Data Presentation

This activity represents a very general demonstration of the effects of the Central Limit Theorem (CLT). The activity is based on the SOCR Sampling Distribution CLT Experiment. This experiment builds upon a RVLS CLT applet (http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/) by extending the applet functionality and providing the capability of sampling from any SOCR Distribution. Goals of this activity: provide intuitive notion of sampling from any process with a well-defined distribution; motivate and facilitate learning of the central limit theorem; empirically validate that sample-averages of random observations (most processes) follow approximately normal distribution; empirically demonstrate that the sample-average is special and other sample statistics (e.g., median, variance, range, etc.) generally do not have distributions that are normal; illustrate that the expectation of the sample-average equals the population mean (and the sample-average is typically a good measure of centrality for a population/process); show that the variation of the sample average rapidly decreases as the sample size increases.

This applet generates confidence intervals for means or proportions. The options for confidence intervals for means include "z with sigma," "z with s," or "t." The options for confidence intervals for proportions are "Wald," "Adjusted Wald," or "Score." Users set the population parameters, sample size, number of intervals, and confidence level. Click "Sample," and the applet will graph the intervals. Intervals shown in green contain the true population mean or proportion, while intervals in red do not. The true mean or proportion is shown by a blue line. The applet displays the proportion of intervals containing the population parameter for each sample and a running total of all the samples. Users can also click on a particular interval to display the numerical interval or sort the displayed confidence intervals from smallest to largest. This applet is part of a collection designed to accompany the textbook "Investigating Statistical Concepts, Applications, and Methods" (ISCAM) and is used in Exploration 4.3 on page 327, Investigation 4.3.6 on page 331, and Exploration 4.4 on page 350. This applet also supplements "Workshop Statistics: Discovery with Data," 2nd edition, Activity 19-5 on page 403. Additional materials written for use with these applets can be found at http://www.mathspace.com/NSF_ProbStat/Teaching_Materials/rowell/final/16_cireview_bc322_2.doc and http://www.mathspace.com/NSF_ProbStat/Teaching_Materials/rowell/final/15_sampdistreview_bc322_1.doc.

This lecture example discusses how two continuous variables relate to one another with a clinical example of the relationship between body mass and fasting blood sugar. It offers three questions to help readers visualize and interpret correlation coefficients.