Appendix 1

Calculation of d' and for phoneme recognition

The total frequency of each of the classes `hits', `misses', `correct rejections' and `false alarms' is available. From these, we can calculate two statistics, d' and . d' is a measure of sensitivity and the criterion.

1. Calculation of
   

   Let us deal with things concretely with a worked example. Here is the matrix with our four categories:
   

   

   From this matrix work out the following probabilities:

   

   

   Here,

   

   

   Here,

   

2. Calculation of d'
   

   For d', Z values are needed for p (H) and p (FA). It is necessary to read a table of the standard normal distribution and get these values making sure the correct sign is obtained.

   1. If the probability is greater than 0.50, it will be negative, that is, to the left of the mean of a normal curve.
   2. If the probability is greater than 0.50, it will be positive, that is, to the right of the mean.
   Since most tables of Zs are based on probabilities as area to the left of a point, either a conversion will be necessary or use the special table provided below.

   The formula:

   

   Here,