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.

Important note:

Whereas this
simple text box applet reports only the right-tail value, the
graphic version shows both left-tail and right-tail values.
You can easily compute the left-tail p value by subtracting the right-tail
p value from 1.00. Thus, a right-tail p value
of .05 and a left-tail p value of .95 share the same
z value of 1.645.

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