
Submission Date: Spring 2007

Executive Summary – The lesson topic is inheritance in Computer Science 1 (CS1) courses. Inheritance is a powerful tool which is generally not fully understood by beginning students in computer science. They may understand the mechanics of making inheritance work, but do not always comprehend the utility and power of it. A deeper understanding of the topic is a learning goal that all teachers strive for in their students. This topic has a broad application as the introduction to programming is a course that is taught by many instructors in colleges and high schools throughout the world.

Learning Goals – The goal of this lesson is to illustrate the power and utility of inheritance as a tool in computer science with the graphics and engagement experienced by students playing video games. The lesson is designed using a familiar Mario game implemented in Java. The students were engaged in the project by first playing the game to identify the sprite objects. This set up a class discussion on how these objects are organized into an inheritance hierarchy through shared characteristics and functionality. The students complete the project by using inheritance to complete the functionality of the game.

Lesson Evaluations – The results of surveys and quizzes compare the results of one section of students that completed the older inheritance laboratory with two sections of students that completed the new video game based laboratory. Student engagement in the new laboratory ranked close to exciting versus a ranking between marginally interesting and interesting for the older lesson. Student surveys show that students believe that the new lesson was exciting and it increased their understanding of inheritance hierarchies, the power of inheritance, and the usefulness of the lab. Student grades on a quiz administered four days after the laboratories show that student scored slightly higher after completing the new lesson compared to students completing the older lesson.

Observations and Exit Interviews  The lessons were observed by members of the lesson study team. Students showed a high level of engagement in the game and identifying the objects for missing functionality. They expressed a sense of accomplishment in extending the functionality of the game. In addition they showed a sense of accomplishment. Two different groups shouted “Yes!” when their new code provided the expected functionality of the game. In addition, students were engaged enough in the lesson to spend extra time to further investigate the code.

Computer Science Lesson Study: Discovering Inheritance through a Popular Video Game (Final Report)
Links to materials used to teach the lesson and data generated by the study.