# Longer Activities

Initial Publication Date: October 13, 2006

- The Evolution of Pearson's Correlation Coefficient/Exploring Relationships between Two Quantitative Variables Using interactive lecture, this activity explores a collection of nine scatterplots to develop the notion of association between two quantitative variables. The activity is designed to help students better understand how statistical measures are "invented," and why certain measures are preferred. Specifically, this activity proposes a non-standard "intuitive" measure of association and, by examining properties of this measure, develops the more standard measure, Pearson's Correlation Coefficient.
- Using an Applet to Demonstrate a Sampling Distribution This in-class demonstration combines real world data collection with the use of the applet to enhance the understanding of sampling distribution. Students will work in groups to determine the average date of their 30 coins. In turn, they will report their mean to the instructor, who will record these. The instructor can then create a histogram based on their sample means and explain that they have created a sampling distribution. Afterwards, the applet can be used to demonstrate properties of the sampling distribution.
- Using an Applet to Demonstrate the Sampling Distribution of an F-statistic This visualization activity combines student data collection with the use of an applet to enhance the understanding of the distributions of mean square treatment (MST), mean square error (MSE) as well as their ratio, an F-distribution. The applet samples from six treatment populations based on user defined parameters and records by means of histogram: mean square treatment, mean square error and their ratio. Students will see theoretical distributions of the mean square treatment, mean square error and their ratio and how they compare to the histograms generated by the simulated data.
- Using an Applet to Demostrate Sampling Distibutions of Regression Coefficients This visualization activity combines student data collection with the use of an applet to enhance the understanding of the distributions of slope and intercept in simple linear regression models. The applet simulates a linear regression plot and the corresponding intercept and slope histograms. The program allows the user to change settings such as slope, standard deviation, sample size, and more. Students will then see theoretical distributions of the slope and intercept and how they compare to the histograms generated by the simulated linear regression lines.
- Count the F's: Why a Sample instead of a Census: Demonstrate that a census, even when it is easy to take, may not give accurate information.
- Psychic test: In the activity, the psychic ability of a student from the class is studied using an applet. The student is asked to repeatedly guess the outcome of a virtual coin toss. The instructor enter the student's guesses and the applet plots the percentage of correct answers versus the number of attempts. With the applet, many guesses can be entered very quickly. If the student is truly a psychic, the percentage correct will converge to a value above 0.5.