ANOVA
Unequal n ANOVA and Types of Sums of Squares.

Illustrates types of sums of squares in a 2 x 3 ANOVA are presented. Concepts: Confounding, unequal n, unweighted means, commonality analysis, hierarchical partitioning.

Robustness of t test and ANOVA.

Simulates t-test/ANOVA with normality and homogeneity of variance assumptions violated. Concepts: Assumptions, robustness, type I error rate, homogeneity of variance, normality.

One-way ANOVA.

Demonstrates partitioning of variance. Concepts: ANOVA, sums of squares, partitioning variance.

Two-way ANOVA

Demonstrates partitioning of variance. Concepts: ANOVA, sums of squares, partitioning variance, interaction.

Binomial Distribution
Normal Approximation to the Binomial Distribution

This demonstration allows you to view the binomial distribution and the normal approximation to it as a function of the probability of a success on a given trial and the number of trials. It can be used to compute binomial probabilities and normal approximations of those probabilities. Concepts: binomial distribution, normal distribution, central limit theorem, correction for continuity.

Confidence Interval on a Proportion.

The effect of violating the assumption that the sampling distribution of p is normal can be investigated by varying N and Pi.
Concepts: binomial distribution, normal distribution, central limit theorem, confidence interval.

Central Limit Theorem
Sampling Distribution Simulation

This applet estimates and plots the sampling distribution of various statistics. You specify the population distribution, sample size, and statistic. An animated sample from the population is shown and the statistic is plotted. This can be repeated to estimate the sampling distribution.
Concepts: sampling distribution, standard deviation, standard error, central limit theorem, mean, median, efficiency, fluctuation, skew, normal distribution.

Normal Approximation to the Binomial Distribution

This demonstration allows you to view the binomial distribution and the normal approximation to it as a function of the probability of a success on a given trial and the number of trials. It can be used to compute binomial probabilities and normal approximations of those probabilities. Concepts: binomial distribution, normal distribution, central limit theorem, correction for continuity.

Confidence Interval on a Proportion.

The effect of violating the assumption that the sampling distribution of p is normal can be investigated by varying N and Pi.
Concepts: binomial distribution, normal distribution, central limit theorem, confidence interval.

Chi Square
Chi Square Test of Deviations from Expected Frequencies

You can specify whether you wish to sample from a uniform or a normal distribution. The applet does the sampling and tests the significance of deviations from these two distributions.
Concepts: goodness of fit, chi square, normal distribution, uniform distribution.

2 x 2 Contingency Tables

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.
Concepts: chi square, correction for continuity, normal approximation.

Confidence Interval
Confidence Intervals

Confidence intervals on the mean are generated for simulated experiments. The confidence level and sample size can be manipulated.
Concepts: confidence interval, mean, standard deviation.

Confidence Interval on a Proportion.

The effect of violating the assumption that the sampling distribution of p is normal can be investigated by varying N and Pi.
Concepts: binomial distribution, normal distribution, central limit theorem, confidence interval.

Correlation
Components of r

The slope, standard error of the estimate, and the standard deviation of X can all be manipulated independently to see the effect on the scatterplot and on r.
Concepts: Correlation, slope, standard error of the estimate, variance, restriction of range, proportion of variance explained.

Regression by Eye

A scatterplot is displayed and you draw in a regression line by hand. You can then compare your line to the best least squares fit. You can also try to guess the value of Pearson's correlation coefficient.
Concepts: Correlation, regression line, mean squared error.

Restriction of Range.

The range of X can be manipulated to investigate its effect on Pearson's r and other aspects of the relationship between X and Y.
Concepts: Correlation, restriction of range, slope, standard error of estimate.

Reliability and Regression Analysis

Demonstrates how the reliability of X and Y affect various aspects of the regression of Y on X.
concepts: reliability, standard error of estimate, slope, correlation.

Transformations

Demonstrates how transformations affect the relationship between two variables.
concepts: transformation, correlation, regression, exponential growth.

Regression to the mean

A simulation illustrating the regression toward the mean phenomenon.
concepts: regression, correlation, reliability, error, luck

Central Tendency
Mean and Median

This applet demonstrates basic properties of the mean and median including (a) the effect of skew on the relative size of the mean and median, (b) the mean deviation from the mean is zero, and (c) the mean squared deviation from the mean is less than or equal to the mean squared deviation from the median (or any other number).
Concepts: central tendency, mean, median, skew, least squares.

Sampling Distribution Simulation

This applet estimates and plots the sampling distribution of various statistics. You specify the population distribution, sample size, and statistic. An animated sample from the population is shown and the statistic is plotted. This can be repeated to estimate the sampling distribution.
Concepts: sampling distribution, standard deviation, standard error, central limit theorem, mean, median, efficiency, fluctuation, skew, normal distribution.

Comparing distributions

Your response times on a simple motor task are recorded under two conditions. Various statistics and graphs used to compare the distributions are presented. Concepts: central tendency, spread, mean, median, skew.

Effect Size
A "Small" Effect Size Can Make a Large Difference

Requires a browser that supports Java.
This applet demonstrates that even a "small" effect can be important under some circumstances. Applicants from two groups apply for a job. The user manipulates the difference between groups on the variable on which selection is made and the cutoff for hiring. The effects on the proportion of hired applicants from each group are displayed. A related phenomenon is discussed in the article:
Martell, R., Lane, D. M., & Emrich, C. (1996) Male-female differences: A computer simulation. American Psychologist, 51, 157-158.
Concepts: normal distribution, selection ratio, effect size, omega squared, proportion of variance explained.

Goodness of Fit
Chi Square Test of Deviations from Expected Frequencies

You can specify whether you wish to sample from a uniform or a normal distribution. The applet does the sampling and tests the significance of deviations from these two distributions.
Concepts: goodness of fit, chi square, normal distribution, uniform distribution.

Histogram
Histograms, Bin Widths, and Cross Validation

Demonstrates how a histogram is affected by bin width and starting point of first bin. Illustrates cross-validation criterion for assessing histograms.
concepts: histogram, bin width, cross validation, density estimation.

Comparing distributions

Your response times on a simple motor task are recorded under two conditions. Various statistics and graphs used to compare the distributions are presented. Concepts: central tendency, spread, mean, median, skew.

Normal Distribution
Sampling Distribution Simulation

This applet estimates and plots the sampling distribution of various statistics. You specify the population distribution, sample size, and statistic. An animated sample from the population is shown and the statistic is plotted. This can be repeated to estimate the sampling distribution.
Concepts: sampling distribution, standard deviation, standard error, central limit theorem, mean, median, efficiency, fluctuation, skew, normal distribution.

Normal Approximation to the Binomial Distribution

This demonstration allows you to view the binomial distribution and the normal approximation to it as a function of the probability of a success on a given trial and the number of trials. It can be used to compute binomial probabilities and normal approximations of those probabilities. Concepts: binomial distribution, normal distribution, central limit theorem, correction for continuity.

Confidence Interval on a Proportion.

The effect of violating the assumption that the sampling distribution of p is normal can be investigated by varying N and Pi.
Concepts: binomial distribution, normal distribution, central limit theorem, confidence interval.

A "Small" Effect Size Can Make a Large Difference

Requires a browser that supports Java.
This applet demonstrates that even a "small" effect can be important under some circumstances. Applicants from two groups apply for a job. The user manipulates the difference between groups on the variable on which selection is made and the cutoff for hiring. The effects on the proportion of hired applicants from each group are displayed. A related phenomenon is discussed in the article:
Martell, R., Lane, D. M., & Emrich, C. (1996) Male-female differences: A computer simulation. American Psychologist, 51, 157-158.
Concepts: normal distribution, selection ratio, effect size, omega squared, proportion of variance explained.

Chi Square Test of Deviations from Expected Frequencies

You can specify whether you wish to sample from a uniform or a normal distribution. The applet does the sampling and tests the significance of deviations from these two distributions.
Concepts: goodness of fit, chi square, normal distribution, uniform distribution.

2 x 2 Contingency Tables

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.
Concepts: chi square, correction for continuity, normal approximation.

Robustness of t test and ANOVA.

Simulates t-test/ANOVA with normality and homogeneity of variance assumptions violated. Concepts: Assumptions, robustness, type I error rate, homogeneity of variance, normality.

Power
Repeated Measures

This applet lets you investigate differences between correlated and independent t tests.
Concepts: t test, within-subject variable, between-subject variable, power, repeated measures.

Regression
Components of r

The slope, standard error of the estimate, and the standard deviation of X can all be manipulated independently to see the effect on the scatterplot and on r.
Concepts: Correlation, slope, standard error of the estimate, variance, restriction of range, proportion of variance explained.

Regression by Eye

A scatterplot is displayed and you draw in a regression line by hand. You can then compare your line to the best least squares fit. You can also try to guess the value of Pearson's correlation coefficient.
Concepts: Correlation, regression line, mean squared error.

Reliability and Regression Analysis

Demonstrates how the reliability of X and Y affect various aspects of the regression of Y on X.
concepts: reliability, standard error of estimate, slope, correlation.

Transformations

Demonstrates how transformations affect the relationship between two variables.
concepts: transformation, correlation, regression, exponential growth.

Regression to the mean

A simulation illustrating the regression toward the mean phenomenon.
concepts: regression, correlation, reliability, error, luck

Repeated Measures
Repeated Measures

This applet lets you investigate differences between correlated and independent t tests.
Concepts: t test, within-subject variable, between-subject variable, power, repeated measures.

Restriction of Range
Components of r

The slope, standard error of the estimate, and the standard deviation of X can all be manipulated independently to see the effect on the scatterplot and on r.
Concepts: Correlation, slope, standard error of the estimate, variance, restriction of range, proportion of variance explained.

Restriction of Range.

The range of X can be manipulated to investigate its effect on Pearson's r and other aspects of the relationship between X and Y.
Concepts: Correlation, restriction of range, slope, standard error of estimate.

Sampling Distribution
Sampling Distribution Simulation

This applet estimates and plots the sampling distribution of various statistics. You specify the population distribution, sample size, and statistic. An animated sample from the population is shown and the statistic is plotted. This can be repeated to estimate the sampling distribution.
Concepts: sampling distribution, standard deviation, standard error, central limit theorem, mean, median, efficiency, fluctuation, skew, normal distribution.

Skew
Mean and Median

This applet demonstrates basic properties of the mean and median including (a) the effect of skew on the relative size of the mean and median, (b) the mean deviation from the mean is zero, and (c) the mean squared deviation from the mean is less than or equal to the mean squared deviation from the median (or any other number).
Concepts: central tendency, mean, median, skew, least squares.

Sampling Distribution Simulation

This applet estimates and plots the sampling distribution of various statistics. You specify the population distribution, sample size, and statistic. An animated sample from the population is shown and the statistic is plotted. This can be repeated to estimate the sampling distribution.
Concepts: sampling distribution, standard deviation, standard error, central limit theorem, mean, median, efficiency, fluctuation, skew, normal distribution.

Robustness of t test and ANOVA.

Simulates t-test/ANOVA with normality and homogeneity of variance assumptions violated. Concepts: Assumptions, robustness, type I error rate, homogeneity of variance, normality.

t-test
Robustness of t test and ANOVA.

Simulates t-test/ANOVA with normality and homogeneity of variance assumptions violated. Concepts: Assumptions, robustness, type I error rate, homogeneity of variance, normality.

Repeated Measures

This applet lets you investigate differences between correlated and independent t tests.
Concepts: t test, within-subject variable, between-subject variable, power, repeated measures.

Transformations
Transformations

Demonstrates how transformations affect the relationship between two variables.
concepts: transformation, correlation, regression, exponential growth.

Credits

The simulations were developed as part of a grant from NSF to David Lane of Rice University. Partial support for this work was provided by the National Science Foundation's Division of Undergraduate Education through grant DUE 9751307. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.