Editing Receiver operating characteristic (section)

==Z-score==

If a [[standard score]] is applied to the ROC curve, the curve will be transformed into a straight line.<ref>{{cite book |first1=Neil A. |last1=MacMillan |first2=C. Douglas |last2=Creelman |edition=2nd |year=2005 |title=Detection Theory: A User's Guide |publisher=Lawrence Erlbaum Associates |location=Mahwah, NJ | isbn=978-1-4106-1114-7 }}</ref>  This z-score is based on a normal distribution with a mean of zero and a standard deviation of one. In memory [[Recognition memory|strength theory]], one must assume that the zROC is not only linear, but has a slope of 1.0. The normal distributions of targets (studied objects that the subjects need to recall) and lures (non studied objects that the subjects attempt to recall) is the factor causing the zROC to be linear.

The linearity of the zROC curve depends on the standard deviations of the target and lure strength distributions. If the standard deviations are equal, the slope will be 1.0. If the standard deviation of the target strength distribution is larger than the standard deviation of the lure strength distribution, then the slope will be smaller than 1.0. In most studies, it has been found that the zROC curve slopes constantly fall below 1, usually between 0.5 and 0.9.<ref>{{cite journal |last1=Glanzer |first1=Murray |first2=Kim |last2=Kisok |last3=Hilford |first3=Andy |last4=Adams |first4=John K. |title=Slope of the receiver-operating characteristic in recognition memory |journal=Journal of Experimental Psychology: Learning, Memory, and Cognition |year=1999 |volume=25 |issue=2 |pages=500–513 |doi=10.1037/0278-7393.25.2.500}}</ref> Many experiments yielded a zROC slope of 0.8. A slope of 0.8 implies that the variability of the target strength distribution is 25% larger than the variability of the lure strength distribution.<ref>{{cite journal |last1=Ratcliff |first1=Roger |last2=McCoon |first2=Gail |last3=Tindall |first3=Michael |title=Empirical generality of data from recognition memory ROC functions and implications for GMMs |journal=Journal of Experimental Psychology: Learning, Memory, and Cognition |year=1994 |volume=20 |issue=4 |pages=763–785 |doi=10.1037/0278-7393.20.4.763|pmid=8064246 |citeseerx=10.1.1.410.2114 }}</ref>

Another variable used is&nbsp;[[D prime|''d<nowiki>'</nowiki>'' (d prime)]] (discussed above in "Other measures"), which can easily be expressed in terms of z-values. Although ''d''<nowiki>'</nowiki>&nbsp;is a commonly used parameter, it must be recognized that it is only relevant when strictly adhering to the very strong assumptions of strength theory made above.<ref>{{cite journal |last1=Zhang |first1=Jun |last2=Mueller |first2=Shane T. |s2cid=122355230 |title=A note on ROC analysis and non-parametric estimate of sensitivity |journal=Psychometrika |year=2005 |volume=70 |doi=10.1007/s11336-003-1119-8 |pages=203–212|citeseerx=10.1.1.162.1515 }}</ref>

The z-score of an ROC curve is always linear, as assumed, except in special situations. The Yonelinas familiarity-recollection model is a two-dimensional account of recognition memory. Instead of the subject simply answering yes or no to a specific input, the subject gives the input a feeling of familiarity, which operates like the original ROC curve. What changes, though, is a parameter for Recollection (R). Recollection is assumed to be all-or-none, and it trumps familiarity. If there were no recollection component, zROC would have a predicted slope of 1. However, when adding the recollection component, the zROC curve will be concave up, with a decreased slope. This difference in shape and slope result from an added element of variability due to some items being recollected. Patients with anterograde amnesia are unable to recollect, so their Yonelinas zROC curve would have a slope close to 1.0.<ref>{{cite journal |last1=Yonelinas |first1=Andrew P. |last2=Kroll |first2=Neal E. A. |last3=Dobbins |first3=Ian G. |last4=Lazzara |first4=Michele |last5=Knight |first5=Robert T. |title=Recollection and familiarity deficits in amnesia: Convergence of remember-know, process dissociation, and receiver operating characteristic data |journal=Neuropsychology |year=1998 |volume=12 |issue=3 |pages=323–339 |doi=10.1037/0894-4105.12.3.323|pmid=9673991 }}</ref>