p-values and z-scores

Before we continue however, we should take a moment to review a few simple statistical transformations that are necessary for SDT calculations.

In the simple case, SDT is based upon two normal distributions whose variances are equal. To calculate SDT measures, we need to convert p-values to z-scores, and vice versa. In SDT, a z-score measures performance in terms of the number of standard deviations that a score is above or below a mean, and a p-value represents the probability of observing a score greater than the observed score.

Later in this tutorial, you will be using a computer program that performs these calculations for you. However, you will have a better understanding of how SDT measures are calculated once you have performed some of these computations yourself.

To perform the conversions between p-values and z-scores, you can use a z table which can be found in most basic statistics textbooks or you can use the WISE p-z converter applet.

To use the WISE p-z converter, input a p-value in the left text box and press the ’p --> z' button or input a z-score into the right text box and press the ’ z --> p' button. The applet shows the ‘right-tail’ p value for a one-tailed application. Press the ‘Graphic’ button to open a graphic representation of the relationship between z and p, showing both right and left tails for one- and two-tailed applications.

Exercise 1. Use the p/z converter applet to convert the following p-values to z-scores.

Click here to check your work.

Exercise 2. Now use the applet to perform these conversions.

Click here to check your work.

Questions, comments, difficulties? See our technical support page or contact us: wise@cgu.edu.