Signal Detection Theory Tutorial
bullet Intro to SDT Tutorial
- SDT Overview
- Basic Vocabulary
- Hits and False Alarms
- p-values and z-scores
- d' Defined
- d' as Sensitivity
- Criterion
- ROCs
- Summary
- Follow-Up Questions
- Follow-Up Answers

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.

only the last parameter read in is used;; for p omit the z param line, for z omit the p parameter line -->


The Java Applet necessary for this exercise did not load!

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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.

A. z when right-tail p = .025

B. z when right-tail p = .50

C. z when right-tail p = .95

Click here to check your work.

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

A. Right-tail p when z = -1.00

B. Right-tail p when z = -0.50

C. Right-tail p when z = 0.50

D. Right-tail p when z = 2.00

Click here to check your work.

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