This applet allows users to play several probability games like Monty Hall, Gambler's Ruin, Galton's Board, etc. Select a game from the drop down menu and click "About" to read its background. Users can manipulate the parameters for each game. Graphs of the theoretical and empirical distributions are shown. Requires JAVA.
Content Quality Concerns:
1) Minimal instructions are given for the applets under each applet's "About" and "i" buttons. The notation is defined in mouse-overs, but could be misleading for some. For example, the histogram applet uses 'n' for the number of interval classes (bins), while standard notation would reserve 'n' for the number of data points. The Red and Black game can be difficult to decipher if users are unaware of the mouse-over definitions; 'I' is the outcome of a particular play, 'X' is the wealth at the end of a particular play, 'J' is the outcome of the game (ruin vs. fortune), and 'N' is the number of plays per game. 2) The Galton Board applet seems to function incorrectly. Although a large Galton board is shown, the ball does not fall past row 15, and once row 15 is reached the reset button above the applet does not work; users must use the reset button to the side. The instructions imply that the subset column is meant to represent the value of the binomial coefficient, but it gives the row number when the ball falls to the right and produces a square when the ball falls to the left. 3) The "Play" and "Clear" buttons on the Fourier and Wavelet games are not visible when the applet is first opened; users must slide the applet window to the left to see them. Also, it is unclear what the play button does, and therefore, unclear if it is functioning correctly. 4) The applets which represent game simulations (Galton Board, Red and Black, Monty Hall) only let the user run one simulation at a time. Users cannot automate multiple runs of the games to see what happens in the long run. For example, depending on the parameters, the Red and Black game may require a large number of clicks to reach a single outcome (ruin or fortune).
Content Quality Strengths:
These demonstrations of some of the classic problems in statistics and probability give users the flexibility to explore different cases. For example, the scatterplot applet allows users to create a large variety of data points and see the least-squares line change with every added point. Similarly, the histogram applet lets users immediately see the associated effects of adding data. The Fourier and Wavelet applets have an impressive number of things users can alter and compare, and the Monty Hall game allows for two methods of playing. In the standard method, Monty knows where the car is and always opens a door with a goat, while the blind method allows Monty to pick a door at random. This comparison of the games gets at the heart of the paradoxical behavior of the game. Additionally, the applets are simple in their presentation, without an overwhelming number of buttons and sliders. These simulations offer tools for teachers to include in their lessons.
Ease of Use Concerns:
There did not seem to be a way to copy the data into other software, and the notation was not always easy to decipher. The "Interactive Histogram" applet without the Error Graph has no instructions. If the applications are done in order, then users will see the "Interactive Histogram with Error Graph" first, which does have instructions. In spite of the simplicity of the applet itself, the interface is not particularly intuitive and will take time to learn due to limited instructions.
Ease of Use Strengths:
The applets load quickly and have quite a bit of flexibility, with an uncluttered, easy to use display and set up. All the applets have a great snapshot feature which allows the user to create a jpeg image of the output in the window. Brief explanations of the applets are provided under the "About" and "i" buttons for each applet. This collection is great for instructors who are interested in creating their own educational materials for technological applications.
Potential Effectiveness Concerns:
In order to use these applets in an introductory statistics course, instructors would have to give a thorough introduction to the problems and notation as well as create an assessment activity to guide student thinking. There is concern over limited functionality on many of the applications which seem to be written for a specific class looking at one or two ideas.
Potential Effectiveness Strengths:
The ease of use and simplicity of presentation of these applets provide great potential for instruction as demonstrations or as part of an assignment that the instructor creates. The scatterplot, histogram, and Monty Hall applets seem especially useful. The Fourier and Wavelet applets appear to be powerful visualization tools for an engineering or time series class.
Potential Effectiveness Rating:
Source Code Available:
Source Code Available
Intended User Role:
Free for All