Exploring, fitting, & predicting
We are now ready to put together everything we have learned about Signal Detection Theory into integrated views of theory and performance.
On this page, we will explore the relationship between model parameters and performance measures. On the next page, we will fit your performance to the model. And then, on the following page, we will predict performance from model parameters.
Visualizing the relationship between model and performance
This exploration incorporates three key visualizations. The table of outcomes summarizes performance. ROC space shows the relationship between behavior and theory. And the model diagram illustrates an explanation of that performance in terms of SDT. Note that every possible pattern of performance can be represented in ROC space in terms of the behavioral measures of hit rate and false alarm rate, and can also be explained by a unique combination of the model parameters sensitivity and bias. However the relationship between the behavioral measures and the model parameters is non-linear and surprisingly unintuitive, as illustrated by the iso-sensitivity curve and the iso-bias curve. Hopefully exploring their relationship through direct manipulation will help you gain a deeper understanding!
The table of outcomes lists the count of each trial outcome: Hits, Misses, False Alarms, and Correct Rejections. These counts are further summarized with Hit Rate, False Alarm rate, and overall Accuracy. You can modify any value, and any dependent values will update too.
In ROC space, performance is plotted as Hit Rate versus False Alarm Rate. All of the points with the same Sensitivity (d′) are illustrated with an Iso-Sensitivity Curve. All of the points with the same Bias (c) are illustrated with an Iso-Bias Curve. Moving the data point will cause the iso-curves to update as well.
The visual representation of the SDT model shows Sensitivity as the distance, d′, between the distributions. And it shows Bias as the location, c, of the threshold. The threshold divides the Signal + Noise Distribution into Hit and Miss areas and divides the Noise Distribution into Correct Rejection and False Alarm areas. Moving the distributions or the threshold adjusts d′ or c, respectively.
Across all three figures, the table of outcomes, ROC space, and the SDT model, adjustments to the performance or the model will be reflected immediately in the other figures as well.