ࡱ                >  	                         L             R o o t   E n t r y                                                                              YVγM   @       C o n t e n t s                                                                                          .      E m b e d d i n g   1                                                  b  rH    L=γNn=γ             O l e                                                         
                                                 4                !   "   #   $   %   &   '   (   )   *   +   ,   -   .   /   0   1   2   3   6   7   8   9   :   ;   <   =   >   ?   @   A   C   D   E   F   G   H   I   J   K   R o o t   E n t r y                                                                              0GYγM   @       C o n t e n t s                                                                                          .      E m b e d d i n g   1                                                  b  rH    L=γNn=γ             O l e                                                         
                                                 4               	   
                                                      6   7   8   9   :   ;   <   =   >   ?   @   A   C   D   E   F   G   H   I   J   K       SPSS Output Document   c   NavLog                       DspSimpleText            	 DspString( Log   NavTreeViewItem        
 NavOleItem                                                1Courier New r   N e w           P                {\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 Arial;}{\f3\fmodern Courier New;}{\f4\fmodern\fprq1 Courier New;}}
{\colortbl\red0\green0\blue0;}
\deflang1031\pard\plain\f4\fs20\cf0 ****************************************************************************.
\par * According to Signal Detection Theory, D-PRIME and BIAS should be unrelated.
\par * Using algorithms derived from http://www.briannosek.com/gnat/gnatspss.sps,.
\par * we actually found a strong, negative correlation of these terms in        .
\par * empirical data.                                                           .
\par *                                                                           .
\par * The present syntax file aims to illustrate that the correlation may be    .
\par * purely due to the use of the CDFNORM function in the computation of the   .
\par * BIAS term. We consider using the PDF.NORMAL function here more appropriate.
\par *                                                                           .
\par * Idea: Gerd Bohner <Gerd.Bohner@uni-bielefeld.de>                          .
\par * SPSS syntax: Frank Siebler <Frank.Siebler@uni-bielefeld.de>               .
\par *                                                                           .
\par *                                           Bielefeld/Germany, November 2003.
\par ****************************************************************************.
\par 
\par 
\par ****************************************************************************.
\par * Set up 25 cases such that hit rate and false-alarm rate are not correlated.
\par ****************************************************************************.
\par 
\par data list free
\par /hit_rate fa_rate.
\par 
\par begin data
\par   .5  .1
\par   .5  .2
\par   .5  .3
\par   .5  .4
\par   .5  .5
\par   .6  .1
\par   .6  .2
\par   .6  .3
\par   .6  .4
\par   .6  .5
\par   .7  .1
\par   .7  .2
\par   .7  .3
\par   .7  .4
\par   .7  .5
\par   .8  .1
\par   .8  .2
\par   .8  .3
\par   .8  .4
\par   .8  .5
\par   .9  .1
\par   .9  .2
\par   .9  .3
\par   .9  .4
\par   .9  .5
\par end data.
\par execute.
\par 
\par 
\par 
\par **********************************************************.
\par ***  From http://www.briannosek.com/gnat/gnatspss.sps  ***.
\par **********************************************************.
\par 
\par *** computing d-prime for each pairing collapsed across response deadlines ***.
\par 
\par * COMPUTE bhbg = PROBIT ((bg75hit+bg60hit)/60).
\par * COMPUTE bhfg = PROBIT ((fg75hit+fg60hit)/60).
\par * COMPUTE bhbb = PROBIT ((bb75hit+bb60hit)/60).
\par * COMPUTE bhfb = PROBIT ((fb75hit+fb60hit)/60).
\par 
\par * COMPUTE bfbg = PROBIT ((bg75fal+bg60fal)/60).
\par * COMPUTE bffg = PROBIT ((fg75fal+fg60fal)/60).
\par * COMPUTE bfbb = PROBIT ((bb75fal+bb60fal)/60).
\par * COMPUTE bffb = PROBIT ((fb75fal+fb60fal)/60).
\par 
\par * COMPUTE dbg=bhbg-bfbg.
\par * COMPUTE dfg=bhfg-bffg.
\par * COMPUTE dbb=bhbb-bfbb.
\par * COMPUTE dfb=bhfb-bffb.
\par 
\par 
\par ************************************************.
\par *** Adapting the formula to our present data ***.
\par ************************************************.
\par 
\par compute z_hit = PROBIT (hit_rate).
\par compute z_fa  = PROBIT (fa_rate).
\par 
\par compute dprime = z_hit - z_fa.
\par 
\par 
\par 
\par 
\par **********************************************************.
\par ***  From http://www.briannosek.com/gnat/gnatspss.sps  ***.
\par **********************************************************.
\par 
\par *** computing bias for each pairing collapsed across response deadlines ***.
\par 
\par * COMPUTE bzbg = PROBIT ((1-(bg75fal+bg60fal)/60)).
\par * COMPUTE bzfg = PROBIT ((1-(fg75fal+fg60fal)/60)).
\par * COMPUTE bzbb = PROBIT ((1-(bb75fal+bb60fal)/60)).
\par * COMPUTE bzfb = PROBIT ((1-(fb75fal+fb60fal)/60)).
\par 
\par * COMPUTE bbg = CDFNORM (bzbg-dbg) / CDFNORM (bzbg).
\par * COMPUTE bfg = CDFNORM (bzfg-dfg) / CDFNORM (bzfg).
\par * COMPUTE bbb = CDFNORM (bzbb-dbb) / CDFNORM (bzbb).
\par * COMPUTE bfb = CDFNORM (bzfb-dfb) / CDFNORM (bzfb).
\par 
\par 
\par ************************************************.
\par *** Adapting the formula to our present data ***.
\par ************************************************.
\par 
\par compute bz = PROBIT (1 - fa_rate).
\par 
\par /* Computing bias using the cumulative distribution function (as above)
\par compute bias_cdf = CDFNORM (bz - dprime) / CDFNORM (bz).
\par 
\par /* Computing bias using the probability density function (new)
\par compute bias_pdf = PDF.NORMAL ((bz - dprime), 0, 1) / PDF.NORMAL (bz, 0, 1).
\par 
\par 
\par 
\par ***************************************************************.
\par *** Testing the statistical independence of dprime and bias ***.
\par ***************************************************************.
\par 
\par corr dprime WITH bias_cdf bias_pdf.
\par }
        (   (     `	       4!  *  	                gC (Continued)   {\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 Arial;}{\f3\fmodern Courier New;}{\f4\fmodern\fprq1 Courier New;}}
{\colortbl\red0\green0\blue0;}
\deflang1031\pard\qc\plain\f2\fs20\cf0 &[PageTitle]
\par }
    {\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 Arial;}{\f3\fmodern Courier New;}{\f4\fmodern\fprq1 Courier New;}}
{\colortbl\red0\green0\blue0;}
\deflang1031\pard\qr\plain\f2\fs20\cf0 Page &[Page]
\par }
      NavRoot                                          (  Output                          NavHead                                         ( Correlations                    Correlations      NavTitle           {   d                (  Title                   Correlations                     "Arial a l                       P                {\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 Arial;}{\f3\fmodern Courier New;}{\f4\fmodern\fprq1 Courier New;}}
{\colortbl\red0\green0\blue0;}
\deflang1031\pard\plain\f2\fs28\cf0\b Correlations
\par }
     NavNote                             ( Notes                  Correlations   PTPivotController = RGB(2d   d   d   d      PVPivotView       PMPivotModel   NDimensional__DspCell       IndexedCollection        DspCell             	 DspNumber B`B26-NOV-2003 04:33:23)           (    )           ( <none>)           ( <none>)           ( <none>)           , (      9@25)           ( 3User-defined missing values are treated as missing.)           ( _Statistics for each pair of variables are based on all the cases with valid data for that pair.)          ( $corr dprime WITH bias_cdf bias_pdf.  )           ,        
0:00:00.00 Notes   Correlations_Notes        PMPivotItemTree    AbstractTreeBranch    PMModelItemInfo         t           ( Contents   K M          t           ( Output Created    K M         t           ( Comments    K M          t           ( Input   K M         t           ( Data    K M         t           ( Filter    K M        	 t           ( Weight    K M        
 t           ( 
Split File    K M         t           ( N of Rows in Working Data File    K M         t           ( Missing Value Handling   K M        t           ( Definition of Missing    K M        t           ( 
Cases Used    K M 	        t           ( Syntax    K M          t           ( 	Resources   K M 
        t           ( Elapsed Time    K M          t           ( 	Resources   K M         t           ( Elapsed Time              Q U ] a e i m u y }                                     	   
                                                                  PVViewDimension J               i   T   K   K   K   K   }      \   K   c   c                               ( Notes           (                     (      PTTableLook       6         PVSeparatorStyle                                                        PVCellStyle            PVTextStyle    x   x                         "Arial                    x                            "Arial                    x                            "Arial                     x                            "Arial                   x                            "Arial                   x                            "Arial                    x                            "Arial                    hh( (                         "Arial                                                                (cont.)$   H   $   x              PVPrintManager                       NavPivot           B                  ( Correlations                   Correlations        d   d   d   d   !    #%    '     '     '     )           ,(q-.902)           ,(].>A	>.000)           , (      9@25'     '     )           ,(,x?.105)           ,(Sc*?.616)           , (      9@25 Correlations   Correlations_Table_Correlations     I K M        t           ( 
Statistics   K M         t           ( Pearson Correlation    K M        t           ( Sig. (2-tailed)    K M        t           ( N                                 I K M        t           ( 	Variables   K M                   ( DPRIME                         I K M        t           ( 	Variables   K M                   ( BIAS_CDF    K M                  ( BIAS_PDF                                             K                                                                  _   K                                K             C                   O   N             O              ( Correlations           (                     (          6                                                                        x   x                         "Arial                    x                            "Arial                    x                            "Arial                     x                            "Arial                   x                            "Arial                   x                            "Arial                    x                            "Arial                    hh( (                         "Arial                                                                (cont.)$   H   $   x                                
                       "Arial                                                                (cont.)$   H   $   x                                                                                                                                                                                                           SPSS Output Document   c   NavLog                       DspSimpleText            	 DspString( Log   NavTreeViewItem        
 NavOleItem                                                1Courier New r   N e w           P                {\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 Arial;}{\f3\fmodern Courier New;}{\f4\fmodern\fprq1 Courier New;}}
{\colortbl\red0\green0\blue0;}
\deflang1031\pard\plain\f4\fs20\cf0 ****************************************************************************.
\par * According to Signal Detection Theory, D-PRIME and BIAS should be unrelated.
\par * Using algorithms derived from http://www.briannosek.com/gnat/gnatspss.sps,.
\par * we actually found a strong, negative correlation of these terms in        .
\par * empirical data.                                                           .
\par *                                                                           .
\par * The present syntax file aims to illustrate that the correlation may be    .
\par * purely due to the use of the CDFNORM function in the computation of the   .
\par * BIAS term. We consider using the PDF.NORMAL function here more appropriate.
\par *                                                                           .
\par * Idea: Gerd Bohner <Gerd.Bohner@uni-bielefeld.de>                          .
\par * SPSS syntax: Frank Siebler <Frank.Siebler@uni-bielefeld.de>               .
\par *                                                                           .
\par *                                           Bielefeld/Germany, November 2003.
\par ****************************************************************************.
\par 
\par 
\par ****************************************************************************.
\par * Set up 25 cases such that hit rate and false-alarm rate are not correlated.
\par ****************************************************************************.
\par 
\par data list free
\par /hit_rate fa_rate.
\par 
\par begin data
\par   .5  .1
\par   .5  .2
\par   .5  .3
\par   .5  .4
\par   .5  .5
\par   .6  .1
\par   .6  .2
\par   .6  .3
\par   .6  .4
\par   .6  .5
\par   .7  .1
\par   .7  .2
\par   .7  .3
\par   .7  .4
\par   .7  .5
\par   .8  .1
\par   .8  .2
\par   .8  .3
\par   .8  .4
\par   .8  .5
\par   .9  .1
\par   .9  .2
\par   .9  .3
\par   .9  .4
\par   .9  .5
\par end data.
\par execute.
\par 
\par 
\par 
\par **********************************************************.
\par ***  From http://www.briannosek.com/gnat/gnatspss.sps  ***.
\par **********************************************************.
\par 
\par *** computing d-prime for each pairing collapsed across response deadlines ***.
\par 
\par * COMPUTE bhbg = PROBIT ((bg75hit+bg60hit)/60).
\par * COMPUTE bhfg = PROBIT ((fg75hit+fg60hit)/60).
\par * COMPUTE bhbb = PROBIT ((bb75hit+bb60hit)/60).
\par * COMPUTE bhfb = PROBIT ((fb75hit+fb60hit)/60).
\par 
\par * COMPUTE bfbg = PROBIT ((bg75fal+bg60fal)/60).
\par * COMPUTE bffg = PROBIT ((fg75fal+fg60fal)/60).
\par * COMPUTE bfbb = PROBIT ((bb75fal+bb60fal)/60).
\par * COMPUTE bffb = PROBIT ((fb75fal+fb60fal)/60).
\par 
\par * COMPUTE dbg=bhbg-bfbg.
\par * COMPUTE dfg=bhfg-bffg.
\par * COMPUTE dbb=bhbb-bfbb.
\par * COMPUTE dfb=bhfb-bffb.
\par 
\par 
\par ************************************************.
\par *** Adapting the formula to our present data ***.
\par ************************************************.
\par 
\par compute z_hit = PROBIT (hit_rate).
\par compute z_fa  = PROBIT (fa_rate).
\par 
\par compute dprime = z_hit - z_fa.
\par 
\par 
\par 
\par 
\par **********************************************************.
\par ***  From http://www.briannosek.com/gnat/gnatspss.sps  ***.
\par **********************************************************.
\par 
\par *** computing bias for each pairing collapsed across response deadlines ***.
\par 
\par * COMPUTE bzbg = PROBIT ((1-(bg75fal+bg60fal)/60)).
\par * COMPUTE bzfg = PROBIT ((1-(fg75fal+fg60fal)/60)).
\par * COMPUTE bzbb = PROBIT ((1-(bb75fal+bb60fal)/60)).
\par * COMPUTE bzfb = PROBIT ((1-(fb75fal+fb60fal)/60)).
\par 
\par * COMPUTE bbg = CDFNORM (bzbg-dbg) / CDFNORM (bzbg).
\par * COMPUTE bfg = CDFNORM (bzfg-dfg) / CDFNORM (bzfg).
\par * COMPUTE bbb = CDFNORM (bzbb-dbb) / CDFNORM (bzbb).
\par * COMPUTE bfb = CDFNORM (bzfb-dfb) / CDFNORM (bzfb).
\par 
\par 
\par ************************************************.
\par *** Adapting the formula to our present data ***.
\par ************************************************.
\par 
\par compute bz = PROBIT (1 - fa_rate).
\par 
\par /* Computing bias using the cumulative distribution function (as above)
\par compute bias_cdf = CDFNORM (bz - dprime) / CDFNORM (bz).
\par 
\par /* Computing bias using the probability density function (new)
\par compute bias_pdf = PDF.NORMAL ((bz - dprime), 0, 1) / PDF.NORMAL (bz, 0, 1).
\par 
\par 
\par 
\par ***************************************************************.
\par *** Testing the statistical independence of dprime and bias ***.
\par ***************************************************************.
\par 
\par corr dprime WITH bias_cdf bias_pdf.
\par }
        (   (     `	       4!  *  	                gC (Continued)   {\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 Arial;}{\f3\fmodern Courier New;}{\f4\fmodern\fprq1 Courier New;}}
{\colortbl\red0\green0\blue0;}
\deflang1031\pard\qc\plain\f2\fs20\cf0 &[PageTitle]
\par }
    {\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 Arial;}{\f3\fmodern Courier New;}{\f4\fmodern\fprq1 Courier New;}}
{\colortbl\red0\green0\blue0;}
\deflang1031\pard\qr\plain\f2\fs20\cf0 Page &[Page]
\par }
      NavRoot                                          (  Output                          NavHead                                         ( Correlations                    Correlations      NavTitle           {   d                (  Title                   Correlations                     "Arial a l                       P                {\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 Arial;}{\f3\fmodern Courier New;}{\f4\fmodern\fprq1 Courier New;}}
{\colortbl\red0\green0\blue0;}
\deflang1031\pard\plain\f2\fs28\cf0\b Correlations
\par }
     NavNote                             ( Notes                  Correlations   PTPivotController = RGB(2d   d   d   d      PVPivotView       PMPivotModel   NDimensional__DspCell       IndexedCollection        DspCell             	 DspNumber B`B26-NOV-2003 04:33:23)           (    )           ( <none>)           ( <none>)           ( <none>)           , (      9@25)           ( 3User-defined missing values are treated as missing.)           ( _Statistics for each pair of variables are based on all the cases with valid data for that pair.)          ( $corr dprime WITH bias_cdf bias_pdf.  )           ,        
0:00:00.00 Notes   Correlations_Notes        PMPivotItemTree    AbstractTreeBranch    PMModelItemInfo         t           ( Contents   K M          t           ( Output Created    K M         t           ( Comments    K M          t           ( Input   K M         t           ( Data    K M         t           ( Filter    K M        	 t           ( Weight    K M        
 t           ( 
Split File    K M         t           ( N of Rows in Working Data File    K M         t           ( Missing Value Handling   K M        t           ( Definition of Missing    K M        t           ( 
Cases Used    K M 	        t           ( Syntax    K M          t           ( 	Resources   K M 
        t           ( Elapsed Time    K M          t           ( 	Resources   K M         t           ( Elapsed Time              Q U ] a e i m u y }                                     	   
                                                                  PVViewDimension J               i   T   K   K   K   K   }      \   K   c   c                               ( Notes           (                     (      PTTableLook       6         PVSeparatorStyle                                                        PVCellStyle            PVTextStyle    x   x                         "Arial                    x                            "Arial                    x                            "Arial                     x                            "Arial                   x                            "Arial                   x                            "Arial                    x                            "Arial                    hh( (                         "Arial                                                                (cont.)$   H   $   x              PVPrintManager                       NavPivot           B                  ( Correlations                   Correlations        d   d   d   d   !    #%    '     '     '     )           ,(q-.902)           ,(].>A	>.000)           , (      9@25'     '     )           ,(,x?.105)           ,(Sc*?.616)           , (      9@25 Correlations   Correlations_Table_Correlations     I K M        t           ( 
Statistics   K M         t           ( Pearson Correlation    K M        t           ( Sig. (2-tailed)    K M        t           ( N                                 I K M        t           ( 	Variables   K M                   ( DPRIME                         I K M        t           ( 	Variables   K M                   ( BIAS_CDF    K M                  ( BIAS_PDF                                             K                                                                  _   K                                K             C                   O   N             O              ( Correlations           (                     (          6                                                                        x   x                         "Arial                    x                            "Arial                    x                            "Arial                     x                            "Arial                   x                            "Arial                   x                            "Arial                    x                            "Arial                    hh( (                         "Arial                                                                (cont.)$   H   $   x                                
                                                                                                                                                                                                                                                                                                                                                    C o n t e n t s                                                                                            B          O l e P r e s 0 0 0                                                                                 5                                                                                                                                                                                                                                                                 %B       	     1                     1Courier New 
hQwZw     0    -     -         ff $                     ff $   '       p $                 p $        $             .      8             1Courier New X
9QwZw     0    -    	    1   2
   K      T$ ***************************************************************************    2
       | . ,   2
  B    * According to Signal Detection Theory, D-PRIME and BIAS should be   2
  
    unrelated.   2
      * Using algorithms derived from "   2
  -    http://www.briannosek.com/gnat/gnatspss.sps,. -   2
  D     * we actually found a strong, negative correlation of these terms in   2
      | .    2
      <* empirical data.    2
{	      | 	.    2
s
      	| 
*    2
k      
| . /   2
c  H    "* The present syntax file aims to illustrate that the correlation may be   2
[      | . 0   2
S  I    \#* purely due to the use of the CDFNORM function in the computation of the*   2
K      | . +   2
C  @     x* BIAS term. We consider using the PDF.NORMAL function here more   2
;      xpappropriate.   2
3      p| h*    2
+      h| `. $   2
#  2    `8X* Idea: Gerd Bohner <Gerd.Bohner@uni-bielefeld.de>   2
      X| P. *   2
  =    PH* SPSS syntax: Frank Siebler <Frank.Siebler@uni-bielefeld.de>o   2
      H| @.    2
      @| 8*    2
      8| 0. /   2
  G    0d"(*                                           Bielefeld/Germany, Novembere   2
      (l 2003. 1   2
  K     T$***************************************************************************    2
      | .01   2
  K     T$***************************************************************************    2
       |  .0,   2
!  A     |!* Set up 25 cases such that hit rate and false-alarm rate are notv   2
"      !T"correlated..1   2
#  K    "T$#***************************************************************************    2
$      #| $.0   2
&      %&data list free   2
'      &'/hit_rate fa_rate.   2
s)  
    ()begin data   2
k*      )*  .5  .1   2
c+      *+  .5  .2   2
[,      +,  .5  .3   2
S-      ,-  .5  .4   2
K.      -.  .5  .5   2
C/      .x/  .6  .1   2
;0      x/p0  .6  .2   2
31      p0h1  .6  .3   2
+2      h1`2  .6  .4   2
#3      `2X3  .6  .5   2
4      X3P4  .7  .1   2
5      P4H5  .7  .2   2
6      H5@6  .7  .3   2
7      @687  .7  .4   2
7      8708  .7  .5   2
8      08(9  .8  .1   2
9      (9 :  .8  .2   2
:       :;  .8  .3   2
;      ;<  .8  .4   2
<      <=  .8  .5   2
=      = >  .9  .1   2
>       >>  .9  .2   2
?      >?  .9  .3   2
@      ?@  .9  .4   2
A      @A  .9  .5   2
B  	    A\Bend data.a   2
C      BCexecute.)   2
{G  ;    FG**********************************************************.e)   2
sH  ;    GH***  From http://www.briannosek.com/gnat/gnatspss.sps  ***.e)   2
kI  ;    HI**********************************************************.e0   2
[K  J    J#K*** computing d-prime for each pairing collapsed across response deadlines   2
SL      KL***.#   2
CN  /    MxN* COMPUTE bhbg = PROBIT ((bg75hit+bg60hit)/60). #   2
;O  /    xNpO* COMPUTE bhfg = PROBIT ((fg75hit+fg60hit)/60). #   2
3P  /    pOhP* COMPUTE bhbb = PROBIT ((bb75hit+bb60hit)/60). #   2
+Q  /    hP`Q* COMPUTE bhfb = PROBIT ((fb75hit+fb60hit)/60). #   2
S  /    XRPS* COMPUTE bfbg = PROBIT ((bg75fal+bg60fal)/60). #   2
T  /    PSHT* COMPUTE bffg = PROBIT ((fg75fal+fg60fal)/60). #   2
U  /    HT@U* COMPUTE bfbb = PROBIT ((bb75fal+bb60fal)/60). #   2
V  /    @U8V* COMPUTE bffb = PROBIT ((fb75fal+fb60fal)/60).    2
W      0W(X* COMPUTE dbg=bhbg-bfbg.   2
X      (X Y* COMPUTE dfg=bhfg-bffg.   2
Y       YZ* COMPUTE dbb=bhbb-bfbb.   2
Z      Z[* COMPUTE dfb=bhfb-bffb.$   2
]  1     ]]************************************************.>$   2
^  1    ]^*** Adapting the formula to our present data ***.>$   2
_  1    ^_************************************************.>   2
a  "    `xacompute z_hit = PROBIT (hit_rate).   2
b  !    abcompute z_fa  = PROBIT (fa_rate)..   2
d      cdcompute dprime = z_hit - z_fa.)   2
ci  ;    hi**********************************************************.e)   2
[j  ;    ij***  From http://www.briannosek.com/gnat/gnatspss.sps  ***.e)   2
Sk  ;    jk**********************************************************.e1   2
Cm  K    lT$xm*** computing bias for each pairing collapsed across response deadlines *** %   2
3o  3    pnho* COMPUTE bzbg = PROBIT ((1-(bg75fal+bg60fal)/60)). %   2
+p  3    ho`p* COMPUTE bzfg = PROBIT ((1-(fg75fal+fg60fal)/60)). %   2
#q  3    `pXq* COMPUTE bzbb = PROBIT ((1-(bb75fal+bb60fal)/60)). %   2
r  3    XqPr* COMPUTE bzfb = PROBIT ((1-(fb75fal+fb60fal)/60)). %   2
t  4    Hs0@t* COMPUTE bbg = CDFNORM (bzbg-dbg) / CDFNORM (bzbg).%   2
u  4    @t08u* COMPUTE bfg = CDFNORM (bzfg-dfg) / CDFNORM (bzfg).%   2
u  4    8u00v* COMPUTE bbb = CDFNORM (bzbb-dbb) / CDFNORM (bzbb).%   2
v  4    0v0(w* COMPUTE bfb = CDFNORM (bzfb-dfb) / CDFNORM (bzfb).$   2
y  1    yz************************************************.b$   2
z  1    z{*** Adapting the formula to our present data ***.b$   2
{  1    { |************************************************.b   2
}  "    |x}compute bz = PROBIT (1 - fa_rate)./   2
  G    ~d"/* Computing bias using the cumulative distribution function (as above)e'   2
  8     ؀compute bias_cdf = CDFNORM (bz - dprime) / CDFNORM (bz).*   2
  >    ЁȂ/* Computing bias using the probability density function (new)1   2
  K    ȂT$compute bias_pdf = PDF.NORMAL ((bz - dprime), 0, 1) / PDF.NORMAL (bz, 0, 1) +   2
k  @     ***************************************************************.+   2
c  @     *** Testing the statistical independence of dprime and bias ***.+   2
[  @     ***************************************************************.   2
K  #    corr dprime WITH bias_cdf bias_pdf.    '   '             "System    
             0    -                        NANI                                                                     1Courier New r   N e w           P                {\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fmodern\fprq1 Courier New;}}
{\colortbl\red0\green0\blue0;}
\deflang1031\pard\plain\f2\fs20\cf0 ****************************************************************************.
\par * According to Signal Detection Theory, D-PRIME and BIAS should be unrelated.
\par * Using algorithms derived from http://www.briannosek.com/gnat/gnatspss.sps,.
\par * we actually found a strong, negative correlation of these terms in        .
\par * empirical data.                                                           .
\par *                                                                           .
\par * The present syntax file aims to illustrate that the correlation may be    .
\par * purely due to the use of the CDFNORM function in the computation of the   .
\par * BIAS term. We consider using the PDF.NORMAL function here more appropriate.
\par *                                                                           .
\par * Idea: Gerd Bohner <Gerd.Bohner@uni-bielefeld.de>                          .
\par * SPSS syntax: Frank Siebler <Frank.Siebler@uni-bielefeld.de>               .
\par *                                                                           .
\par *                                           Bielefeld/Germany, November 2003.
\par ****************************************************************************.
\par 
\par 
\par ****************************************************************************.
\par * Set up 25 cases such that hit rate and false-alarm rate are not correlated.
\par ****************************************************************************.
\par 
\par data list free
\par /hit_rate fa_rate.
\par 
\par begin data
\par   .5  .1
\par   .5  .2
\par   .5  .3
\par   .5  .4
\par   .5  .5
\par   .6  .1
\par   .6  .2
\par   .6  .3
\par   .6  .4
\par   .6  .5
\par   .7  .1
\par   .7  .2
\par   .7  .3
\par   .7  .4
\par   .7  .5
\par   .8  .1
\par   .8  .2
\par   .8  .3
\par   .8  .4
\par   .8  .5
\par   .9  .1
\par   .9  .2
\par   .9  .3
\par   .9  .4
\par   .9  .5
\par end data.
\par execute.
\par 
\par 
\par 
\par **********************************************************.
\par ***  From http://www.briannosek.com/gnat/gnatspss.sps  ***.
\par **********************************************************.
\par 
\par *** computing d-prime for each pairing collapsed across response deadlines ***.
\par 
\par * COMPUTE bhbg = PROBIT ((bg75hit+bg60hit)/60).
\par * COMPUTE bhfg = PROBIT ((fg75hit+fg60hit)/60).
\par * COMPUTE bhbb = PROBIT ((bb75hit+bb60hit)/60).
\par * COMPUTE bhfb = PROBIT ((fb75hit+fb60hit)/60).
\par 
\par * COMPUTE bfbg = PROBIT ((bg75fal+bg60fal)/60).
\par * COMPUTE bffg = PROBIT ((fg75fal+fg60fal)/60).
\par * COMPUTE bfbb = PROBIT ((bb75fal+bb60fal)/60).
\par * COMPUTE bffb = PROBIT ((fb75fal+fb60fal)/60).
\par 
\par * COMPUTE dbg=bhbg-bfbg.
\par * COMPUTE dfg=bhfg-bffg.
\par * COMPUTE dbb=bhbb-bfbb.
\par * COMPUTE dfb=bhfb-bffb.
\par 
\par 
\par ************************************************.
\par *** Adapting the formula to our present data ***.
\par ************************************************.
\par 
\par compute z_hit = PROBIT (hit_rate).
\par compute z_fa  = PROBIT (fa_rate).
\par 
\par compute dprime = z_hit - z_fa.
\par 
\par 
\par 
\par 
\par **********************************************************.
\par ***  From http://www.briannosek.com/gnat/gnatspss.sps  ***.
\par **********************************************************.
\par 
\par *** computing bias for each pairing collapsed across response deadlines ***.
\par 
\par * COMPUTE bzbg = PROBIT ((1-(bg75fal+bg60fal)/60)).
\par * COMPUTE bzfg = PROBIT ((1-(fg75fal+fg60fal)/60)).
\par * COMPUTE bzbb = PROBIT ((1-(bb75fal+bb60fal)/60)).
\par * COMPUTE bzfb = PROBIT ((1-(fb75fal+fb60fal)/60)).
\par 
\par * COMPUTE bbg = CDFNORM (bzbg-dbg) / CDFNORM (bzbg).
\par * COMPUTE bfg = CDFNORM (bzfg-dfg) / CDFNORM (bzfg).
\par * COMPUTE bbb = CDFNORM (bzbb-dbb) / CDFNORM (bzbb).
\par * COMPUTE bfb = CDFNORM (bzfb-dfb) / CDFNORM (bzfb).
\par 
\par 
\par ************************************************.
\par *** Adapting the formula to our present data ***.
\par ************************************************.
\par 
\par compute bz = PROBIT (1 - fa_rate).
\par 
\par /* Computing bias using the cumulative distribution function (as above)
\par compute bias_cdf = CDFNORM (bz - dprime) / CDFNORM (bz).
\par 
\par /* Computing bias using the probability density function (new)
\par compute bias_pdf = PDF.NORMAL ((bz - dprime), 0, 1) / PDF.NORMAL (bz, 0, 1).
\par 
\par 
\par 
\par ***************************************************************.
\par *** Testing the statistical independence of dprime and bias ***.
\par ***************************************************************.
\par 
\par corr dprime WITH bias_cdf bias_pdf.
\par }
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