http://www.merlot.org:80/merlot/ A search of MERLOT materials Copyright 1997-2013 MERLOT. All rights reserved. Wed, 22 May 2013 14:41:14 PDT Wed, 22 May 2013 14:41:14 PDT http://www.merlot.org:80/merlot/images/merlot.gif http://www.merlot.org:80/merlot/ 44 34 http://www.merlot.org/merlot/viewMaterial.htm?id=751425 Statcato is an open source Java based software for elementary statistics. It includes just about every chart, statistics, confidence interval, and hypothesis test that is used in the standard elementary statistics course. http://www.merlot.org/merlot/viewMaterial.htm?id=710136 The WISE Bootstrapping Applet can be used to demonstrate bootstrapping by creating a confidence interval for a population mean or median. The user can manipulate the population distribution, sample size, and number of resamples. An associated guide gives suggestions for teaching bootstrapping. http://www.merlot.org/merlot/viewMaterial.htm?id=686970 Teachers and researchers, along with students, often misinterpret confidence intervals on bar graphs. A Guide that accompanies the applet describes how the applet can be used in a demonstration. http://www.merlot.org/merlot/viewMaterial.htm?id=671721 This activity allows users to create and manipulate boxplots for either built-in data or their own data. Discussion, exercise questions, and lesson plans regarding boxplots are linked to the applet. http://www.merlot.org/merlot/viewMaterial.htm?id=641891 The interactive WISE Confidence Interval Creation Applet allows instructors to demonstrate how sample size, alpha level, population shape, and variance affect confidence intervals. The user can generate a population distribution of interest or select a distribution from a menu, select a sample size and an alpha level.A press of the 'Sample' button displays a simulated sample and confidence interval for the population mean. The sample mean, standard deviation, and confidence interval are displayed, along with the option to display calculations for the confidence interval limits. Subsequent presses of the 'Sample' button produce new random samples with their associated confidence intervals. Up to 20 confidence intervals are displayed at one time, showing how confidence intervals differ by chance.This applet provides graphic evidence for why it is wrong to say that the population mean falls within a given confidence interval 95% of the time. Rather, 95% of confidence intervals are expected to contain the population mean IF assumptions are met. Manipulations of the population shape and the sample size easily produce situations where the assumption of normality is violated to an extent where standard procedures for constructing confidence intervals are clearly wrong. Students and instructors can have fun playing with the applet and interpreting findings.The applet is linked to a demonstration guide. http://www.merlot.org/merlot/viewMaterial.htm?id=641900 Researchers and students alike often mistake any overlap among confidence intervals to denote a statistically non-significant p value. However, confidence intervals can overlap and still correspond to a statistically significant p value for an independent sample t test. The WISE confidence interval applet can help people understand the relationship between confidence interval overlap and statistical significance.The applet simulates a comparison of the confidence intervals for two group means. The means are displayed as a bar graph with confidence intervals around each group mean. The user can 'grab' one of the means and slide it up or down to change the amount of overlap of the two confidence intervals. The applet displays the p value associated with an independent samples t test for the difference between the two population means.A common misperception is that statistical significance with p=.05 is attained when the two 95% confidence intervals just touch, but that statistical significance is lost when the intervals overlap. First time users will be surprised to see that the p value is only about .005 when the intervals just touch.To facilitate an understanding of why the p value is so small when the intervals just touch, the confidence intervals in the display include a representation of the underlying normal sampling distributions. Now it is apparent that when the two intervals just touch, only the very thin tails overlap, and it is highly unlikely that a mean drawn from one distribution would be mistaken for a mean drawn from the other distribution.Manipulation of the applet allows the user to gain an accurate understanding of how the degree of overlap between confidence intervals is associated with p values for the test of the difference between means. The amount of overlap for p=.05 is likely to be surprising at first encounter.A Demonstration Guide is linked to the applet. http://www.merlot.org/merlot/viewMaterial.htm?id=627519 This applet simulates experiments using 2 x 2 contingency tables. You specify the population proportions and the sample size and examine the effects on the probability of rejecting the null hypothesis. http://www.merlot.org/merlot/viewMaterial.htm?id=626915 An applet that allows users to see plots with a specified correlation; to compare plots, varying the correlation and standard deviations of the variables; and to play games to test ability to estimate the correlation coefficient for a given plot. http://www.merlot.org/merlot/viewMaterial.htm?id=611033 This applet demonstrates the theory behind linear regression. http://www.merlot.org/merlot/viewMaterial.htm?id=611002 This is an applet that demonstrates least squares regression.