Illustrates types of sums of squares in a 2 x 3 ANOVA are presented. Concepts: Confounding, unequal n, unweighted means, commonality analysis, hierarchical partitioning.
Simulates t-test/ANOVA with normality and homogeneity of variance assumptions violated. Concepts: Assumptions, robustness, type I error rate, homogeneity of variance, normality.
Demonstrates partitioning of variance. Concepts: ANOVA, sums of squares, partitioning variance.
Demonstrates partitioning of variance. Concepts: ANOVA, sums of squares, partitioning variance, interaction.
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.
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.
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.
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.
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.
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.
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 intervals on the mean are generated for simulated experiments. The confidence level and sample size can be manipulated.
Concepts: confidence interval, mean, standard deviation.
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.
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.
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.
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.
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.
Demonstrates how transformations affect the relationship between two variables.
concepts: transformation, correlation, regression, exponential growth.
A simulation illustrating the regression toward the mean phenomenon.
concepts: regression, correlation, reliability, error, luck
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Simulates t-test/ANOVA with normality and homogeneity of variance assumptions violated. Concepts: Assumptions, robustness, type I error rate, homogeneity of variance, normality.
This applet lets you investigate differences between correlated and independent t tests.
Concepts: t test, within-subject variable, between-subject variable, power, repeated measures.
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.
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.
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.
Demonstrates how transformations affect the relationship between two variables.
concepts: transformation, correlation, regression, exponential growth.
A simulation illustrating the regression toward the mean phenomenon.
concepts: regression, correlation, reliability, error, luck
This applet lets you investigate differences between correlated and independent t tests.
Concepts: t test, within-subject variable, between-subject variable, power, repeated measures.
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.
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.
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.
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.
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.
Simulates t-test/ANOVA with normality and homogeneity of variance assumptions violated. Concepts: Assumptions, robustness, type I error rate, homogeneity of variance, normality.
Simulates t-test/ANOVA with normality and homogeneity of variance assumptions violated. Concepts: Assumptions, robustness, type I error rate, homogeneity of variance, normality.
This applet lets you investigate differences between correlated and independent t tests.
Concepts: t test, within-subject variable, between-subject variable, power, repeated measures.
Demonstrates how transformations affect the relationship between two variables.
concepts: transformation, correlation, regression, exponential growth.
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.
