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4434Sampling Distribution of the Mean Tutorial
http://www.merlot.org/merlot/viewMaterial.htm?id=82347
This tutorial will help you determine how accurate a sample mean is likely to be, and how this accuracy is related to the sample size. Brief reviews of the normal distribution and the Central Limit Theorem are included as supplemental materials.Introduction to Hypothesis Testing -- The Z-Test
http://www.merlot.org/merlot/viewMaterial.htm?id=82334
This exercise will help the user understand the logic and procedures of hypothesis testing. To make best use of this exercise, the user should know how to use a z table to find probabilities on a normal distribution, and how to calculate the standard error of a mean. Relevant review materials are available from the links provided. The user will need a copy of the hypothesis testing exercise (link is provided), a table for the standardized normal distribution (z), and a calculator. The user will be asked several questions and will be given feedback regarding their answers. Detailed solutions are provided, but users should try to answer the questions on their own before consulting the detailed solutions. The end of the tutorial contains some "thought" questions.An Introduction to Statistical Power
http://www.merlot.org/merlot/viewMaterial.htm?id=82345
This tutorial illustrates the relationship between statistical power and four features of the test situation. An applet allows the user to manipulate a factor and immediately see the effects on other factors.WISE confidence interval creation
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.Comparison of Cultures: A t-test Tutorial
http://www.merlot.org/merlot/viewMaterial.htm?id=82349
This tutorial takes the learner step-by-step in applying descriptive and inferential statistics using a real world situation.Signal Detection Theory Tutorial
http://www.merlot.org/merlot/viewMaterial.htm?id=84498
Every day we have to make decisions about uncertain events like, 'Is that my phone ringing or one on the television?', or, 'Is the person talking to me telling the truth?' In this tutorial, you will learn about the Signal Detection Theory (SDT) model of how people make decisions about uncertain events. This tutorial explains the theory behind signal detection, covers several SDT measures of performance, and introduces Receiver-Operating Characteristics (ROCs). The tutorial is at an introductory level, but also has optional sections appropriate for more advanced students and researchers. The tutorial consists of explanatory text, interactive examples, and a question section suitable for a classroom assignment. The tutorial also contains a Java applet for computing and graphically portraying SDT models. This tutorial is introductory in level and builds upon other tutorials on the WISE Project's web site. The hypothesis testing tutorial is particularly appropriate, and it is also helpful to be comfortable working with z-scores.WISE Confidence Interval Overlap Fallacy
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.WISE Bootstrapping Applet
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.WISE Confidence Interval Game
http://www.merlot.org/merlot/viewMaterial.htm?id=729472
This is a game students can play where they are scored on how well they interpret overlap of confidence intervals.Introduction to Hypothesis Testing Applet
http://www.merlot.org/merlot/viewMaterial.htm?id=82336
This applet serves to introduce the logic of hypothesis testing using z-scores.