The interactive distributions section of the Statistics Online Computational Resource (SOCR) provides an extensive series of interactive probability distribution calculators. This Java based applet includes most of the standard distributions such as binomial, beta, gamma and normal, but also some more esoteric such as Gilbrats, Triangle or Rayleigh. These calculators are well featured in that they produce a graphical representation of the distribution along with calculation of the mean and variance of the distribution. It also allows the user to select a point on the graphic and produce probabilities above and below the selected point. Moving the mouse along the plot shows probability/density values. Dragging edges of the shaded region shows probability to right/left and between endpoints. The applet includes a snapshot button that allows the user to take a screen shot of the applet.
Type of Material:
This material can be used in a variety of in class and out of class senerios. Some recommended uses include (a) As a replacement for paper statistics tables to look up probabilities and percentiles, and (b) To allow students to visualize shapes of distributions as parameters change.
Java capable browser.
Identify Major Learning Goals:
This material will help the user better understand probability distributions by replacing textbook based "look-up" on stat tables with an applet that works for any reasonable endpoint and parameter values. It will also assist in visualizing ideas that stem from probability distributions such as p-values.
Target Student Population:
Any level statistics student who would be using paper tables and familiar with probabilites such as areas under density curves could use the applet. Many of the distributions provided will only be recognized by students from more advanced probability/mathematical statistics courses.
Prerequisite Knowledge or Skills:
General idea of probability as areas under density curves - or sums from probability functions.
Evaluation and Observation
The key strengths of this applet include the consistent interface for all distributions. It also includes depictions for an extremely lengthy list of distributions.
In some discrete distributions (e.g. binomial, Poisson) the left/right/between probabilities change continuously as the endpoint is dragged within the "bar" for a single discrete value - as if it were a continuous variable. Automatic axis rescaling makes it difficult at times to see the effect of changing a parameter with a slider. A number of distribution options are listed in the menu but not yet implemented.
Potential Effectiveness as a Teaching Tool
The consistent interface allows students to "look-up" p-values and critical values with the same basic tool for all distributions. This applet is good way to easily "see" lots of distributions and how the parameters affect their shape. This may allow courses to include more distributions than the traditional binomial, normal, and t-distribution. For more advanced students, the links to find out more about each distribution (from Wolfram's Mathworld) are a nice touch.
Long list of (40+) potential distributions may be intimidating to a beginner student who might just need normal and t-distributions. Listing of (endpoint, density function value) pair as one scrolls along a density curve might confuse a student to read the density as a probability (as it is for a discrete random variable).
Ease of Use for Both Students and Faculty
Users can easily change the shaded area of a distribution by dragging endpoints. This works fairly intuitively and will help students visualize the connection between probabilities and the density/probability function. Sliders allow easy specification/modifications of parameters.
Mouse resolution can make it difficult to get an endpoint precisely. For example, in finding a p-vlaue for a t.s.=2.18, student might have to "settle" for endpoint of 2.172 or 2.19. This resource could be greatly enhanced by allowing students to put in a specific value rather than trying to find it with the mouse. This is especially important for students who will replace traditional tables with this applet. Although you can enter values for parameters in a text box you must hit enter to have it recorded. Just typing it in and tabbing to different field or clicking on a different box appears to leave the parameter unchanged - even though the typed value is changed. Default parameters on some distributions are not reasonable - eg. p=0.0 is shown by default for a geometric, when p-0.05 is apparently plotted.
The applet includes a snapshot feature that should take a screen shot of the applet. However, the reviewers could not get this feature to work.
Other Issues and Comments:
The use of paper tables has been necessary in statistics but has not had a good alternative. The use of electronic "tables" like these is favored by many in the statistics community. However, the question of how to give pencil and paper exams without tables has yet to be solved. Instructors that spend a lot of time with these type of applets should be sure to plan how they will give exams to their students related to finding probabilities.