Chapter 5: d-prime

To compute d-prime we will proceed in three steps. First we must compute probability distributions over hit and false alarm rates based on the binomial likelihood:

N=50; hits=round(N*.8414); fa=round(N*.5); %criterion at 0 for dprime=1 case

pri=@(x) ones(size(x)); %uniform prior

ftx=@(x) ninv(x); %cumulative inverse normal transform

Fnum=1;

figure(Fnum); clf

subplot(2,1,1); hold on;

[~, ~, Lhit]=Lrate([hits N],pri,Fnum);

[~, ~, Lfa]= Lrate([fa N],pri);

%and then z-transform these rates:

[Lhit]=LTX(Lhit(:,2),(Lhit(:,1)),ftx);

[Lfa ]=LTX(Lfa(:,2) ,(Lfa(:,1)) ,ftx);

subplot(2,1,2); plot(Lhit(:,2),exp(Lhit(:,1)),'k-','LineWidth',2)

xlabel('z','FontName','Arial','FontSize',13,'FontWeight','Bold')

%before finally computing the probability over differences of z-transformed rates:

%but note that here it is important to first re-linearize abscissa values, or nonlinearities from the previous transform will build up and create problems

xhit=linspace(Lhit(100,2),Lhit(end-100,2),1001)';

xfa=linspace(Lfa(100,2),Lfa(end-100,2),1001)';

phit=interp1(Lhit(100:end-100,2),Lhit(100:end-100,1),xhit,'pchip'); phit=exp(phit-max(phit));

pfa=interp1(Lfa(100:end-100,2),Lfa(100:end-100,1),xfa,'pchip'); pfa=exp(pfa-max(pfa));

[pS, pD, sSD]=SumDiffFig([pfa xfa],[phit xhit],[45 46],0,0); %noScale; Continuous

figure(Fnum+1); clf

plot(pD(:,2),pD(:,1)/max(pD(:,1)),'k.')

axis([-3 3 0 1])

xlabel('d''','FontName','Arial','FontSize',13,'FontWeight','Bold')

ylabel('p','FontName','Arial','FontSize',13,'FontWeight','Bold')