The Probability Calculator

In my years of teaching statistics two technical advances have simplified the material for the student. The first is the statistical calculator and statistical packages to ease the computational burden. The second is the use of the computer to replace the normal curve table. This page and corresponding program expand the earlier normal curve program to include additional distributions and a visual representation of the curves.

This program and Java Applet replace the tables that are normally found in statistics texts. They have great advantages over traditional tables in that they are visual, allowing the student to see both the shape of the distribution and the area in question. An additional advantage of these programs over traditional statistical tables is that exact significance levels can be found from observed statistics. This means that in hypothesis testing it is no longer necessary to find a critical value of a statistic and compare it to the observered value. All the student has to do is compare the probability of the statistic to the value selected for alpha. This procedure eliminates a step from all hypothesis testing procedures and corresponds to the output of most statistical packages. It has an additional advantage of freeing the statistician from the tyranny of only using alpha levels that are presented in statistical tables.

I have attempted to construct the interface consistantly for all statistical tables. To use the tables, enter appropriate values for distribution parameters followed by either a value for the statistic or a probability. Clicking on the button labelled

Right arrow button on Probability Calculator. images/pdfright.gif 25 25 right arrow will find the probability (exact significance level) of the statistic for the value entered in the text box.

For example, to find the area that falls below a given value on a given normal curve, enter the values for mu, sigma, and X. The following has mu equal 100, sigma equal 15, and X equal 123.

Finding area given scores on the normal curve. images/pdf01.gif 377 77 Finding area given scores on the normal curve.

The following display is the result.

Finding area given scores on the normal curve - resulting display. images/pdf02.gif 373 285 Finding area given scores on the normal curve - resulting display.

Clicking on the

Leftt arrow button on Probability Calculator. images/pdfleft.gif 24 25 left arrow button will find the value of the statistic that cuts off the probability that was entered in the probability text box.

Critical values corresponding to traditional statistical tables may be calculated by entering ".05" or ".01" in the probability text box and finding the value by clicking the

Leftt arrow button on Probability Calculator. images/pdfleft.gif 24 25 left arrow button.

I have included the parameters mu and sigma in the t distribution to be consistent with the normal distribution interface and to encourage the user to find confidence intervals rather than simply testing hypotheses. Values for traditional t tables can be found by setting the value of mu to 0 and sigma to 1.

For example, the critical values for a t distribution with ten degrees of freedom can be found as follows:

Finding critical values of the t distribution with Probability Calculator. images/pdf03.gif 394 82 Finding critical values of the t distribution with Probability Calculator.

Finding critical values of the t distribution with Probability Calculator - result. images/pdf04.gif 389 287 Finding critical values of the t distribution with Probability Calculator - result.