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# How well can hand size predict height?

This material was originally developed through CAUSE
as part of its collaboration with the SERC Pedagogic Service.

#### Summary

This activity uses student's own data to introduce bivariate relationship using hand size to predict height. Students enter their data through a real-time online database. Data from different classes are stored and accumulated in the database. This real-time database approach speeds up the data gathering process and shifts the data entry and cleansing from instructor to engaging students in the process of data production.

## Learning Goals

This activity is designed to help students learn the issues related to data measurement and production, to learn the relationship of two variables. By the end of this activity, students will be able to
• explain the importance of data measurement and production in a given context,
• compare different measurements and distinguish which one has smaller variation when measured repeatedly,
• apply graphical and numerical techniques to describe and interpret the relationship between two variables in a given context,
• explain the least square method in a given context,
• distinguish between causation and association,
• determine if a linear model is appropriate or not using graphical residual analysis tools,
• identify outlying cases and determine the effect of the outlying cases.

## Context for Use

• This activity is appropriate for introducing bivariate relationship at introductory level with high school algebra as prerequisite.
• This activity can be conducted as a group project, an individual project or a home work project.
• The activity is easy to conduct. The actual time for guiding students collect, enter and download the data is usually less than 10 minutes for the entire class.

## Teaching Materials

The detailed description and materials of this activity are located at the site:
Real-Time Hands-on Activities
The following materials are used to introduce the bivariate relationship. One may choose to use a subset of the materials her/his class.
• The power point slides: used for introducing bivariate relationships. (PowerPoint 1.4MB May16 07) This is a complete set of materials for class lecture. You may already have your own lecture notes. Feel free to take any part of the slides.
• Hand size data (20 cases): (Excel 6kB May15 07) This data set is part of the hand-size data randomly selected from the activity database. This is used throughout the power point sildes as the class demonstration to introduce the bivariate relationship.
• Activity Worksheet - Hand Size: (Microsoft Word 37kB May17 07) This is a set of questions that guides students to investigate how well hand size can predict height. This is usually used as a group activity. It is suggested starting the group activity during the class period (or lab sessions), completing the activity after class and turning the worksheet the next class period.
• The hand size data (50 cases): (Excel 11kB May15 07) This data is a subset of the hand size data. The questions in the Hand-Size worksheet are based on the analysis of this data set.
• Activity Worksheet - online applet: (Microsoft Word 26kB May15 07) This worksheet is for students to learn the effects of outliers and influential cases. It may be assigned as a group activity or as an individual homework activity.
• Questions for assessing learning outcomes (Microsoft Word 99kB May3 07).

## Teaching Notes and Tips

Features about the Real-Time online data collection the instructor should be aware of:
• This activity requires students to collect data and enter their own data to an online database. Here is the instruction sheet for instructor: Instruction for instructor to facilitate the data collection. (Microsoft Word 28kB May17 07)
• The equipment for conducting this activity are (a) one-foot actual or paper-copy ruler and (b) Computer station with Internet connection.
• The best classroom setting is a computer classroom with Internet connection. Students can also enter their own data using any computer that has Internet connection after class.
Prior to conducting this activity, the instructor needs to:
• spend half an hour to navigate the Real-Time Hands-on Activities site to get familiar with the site.
• register to request for an activity code for the activity before the class.
• prepare paper rulers or actual rulers and make sure the Internet connection works in the computer lab.
During the session of conducting the group activity,
• Start with the discussion on how to measure hand size and ask students to compare different ways of measuring hand size in terms of (a) is the measurement measures 'hand size', (b) is it easy to measure, and (c) how well can it be measured repeatedly.
• Comparing Hand-length(from wrist to tip of the middle finger) and hand-width(from the tip of the thumb and the tip of little finger, when stretching out the hand), They both are valid measurements, easy to measure. Hand length is more repeatable.
• Ask students to go to the Real-Time Hands-on Activities and direct them to enter the data. See Instruction for Instructor (Microsoft Word 28kB May17 07) for step-by-step instruction.
• Ask student to make an 'educated' guess as to which one 'hand length' or 'hand width' a better predictor and their reasons. Then, make a comparison later after the analysis.
• Outlier cases may occur. For example, Based on how hand-length and width are measured in this activity, hand-width is always longer than hand-length. If a case that shows hand width is shorter than hand-length, this provide a discussion on measurement error and the effect of outliers.
• The hand-size data for the worksheet has a case with hand-width shorter than hand-length. Students are asked to analyze the data, firtst, without knowing this case, then, investigate the data, and delete this case, re-analyze the data and make a comparison.
The use of this activity beyond introductory level:
• This activity may be used to introduce models with both qualitative (gender) and quantitative (hand length) predictors.
• This activity may be used to introduce the concept of muliticollinearity by using both hand length and hand width as predictors.
• This activity may be used to introduce variable selection techniques by including gender, hand width, and hand length as predictors.

## Assessment

Students are assessed using
• Classroom Group activity worksheet: Activity Worksheet - Hand Size: (Microsoft Word 37kB May17 07) The data set used for this activity is The hand size data (50 cases): (Excel 11kB May15 07).
This activity assesses students' overall knowledge of bivariate relationships. In this data, there is a case that has measurement error; Hand-width is shorter than Hand-length. This error occurred when the student did not stretch out the hand for taking the hand width. Students are asked to analyze this entire data. Then, they are asked to locate this measurement error case, identify at least two more possible errors that may occur. Delete the case, re-analyze the data and make a comparison.
• Activity Worksheet - Using an online applet (see reference for the source):Activity Worksheet - online applet: (Microsoft Word 26kB May15 07) This activity assesses their understanding of the effects of outliers and influential cases. It may be assigned as a group activity or as an individual homework activity.
• Questions for assessing learning outcomes (Microsoft Word 99kB May3 07). This is a set of multiple choice questions for assessing learning outcomes at the end of the topic or used for final exam. It doees mean to use all of them at once. You may choose any subset of these questions for your class.

## References and Resources

• Real-Time Hands-on Activities site: This site consists of the detailed description of this activity, and all of the materials related to this activity. In addition, there are several other real-time online activities available on this site.
• Online Applet for Bivariate Relationship. This applet allows students to create their own scatter plots, observe and compare the patterns and correlation coefficients as well as least square lines. It is especially useful for students to create different situations involving outliers and observe the effect of the outliers.