# TigerSAMPLING

TigerSAMPLING is almost identical to TigerSTAT. However in the TigerSAMPLING game there are additional questions that emphasize BIAS and GENERALIZABILITY. These games collect data and explore models for estimating the age of a Siberian tiger. In this game, students act as researchers on a national preserve where they are expected to catch tigers, collect data, analyze their data (using the simple linear regression on transformed data), and draw appropriate conclusions.

This lab provides an engaging way to practice simple linear regression applied to a real problem. Students are exposed to messy data and issues associated with data collection through the game. The realism of the lab can be increased if they also read and discuss the research article discussing current methods of estimating age in lions through the use of proxy variables. One goal of this lab is to encourage students to consider the implications of more complicated research design topics like sampling and bias. The usefulness of a model versus the statistical significance is also addressed in a very practical way students understand since they “own the data”. Multiple opportunities to highlight subtleties not often addressed in traditional textbook problems are natural outcomes from using the lab. Examples of these opportunities include sampling bias, the cost of data collection, and consideration of how a model is used rather than simply its statistical significance.

• Level: Introductory or Intermediate Statistics
• Topics Covered: Simple Linear Regression, prediction, model assumptions and adequacy.
• Software Required: Data analysis software such as Minitab, R, Stata, or Excel for descriptive statistics and regression analysis. Students will also need computer access to play the TigerSTAT game on the web (the game can be played inside or outside of the regularly scheduled class time).
• Prerequisites: Prior to this lab, students should know how to analyze data using summary statistics, graphical methods and hypothesis testing. In this lab students create a simple linear regression model, evaluate a residual plot, and conduct a hypothesis test for the slope of the regression line; this material can be learned as part of the lab or prior.
• Time: 1 to 2 hours in class + 2 to 4 hours of homework

This lab provides an engaging way to practice simple linear regression applied to a real problem. Students are exposed to messy data and issues associated with data collection through the game. The realism of the lab can be increased if they also read and discuss the research article discussing current methods of estimating age in lions through the use of proxy variables. One goal of this lab is to encourage students to consider the implications of more complicated research design topics like sampling and bias. The usefulness of a model versus the statistical significance is also addressed in a very practical way students understand since they “own the data”. Multiple opportunities to highlight subtleties not often addressed in traditional textbook problems are natural outcomes from using the lab. Examples of these opportunities include sampling bias, the cost of data collection, and consideration of how a model is used rather than simply its statistical significance.

The following link allows you to play to the TigerSAMPLING Game. You will be asked to install Unity Web Player, this may take a few minutes.

Many browsers will require you to allow popups before they will run these stat2labs games.

All datasets from this game can be found at TigerSAMPLING Data.

#### Research Article: Student Handout

Before conducting the Simple Linear Regression Lab, students can read an optional scientific paper discussing current methods of estimating age in lions largely through the use of proxy variables: Sustainable trophy hunting of African lions (2004 Nature article by Whitman et al.).

#### Simple Linear Regression: Student Handout and Instructor's Notes

This lab is essentially identical to the TigerSTAT simple linear regression lab, but collects data from a reserve with distinct regional differences. However, these biases are not addressed until the Sampling Bias lab. This lab can be used to emphasizes how much a regression model can vary from sample to sample. Data transformations are also discussed.

#### Sampling Bias: Student Handout and Instructor's Notes

This activity builds upon the simple linear regression lab. It discusses issues with sampling bias by emphasizing the six distinct regions within the reserve. There are clear regional differences (some regions have mostly older male tigers where other regions contain mostly mothers and their cubs). This lab discusses strategies for collecting an appropriate sample. Students may not be formally introduced to sampling schemes such as cluster/stratified sampling but in this exercise will recognize simple random sampling is not always best.