# Tangrams

Tangrams are puzzles in which a person is expected to place geometrically shaped pieces into a particular design. In the following activities, students will have the opportunity to design and analyze an experiment. They will

• Formulate a hypothesis test about the number of items subject can remember
• Determine how to collect data that best addresses their research question.
• Collect data
• Check model assumptions
• Analyze the data
• Draw conclusions within the context of their study

The on-line Tangram Game provides students the opportunity to design many versions of the original game in order to test which variables have the largest effect on game completion time. For example:

• Have each student in the class play the game and then conduct a hypothesis test to determine if males and females have the same average completion time.
• Have each student in the class play two games (in random order). Are some versions of the harder than others? Do people tend to do better the second time they play the game? Is it the puzzle type or order that has the largest influence on completion time?
• If students play the game with the help option, how long does it take before they resort to using it to get assistance?

The following link allows you to play the Tangram Game.

Click on the Tangrams tab. These games may not run on the most recent versions of Chrome or Firefox. We are currently working on fixing the issue.

All data from the game is available at Tangram Data.

Enter your Group ID and then click the Tangrams Data button.

#### 1-sample t-tests or Z-test: Student Handout and Instructor's Notes

This activity uses a simple game to help introductory statistics students bridge the gap between traditional homework problems and a true research project. The emphasis is on understanding experimental design and the impacts of model assumptions.

#### 2-sample t-tests or paired t-test: Student Handout and Instructor's Notes

This activity is designed to build upon students' knowledge of 2-sample t-tests or ANOVA. The emphasis is on understanding experimental design and the impacts of model assumptions.

If you have a small number of students in your class, or would like data to compare your class to other classes:

1. The USMA Data Set consists of game results from several sections of introductory statistics students from West Point Military Academy
2. The Grinnell Sample Data is collected from two sections of an introductory statistics course. Note that four observations are highlighted due to questionable data (player used hints, used a timer, played the wrong game, and one student admitted that they stopped and talked to friends while playing the game).

You can find more details about this lab in the free online publication, “Using classroom data to teach students about data cleaning and testing assumptions” published in Frontiers in Quantitative Psychology and Measurement.