Choose yes/no d′, a rate inverse, response counts or 2AFC proportion correct. Rates use an explicit proportion or percent unit; the count mode applies a disclosed loglinear correction.

Choose proportion or percent. Rates must be strictly between 0 and 1 (0% and 100%); use counts for endpoint correction.

Related Calculators

D Prime Formula

Under the equal-variance normal signal-detection model, the following formula calculates yes/no d′. Rates must be strictly between zero and one; endpoint counts can use the loglinear correction.

D' = Z(Hit Rate) - Z(False Alarm Rate)

Variables:

  • D' is the D Prime value
  • Z(Hit Rate) is the Z score of the hit rate
  • Z(False Alarm Rate) is the Z score of the false alarm rate

To calculate the D Prime value, first calculate the Z scores of the hit rate and the false alarm rate. Here Z is the inverse standard-normal cumulative distribution (quantile) of a response probability. Subtract the Z score of the false alarm rate from the Z score of the hit rate. The result is the D Prime value, which is a measure of signal detection ability.

What is a D Prime?

D Prime (d') is a statistical measure used in signal detection theory to quantify the ability to distinguish between signal and noise. Under the equal-variance normal model, it represents the separation between signal and noise means divided by their common standard deviation. A higher d' indicates a greater ability to differentiate signal from noise, while a lower d' suggests difficulty in distinguishing the two. It is commonly used in psychology, neuroscience, and other fields that involve decision making under uncertainty.

How to Calculate D Prime?

The following steps outline how to calculate the D Prime value using the formula: D' = Z(Hit Rate) - Z(False Alarm Rate).

  1. First, determine the Z score of the hit rate.
  2. Next, determine the Z score of the false alarm rate.
  3. Next, subtract the Z score of the false alarm rate from the Z score of the hit rate.
  4. Finally, calculate the D Prime value.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

D' is the D Prime value

Z(Hit Rate) is the Z score of the hit rate

Z(False Alarm Rate) is the Z score of the false alarm rate