## Programs that a browser can run (applets etc.)

• This applet is designed to help students understand confidence intervals. Each of the 50 lines on the graph represents a confidence interval for the mean (assuming known variance). Each interval is based on a sample of size 5 taken from a standard normal distribution (mean=0 and variance=1). By changing alpha, students can see how the confidence intervals are affected by this parameter. Also, students can get a good idea of what a confidence interval really means in terms of covering the true mean.
• Statiscope presents summarizing data and descriptive statistical charts. In the applet you can enter data manually or download data over the Internet. Charts included: Distribution, Probability mass, Density, Box plot, Stem & leaf. Other features such as hypothesis testing and calculation of confidence intervals are also included. You can easily import data from other web sites. Be sure to read the help document. Also be sure that your window is set wide enough to see all the options.
• VRML stands for Virtual Reality Modeling Language and it allows one to construct three dimensional graphics that can be manipulated by the user to look at different angles etc. To view this you need some special software on your computer. If you are using Netscape to view it you need only download the Netscape 3D plug in from their homepage. (If you are using a Mac you will need a Power Mac).
• This applet is designed to teach students the effect of leverage points on a regression line. Students may add points to the plot by clicking the mouse button. Students should note that adding points close to the existing line barely changes the line. By adding points far from the existing line, the regression line changes considerably. This is particularly true for points added outside the range of the data. This should help students understand the effect of outliers on regression analysis.
• This applet is designed to teach students how bin widths (or the number of bins) affect a histogram. The histogram below is for the Old Faithful data set. Students should interactively change the bin width by dragging the arrow underneath the bin width scale. For large bin widths, the bimodal nature of the dataset is hidden, and for small bin widths the plot reduces to a spike at each data point. What bin width do you think provides the best picture of the underlying data?
• This applet demonstrates the central limit theorem using simulated dice-rolling experiments. An "experiment" consists of rolling a certain number of dice (1-5 dice are available in this applet) and adding the number of spots showing. This experiment is "performed" repeatedly, keeping track of the number of times each outcome is observed. These outcomes are plotted in the form of a histogram. According to the Central Limit Theorem, if the number of dice rolled is not too small, the histogram's shape should resemble that of the "bell-shaped curve" when the experiment is repeated many times.
• This demonstration allows the user 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.
• 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.
• Press the "New Plots" button. Four scatter plots should appear. Your job is to match the plots with the correlations at the bottom left. Choose which plot you think goes with each correlation, then press "Answers" to see the answers. To try again, press "New Plots."
• This applet lets you calculate the chisquare statistic for a simple table, then simulate the chisquare statistic to estimate the P-Value. Under the "Observed" and "Expected" columns, fill in the observed and expected counts for your data. When you have filled them in, press "OK". If everything is ok, the chisquare statistic from the data will appear at the bottom. You can then simulate the distribution of the chisquare statistic under the hypothesis that the data is multinomial with probabilities proportional to the expected counts. The buttons at the top allow you to choose how many simulations you wish to do. The estimated P-Value, i.e., the percentage of simulated chisquares that are greater than or equal to the chisquare obtained from the data, appears at the bottom. In addition, a histogram of the simulated chisquares, with the ones greater than or equal to the obtained one, are represented in green.
• Use the mouse to put points in the blue area. After each point, the correlation coefficient and the regression equation will be calculated. To remove points, select the "Erase point" option, then click on the point you want removed. "Clear plot" will remove all the points; "Residuals" will pop up a scatter plot of X versus the residuals, as well as a histogram of the residuals. To add random points to the plot, press "Random points," after changing the number and correlation for the new points if you wish.
• This applet lets you perform some simple simulations using Box Models. The first task is to create a box model, which is a box containing a number of tickets with values. Choose "Choose the box" to pop up a window. You can either enter the values on the tickets, and the number of tickets with each value, directly, or choose "Named Distribution" from the "Type" menu to choose a familiar distribution. This applet works fine but may take more time to run than is practical for most of us.
• This applet allows you to do simple statistical analyses of data sets chosen from "Data and Story Library", "Statlib", and the "Journal of Statistical Education Data Archive". Again this runs fine but may be too slow to be practical for most of us.
• Let's Make a Deal: On the TV show of that name, contestants would often be confronted with three boxes, one of which contains the keys to a new car. After choosing one, Monty Hall (the host) opens one not chosen, and lo, it is empty. The contestant must then either keep the chosen box, or trade for the one left unopened. This applet l ets you make a choice a number of times and keeps track how you do.
• Here is a Java applet that shows how sample means tend to the population mean as the sample size increases. The samples can be taken from the distributions Gaussian, Exponential and Uniform. The Probability Density Function (PDF) is overlaid on the sample histogram to show the expected shape of the sample distribution. Population data is shown in red and sample data in blue. The vertical lines show the population and current sample means.