DPRIME(1)                          |STAT                    August 21, 1990

NAME
     dprime - compute d' and beta for signal detection data

SYNOPSIS
     dprime [-p] [hit-rate false-alarm-rate]
     [hits false-alarms misses correct-rejections]

DESCRIPTION
     _d_p_r_i_m_e works from data collected in a signal detection task in which a
     signal is either present or not in a stimulus, and an observer either
     indicates that a signal was detected or not.

                         Signal Presented?
                         Yes                 No
     Signal Detected?
     Yes                 hit                 fa
     No                  miss                cr

     In the table above, a _h_i_t is a signal that was presented and detected,
     a _m_i_s_s is a signal that was presented but not detected, a _f_a (for
     false alarm) is a signal that was not presented but mistakenly
     detected, and a _c_r (for correct rejection) is a signal that was not
     presented and not reported as detected by the observer.  The hit rate,
     sometimes called _h_r, is the percentage of signals that were detected
     and is based on the number of hits and misses:
                          hr = #hit / (#hit + #miss).
     The false alarm rate, sometimes called _f_a_r, is  the percentage of
     non-signals that were reported as signals and is based on the number
     of false-alarms and correct-rejections:
                            far = #fa / (#fa + #cr).

     _d_p_r_i_m_e reads its input in several formats.  _d_p_r_i_m_e can be given two
     arguments: the hit-rate and the false-alarm-rate, for which _d_p_r_i_m_e
     will compute d', beta, and the criterion.  _d_p_r_i_m_e can also be give
     four arguments: the number of hits, the number of false-alarms, the
     number of misses and the number of correct-rejections, for which
     _d_p_r_i_m_e will compute the hit-rate and false-alarm-rate and then compute
     d', beta, and the criterion.  Otherwise, if no values are provided on
     the command line, _d_p_r_i_m_e reads raw data from the standard input.  If
     raw data are input, _d_p_r_i_m_e assumes a two column input in which the
     first column tells whether signal+noise or just noise were presented,
     and the second column tells how the observer responded.  The following
     strings can be used to indicate affirmative answers
                                 signal, yes, 1
     while the following can be used to indicate negative:
                                  noise, no, 0
     Upper case forms for the above are allowed.  When reading the standard
     input, _d_p_r_i_m_e allows an optional third column that gives a repetition
     count for the case.

OPTIONS
     -p   print the `precision' of the observer, calculated as:
                            #hit / (#hit + #false-alarm)
          In the information retrieval field, it is common to evaluate the
          effectiveness of a retrieval with two values:
            R = recall = proportion of relevant items retrieved (the hit-rate)
            P = precision = proportion of retrieved items that are relevant
          The correspondence to signal detection is that `relevance' is the
          signal to be detected and has been discussed in Swets, J. A.
          (1969) _E_f_f_e_c_t_i_v_e_n_e_s_s _o_f _I_n_f_o_r_m_a_t_i_o_n _R_e_t_r_i_e_v_a_l _M_e_t_h_o_d_s.  American
          Documentation, 20, 72-89.

ALGORITHM

     The value for d' is the Z value of the hit-rate minus that of the
     false-alarm-rate.
                              d' = Z(hr) - Z(far)
     This reflects the distance between the two distributions: signal, and
     signal+noise.  Though Z values can have any real value, normally
     distributed ones are between -2 and 2 about 95% of the time, so
     differences of twice that would be rare.

     The value for beta is the ratio of the normal density functions at the
     criterion of the Z values used in the computation of d'.  This
     reflects an observer's bias to say `yes' or `no' with the unbiased
     observer having a value around 1.0.  As the bias to say `yes'
     increases, resulting in a higher hit-rate and false-alarm-rate, beta
     approaches 0.0.  As the bias to say `no' increases, resulting in a
     lower hit-rate and false-alarm-rate, beta increases over 1.0 on an
     open-ended scale.  A major reason for doing a signal detection
     analysis is to get a measure of discrimination that is constant over
     observer biases, but the invariance of d' over different beta is often
     not certain.  The `criterion' is the distance from the mean of the
     noise (non-signal) distribution to the point above which the observer
     says `yes' and is in the same units as d'.

     If results indicate a perfect observer (e.g., all hits and no misses),
     then then d' would be infinite.  In realistic conditions, this would
     never happen.  In such cases, d' is reported as 0.0, and beta is
     reported as 1.0.

EXAMPLE
     dprime .7 .4     # will print
     hr     far    dprime beta   criterion
     0.700  0.400  0.778  0.900  0.253

     dprime 70 400 30 600 # will print the same, but with a table

REFERENCE
     Coombs, C. H., Dawes, R. M., and Tversky, A. (1970) Mathematical
     Psychology, Englewood Cliffs, NJ: Prentice-Hall.  See Chapter 6 on _T_h_e
     _T_h_e_o_r_y _o_f _S_i_g_n_a_l _D_e_t_e_c_t_a_b_i_l_i_t_y, pp. 165-201.

     Salton, G, & McGill, M. J. (1983) Introduction to Modern Information
     Retrieval, New York: McGraw-Hill.  See Chapter 5 on _R_e_t_r_i_e_v_a_l
     _E_v_a_l_u_a_t_i_o_n, _e_s_p_e_c_i_a_l_l_y _p_p. _1_6_4-_1_8_4.

BUGS
     The program has not been tested extensively.
