Sensitivity and responsivity measures for discrimination learning

LEARNING

AND

4,

327-342

MOTIVATION

( 1973)

Sensitivity for

and Responsivity Measures Discrimination Learning’

PETER W. FREY AND JERRY A. COLLIVER Nmthwestern University The present report considers alternative measures of sensitivity and response bias for the discrimination learning paradigm. The classical signal detection measures, d’ and p, were compared with their nonparametric equivalents, A’ and B”, with theoretical measures derived from threshold theory and with empirical measures derived from the ROC graph. Differential rabbit eyelid conditioning data from three experiments were analyzed with these measures, and the results of these analyses were used along with other information to determine which measures of sensitivity and response bias are most useful for the analysis of discrimination learning data.

Although classical signal detection theory (TSD) was initially developed as a performance model for specific psychophysical paradigms (e.g., Egan & Clark, 1966; Green & Swets, 1966), it has subsequently been applied more broadly to analyze data from experiments in recall and recognition memory (Murdock, 1965; Donaldson & Glathe, 1970; Banks, 1970) and in discrimination learning (Rilling & McDiarmid, 1965; Suboski, 1967; Colliver, 1970). The present report considers the feasibility of TSD application to the discrimination learning paradigm and makes comparisons between application of the classical model and other models. Suboski ( 1967) has emphasized the need for response measuresin the classical conditioning situation that separate the general response tendency from CS-related responding. To make this distinction, Suboski advocated the application of classical TSD methods in the differential conditioning situation. The procedure for applying TSD methods to this situation is relatively simple. Response frequency to CS + is used as an estimate of hit rate and response frequency to CS- as an estimate of false-alarm rate. By assuming that the sensory effects of CS + and CS 1 This investigation was supported NSF Grant GY-8807. Reprint requests of Psychology, Northwestern University, like to thank Janet Zitz for her data

by PHS research should be directed Evanston, Illinois analysis assistance.

327 Copyright All rights

0 1973 by Academic Press, Inc. of reproduction in any form reserved.

Grant MH 17264 and by to Peter Frey, Department 80201. The authors would

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can be represented by normal probability density functions with equal variance, values of d’ and p can be calculated for each subject from a table of the normal distributions (Green & Swets, 1966). The subject’s ability to discriminate between two signals is indexed by d’, the distance in (7 units between the means of the two distributions representing the effects of the two sensory inputs. Response bias is measured by p, the ratio of the ordinates of the two distributions at the point where the subject places his decision criterion for responding or not responding (Green & Swets, 1966). Traditional data analyses can then be performed on these derived dependent measures. For several reasons this procedure has not been widely adopted. Many investigators have been concerned about the suitability of the normal, equal variance assumptions. In the absence of positive evidence, investigators have tended to doubt the validity of these stringest assumptions. An explicit test of these assumptions with animal subjects (Colliver, 1973), assuming that different amplitude CRs represent different confidence levels, has indicated that the equal variance assumption is probably not valid for differential rabbit eyelid conditioning. According to classical TSD, if hit and false-alarm rates at different criterion levels are plotted on double-probability paper, the Gaussian assumption predicts a straight line function and the equal variance assumption predicts a unitary slope (Green & Swets, 1966, Chapter 3). Colliver’s data provided support for the Gaussian assumption, but the slope measurements were reliably greater than 1.0. It is possible to compute a special form of d’ for the unequal variance case if the ratio of the two variances can be estimated. Empirical procedures for these calculations have been detailed by Richards and Thornton (1970). However, the assumption of unequal variances leads to a separate problem, in that ,0 can no longer be computed since its function is nonmonotonic for these cases. An alternative method to surmount this problem has been provided by the development of nonparametric substitute measures for d’ (Pollack & Norman, 1964) and /3 (Hodos, 1970) f rom consideration of the characteristics of the ROC graph. Grier (1971) has developed computational formulas for the nonparametric sensitivity measure (A’) and for a modified response bias measure (B”). These nonparametric measures permit the use of TSD methodology when the investigator is not willing to accept the normal, equal variance assumptions, The nonparametric measures also have another empirical advantage in that, unlike d’ and /3, each can be calculated when the hit rate is 1.00 or the false-alarm rate is 0.0. This can readily be seen from the computational formulas:

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329

A, = (HIT-FA) + (HIT-FA)’ 4HIT (l-FA) B,, = (HIT-HIT2) - (FA-FA2), HIT-HIT2 + FA-FA2 where HIT is the hit rate and FA is the false-alarm rate. The benefits and limitations of these measures are discussed by Grier ( 1971). For the reasons indicated above, these nonparametric measures are usually preferable to d’ and p as dependent measures in data analysis. However, the B” measure does not avoid a major problem associated with TSD applications to discrimination learning. Suboski (1967) advocated the TSD methodology because it permitted a distinction between sensitivity and responsivity. Suboski’s idea of responsivity, however, is quite different from the aspects of performance indexed by /3 or B”. These indices measure the amount of “signalness” a subject requires on a given trial before he will respond. Essentially, it is a measure of perceptual bias rather than of general response bias. This can be shown rather easily by calculating values of p when sensitivity is low, i.e., en P(HIT) = P(FA), ,6 = 1.0, neutral bias. P(HIT) rP(FA). Wh However, a common sense notion of general responsiveness would normally reflect very different values for P( HIT) = P( FA) = .lO and P( HIT) = P( FA) = .90. The performance bias that exists in discrimination learning is generally thought to be independent of the special characteristics of the input signals (CS + and CS - ) and to be dependent only on the subjects’ basic level of responsivity. Since both ,6 and B” index perceptual rather than general responsivity, neither measure seems to be particularly suited to the analysis of discrimination learning data. A more useful criterion measure for discrimination learning can be derived from a special case of Lute’s (1959) threshold model of signal detection. In this case, the criterion measure represents a kind of guessing rate for the subject when he is uncertain about which input signal has been presented. As a guessing rate, Lute’s criterion measure more nearly approximates the notion of a general responsivity measure. A restricted form of Lute’s threshold model is presented here to demonstrate the application of a threshold model to the discrimination learning situation. Assume that CS+ and CS- produce discrete detection states in the organism of either veridical perception with probability (Y or uncertainty with probability l- (Y. At asymptote, if the organism is certain of a CS + event, a CR always occurs. If the organism is certain of a CS- event, a CR never occurs. If the organism is in the uncertain state, however, a CR occurs with probability g and no CR occurs with probability l-g. Recent neurophysiological evidence ( Hillyard, Squires,

330

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Bauer & Lindsey, 1971) provides support for threshold-like processes in human signal detection that are consistent with the postulates of this threshold model. The best estimates of the parameters a and g for this model can be shown to be LY= HIT - FA FA g = l-HIT + FA’ where HIT is the hit rate and FA is the false-alarm rate as before. Given index the postulates of this model, a can be identified as a sensitivity and g as a responsivity index. It is interesting that Q:equals the difference between hit and false-alarm rates, a measure that has been used for data analysis in differential conditioning for many years. The derivation of indices of sensitivity and responsivity from the restricted form of Lute’s (1959) threshold model provides dependent measures that are consistent with the notion of sensitivity and responsivity in discrimination learning as expressed by Suboski (1967). Both of these measures can be calculated for a hit rate of 1.0 or a false-alarm rate of 0.0. HOWever, the strict assumption of the model that only two sensory states (certainty and uncertainty) exist may not be acceptable to many investigators. Krantz (1969) has discussed the advantages and limitations of threshold theories of signal detection and provided arguments that question the validity of restricted forms of the general threshold model as employed in the present derivations of a and g. Another alternative is to derive empirical measures of sensitivity and responsivity from the ROC graph of hit and false-alarm rates. These measures should be defined consistent with Suboski’s notions of sensitivity and responsivity and should be calculable directly from hit rate and false-alarm rate. In addition, both indices should have determinate values when P( HIT) = 1.0 or P( FA) = 0.0. Two measures that fulfill these requirements are suggested in this report. The sensitivity measure is based on the assumption that neutral sensitivity is reflected by performance in which P( HIT) = P( FA), i.e., the positive diagonal of the ROC graph, and that the degree of sensitivity is proportional to the distance of the point in the ROC unit space above the positive diagonal. The responsivity measure is based on the assumption that neutral responsivity is reflected by performance in which P( HIT) = 1 - P( FA), i.e., the negative diagonal of the ROC graph, and that positive response bias is proportional to the distance of the point above the negative diagonal while negative response bias is proportional to the distance below the negative diagonal. Essentially, the present endeavor requires a transformation of the

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outcome space by rotating the P( HIT), P( FA) axes of the unit square to a new set of axes represented by the positive and negative diagonals. Unfortunately, the procedure for specifying a point in the unit square in terms of units on this new set of axes is ambiguous. Quite a few different procedures could be developed. One solution to this dilemma is to develop a procedure that reflects each point in the square upon the diagonals in such a manner that the point’s relative position above or below each diagonal can be assessed by measuring the distance from the center of the unit square to the point’s reflection on each diagonal. A procedure that is consistent with this approach follows. The procedure for defining these two indices is presented in Figs. 1 and 2. Specification of a hit rate and a false-alarm rate defines a unique point, T, in the unit square. To define a sensitivity index (SI), a straight line, AH, is drawn from (0, 0) through the point (HIT, FA) to the margin and a second straight line, CJ, is drawn from (1, 1) through (HIT, FA) to the margin as indicated in Fig. 1. The angle JTA is then bisected by the straight line, TQ. The sensitivity index (SI) is defined as the l/i times the distance along the negative diagonal from point Q to the midpoint of the unit square, E, where the diagonals intersect. The definition of the response bias measure follows the same basic pattern. A straight line, BK, is drawn from (1.0, 0.0) through the point (HIT, FA) to the margin and a second straight line, DM, is drawn from (0.0, 1.0) through the point (HIT, FA) to the margin as indicated in Fig. 2. The angle DTK is bisected by the straight line, TZ, The responsivity index (RI) is defined as the fi times the distance along the positive diagonal from point Z to point E.

o.oA‘j 0.0

1.0

f’(FAl

FIG.

1. Definition

of SI measure

from

ROC

graph.

332

FREY

AND

COLLIVER

I FA

P(FAl FIG. 2. Definition

of RI measure from ROC graph.

The graphical method used for defining these indices is an imprecise and cumbersome procedure for determining SI and RI for individual subjects. Fortunately, the geometry of the unit square permits the expression of these measures in terms of hit rate (HIT) and falsealarm ( FA) . HIT - FA ‘I = B(HIT + FA) - (HIT + FA)” HIT + FA - 1 R1 = 1 - (HIT - FA)” The operating characteristics for SI and RI are presented in Fig. 3. The Iso-sensitivity contours for SI are similar to those for d’ and A’. The Iso-bias contours for RI, however, are quite different from those for /3 and B”. Examination of the four sensitivity measures discussed in this report indicates only small differences in their operating characteristics as hit and false-alarm rates are varied. The four response bias measures share less similar operating characteristics. The measures /3 and B” have neutral bias values when P( HIT) = 1 - P( FA) and also when P( HIT) = P( FA), The other two measures, g and RI, have neutral bias values only when P( HIT) = 1 - P( FA). These differences are related to the fact that p and B” are perceptual criterion measures (i.e., the amount of “signalness” in the input required by the subject before he will respond), while g and RI are general responsivity type measures. Since there exist no generally acceptable criteria that could be employed to evaluate the validity of these several measures, an attempt was

SENSITIVITY

0

0

AND

/SO-BIAS ,III!IIII .2 A

333

RESPONSIVITY

CONTOURS

.6

.a

WA) FIG.

3. Iso-sensitivity

contours for the SI index and Iso-bias contours for the RI

index.

made to examine their empirical utility. The data from three differential conditioning experiments that involved the manipulation of variables known to affect sensitivity and/or responsivity were submitted to a routine analysis of variance using each of these dependent measures. The rationale for the evaluation procedure is based on the assumption that appropriately chosen dependent measures would minimize within-group (error) variance and would thereby maximize the relevant F ratios. In a differential rabbit eyelid conditioning experiment, Colliver ( 1970) manipulated the similarity of CS + and CS- and the ratio of CS + to CS- trials in a factorial between-groups design. Figure 4 presents an ROC graph of the asymptotic data for the 72 Dutch rabbits in this study. The dissimilar cues groups had a lOOO-Hz tone as CS + and either a 900-Hz or 700-Hz tone as CS-. The similar cues groups had a lOOO-Hz tone as CS+ and a 990-Hz tone as CS-, The ratio of CS+ to CS - trials in each session was either 2: 1, 1: 1, or 1:2 with 84 trials per sessionat a 40-set ITI. The CS-US interval was 0.5 sec. The ROC plot of asymptotic response level to CS+ and CS- pro-

334

FIG. similarity

FREY

4. Differential and CS +/CS

AND

eyelid conditioning - ratio.

COLLIVER

in

Dutch

rabbits

as a function

of

cue

vides an excellent summary of the rabbit’s differential conditioning performance. The figure indicates that the experimental manipulations produced effects that were generally in accord with preexperimental expectations. The dissimilar cues groups showed greater differential responding (i.e., greater sensitivity) than the similar cues groups. The groups having two CS+ trials for every CS - trial showed a higher level of general responsiveness than groups having one CS + trial for every two CS - trials. The analysis of these data in terms of explicit measures of sensitivity and response bias is presented in Table 1. All four sensitivity measures, d’, A’, a, and SI, indicated a very reliable effect of cue similarity on sensitivity. A’ produced the largest F ratio and d’ produced the smallest. The A’ and LYmeasures also suggested a marginal effect of CS+/CSratio on sensitivity. The four response bias measures showed less consistency. The general responsivity measures, g and RI, indicated very reliable effects of both cue similarity and ratio on response bias. The perceptual bias measures, ,6 and B”, indicated marginal effects of cue similarity on response bias but no effect of the ratio manipulation. The results of using SI and RI to analyze the Colliver (1970) experiment can be summarized by the statement that an increase in cue similarity produced a decrease in differential responding and an increase in the general level of responsiveness, whereas an increase in the ratio of CS + to CS - trials produced no effect on differential responding but increased the rabbit’s general level of responsiveness. This summary of

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TABLE 1 Effect of Cue Similarity and CS+ /CS - Ratio on Sensitivity and Response Bias Measures in Differential Rabbit Eyelid Conditioning Group means Similar cues 2:l

Dissimilar

1:l

1:2

d’ A’

.20 .56

.55 .66

.24 .58

:I P B” g RI

.04 .09 .83 - .13 .86 .69

.16 .21 .73 -.21 .80 .52

.07 .lO .85 - .ll .66 .29

cues

2:l

1:l

1:2

1.38 .78 .42 .46 .82 - .19 .69 .32

1.69 .84 .52 .56 .96 - .14 .62 .19

2.03 .89 .64 .65 1.15 -.03 .52 .04

F Ratios Sensitivity

Source

Cue

d’

A’

25.02**

40.26**

2.10 1.06

3.54* 1.59

similarity Ratio Interaction

Response bias CY

SI

B

B”

g

RI

34.68**

33.87**

4.81*

3..50*

9.05**

12.12**

3.46* 1.54

2.74 1.33

1.06 1.03

1.50 1.15

6.28** 1.42

7.97** 1.42

*p < .05. **p < .Ol.

these data provides an insight into the animal’s discrimination performance, which a conventional analysis would not disclose. A second experiment germane to the present topic involved a betweengroups factorial manipulation of cue similarity and B-US interval in differential rabbit eyelid conditioning ( Frey, 1969). The asymptotic performance of 32 albino rabbits is presented in Fig. 5 in ROC form. The similar cues group had a lOOO-Hz tone as CS + and an 800-Hz tone as CS -. The dissimilar cues groups had a lOOO-Hz tone as CS -t and a 400-Hz tone as CS-. The CS-US intervals for different groups were either 400, 600, or 800 msec. The intertrial interval was 30 set with 240 trials per session. The graph suggests that an increase in cue similarity produces poorer differential responding and an increase in general responsiveness as was observed in the previous study ( Colliver, 1970) with Dutch rabbits. The ROC plot also suggests that increasing the CS-US interval enhances

336

FREY

-DISSIMILAR

AND

COLLIVER

CUES SIMILAR

FIG. 5. Differential ilarity

and

B-US

eyelid interval.

conditioning

CUES

in albino

rabbits

as a function

of cue sim-

differential performance when the cues are similar but not when they are dissimilar. These observations were verified when these data were analyzed in terms of sensitivity and response bias measures as indicated in Table 2. All four sensitivity measures indicate a very reliable main effect of cue similarity and an interaction between cue similarity and the CS-US interval, With the exception of p, all the response bias measures also indicated a very reliable main effect of cue similarity on response bias, although g and RI appeared to be more powerful in this respect than B”. According to TSD, the cue similarity manipulation should, ‘n principle, affect sensitivity but not response bias. Both of the previous studies indicated that responsivity is higher when CS + and CS - are similar. A comparison of the two previous studies indicates a large difference in the general level of responsiveness in the differential conditioning situation between Colliver’s (1970) Dutch rabbits and Frey’s (1969) New Zealand white (albino) rabbits. A third study was undertaken to assessdifferences in differential responding of the two rabbit strains (Frey & Sheldon, 1970). The subjects, 16 American Dutch rabbits and 16 New Zealand white (albino) rabbits, were placed on either a 0- or 18-hr daily food deprivation schedule. The CSs were 600- and 1500-Hz tones and the CS-US interval was 0.55 sec. The intertrial interval was 90 set with 40 trials per daily session, Figure 6 presents the asymptotic performance levels for these rabbits in ROC form. The ROC graph demonstrates a large difference in responsivity be-

SENSITIVITY

Effect

AND

TABLE 2 and CS-US Interval on Measures of Sensitivity in Differential Rabbit. Eyelid Condihoning

of Cue Simi1arit.y Response Bias

Group Similar 400 d’ A’ a SI B B” g RI

Dissimilar

600 .54 .66 .20 .31 .89

.I1

-.06

.70 .36

.64 .25

and

means

cues

.42 .64 .14 .17 .s5 -

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RESPONSIVITY

cues

800

400

600

800

1.10 .78 .40 .41 .92 -.08 .58 .12

2.13

2.46 .9l .68 .72 7.32 .52 .23 - .32

1.78 .87 .59 .61 1.91 .26 .a4 - .20

.90 .66 .68 2.15 .I1

.45 - .04 F ratios

Sensitivity Source Cue similarit’y cs-us interval Interact,ion

d 70.48**

A’

Response 01

SI

P

B”

bias g

RI

56.30**

63.68**

69.93**

3.30

12.16**

17.15**

16.65**

.62

1.76

1.21

1.02

1.22

1.32

1.40

1.77

5.05*

4.26*

4.21*

4.50*

1.22

1.26

.65

.24

* p < .05. **p < .Ol.

tween the two strains, with the Dutch animals more responsive than the albinos as was anticipated from the results of the two previous experiments. However, the effects of food deprivation in this shock-motivated conchtrvnin~ task were unexpected. Food deprivation appeared to make the Dutch animals more sensitive, but the albinos reacted to this manipulation by becoming less responsive. The analysis of these data by the explicit measures of sensitivity and response bias is presented in Table 3. All four sensitivity measures indicated that the albino rabbits showed better differential responding than the Dutch. All except (Y also indicated that food deprivation enhanced differential responding. All the response bias measures with the exception of ,8 indicated that the Dutch rabbits were more responsive than the albinos and that there was a reliable strain by deprivation interaction.

338

FREY

.60

AND

COLLIVER

-

i=

A0

FIG. 6. Differential eyelid of hours of food deprivation.

Effect

conditioning

in Dutch

TABLE on Measures Conditioning

of Food Deprivation Differential Eyelid

Group

and

ii1 B B” :I

albino

rabbits

as a function

3 of Sensitivity and Response in Dutch and Albino Rabbits

Bias

in

means

Albino

d’ A’

1 ‘0

Dutch

0

18

0

18

1.72 .84 .48 .57 .96 - .29 .69 .26

2.19 .87 .58 .64 7.37 .39 .31 --.20

.83 .69 .24 .29 .72 - .21 .77 .47

1.77 .84 .41 .58 .29 --.65 .88 .58

F ratios Sensitivity

Response

Source

d’

A’

Q

SI

P

Strain Deprivation Interaction

5.19* 4.48* 0.58

6.73* 5.64* 2.57

4.86* 2.14 0.15

5.08* 5.62* 2.08

3.55 2.36 3.10

*p < .05. ** p < .Ol.

B” lO.OO** .63 13.71**

bias g

11.84** 1.98 6.64*

RI 13.20** 1.64 4.43*

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339

The relative power of the several dependent measures in detecting the effects of independent variable manipulation in these three experiments provides information for selecting useful measures of sensitivity and responsivity. Several conclusions seem to be justified on the basis of these analyses, The sensitivity measures, d’, A’, (Y, and SI, all seem to have relatively similar power in detecting the degree of differential responding of different groups. In the Colliver (1970) study, A’ and a! were slightly more powerful than d’ or SI, but in the Frey (1969) study, d’ and SI appeared to be slightly more powerful than A’ or LY. In the Frey and Sheldon (1970) study, d’, A’, and SI seemed to show more power than (Y. Although no measure appeared to be dramatically superior or inferior to any other, (Y seemed to be the least impressive of the group. The implications of these analyses in terms of the relative power of the responsivity measures is more obvious. The classical signal detection measure, ,8, was uniformly inferior to the other three. It failed to indicate response bias effects in each of the three experiments, which were picked up by other response bias measures. This poor performance is probably related to p’s role as a perceptual bias measure and to its skewed sampling distribution such that it fails to meet analysis of variance assumptions. Although B” appeared to be more powerful than ,0 in picking up effects, it showed less power than either g or RI. The two general responsivity measures, g and RI, appeared to be the most useful response bias measures for the differential conditioning data analyzed in the present report. Two points seem to merit emphasis. The analysis of the three differential conditioning studies in this report provides ample evidence to support both the validity and the usefulness of employing sensitivity and responsivity measures. The data in the report provide strong corroborative evidence for Suboski’s (1967) contention that the distinction between discrimination and response bias is necessary and useful. The second conclusion from this differential conditioning data is that response bias measures which index general responsivity (e.g., g or RI) seem to be more valuable in this situation than perceptual bias measures (e.g., /? or B”). Although the d’ and A’ measures seem to be as powerful as CYor SI, the lack of power of the ,8 and B” measures in this situation indicates that neither d’ and ,Q nor A’ and B” are the measures of choice for the differential conditioning situation. Another factor that is germane to this decision is the acceptability of the theoretical assumptions underlying the derivation of the several measures. The classical signal detection measures, d’ and p, are based on relatively strigent assumptions that are seldom satisfied (Green & Swets, 1966, Chapter 3). The threshold theory measures, cy and g, are based on

340

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COLLIVEX

the assumption that only two sensory states are possible. Krantz (1969) has argued cogently against this strong assumption. The remaining two sets of measures, A’ and B” and ST and RI, are based on less restrictive assumptions. A third consideration that is relevant to a choice among these measures is the practical matter of applying each of them to real data. Although the data sets analyzed in the present report were selected to avoid empirical hit rates of unity and false-alarm rates of zero, it is not unusual in differential conditioning studies with a small number of observations per subject to have subjects with one of these outcomes. The values of d and ,G are indeterminate for either of these outcomes. The value of g is constant for all hit rates when the false-alarm rate is 0.0. Thus all three of these measures are empirically less useful than the others. In consideration of these several factors, a selection of one set of measures for discrimination learning seems possible. The use of d’ and p seems inadvisable on several counts; lack of power of p, difficulty in satisfying the underlying assumptions for both measures, and the difficulty with hit rates of 1.0 or false-alarm rates of 0.0 for both measures. The choice of A’ and B” seems to be inadvisable primarily on the grounds of the lack of power of the B” measure in the discrimination learning situation. A perceptual bias measure seems to be less useful than the general responsivity measures for this situation. The selection of CYand g also seems inadvisable because of the restricted threshold model on which they are based and because of the computational problems with g when the false alarm rate is 0.0. The SI and RI measures, in contrast, seem to be quite adequate indices of sensitivity and responsivity without the common difficulties associated with strigent underlying assumptions or calculation difficulties. Their mode of derivation based on the geometry of the unit square gives them a relatively neutral stance in the present controversy concerning the relative merits of classical TSD and the threshold detection models. Although the ultimate determination of appropriate dependent measures for discrimination learning data will probably depend on the development of an adequate theoretical model for this situation, the present empirical approach appears to be useful as an interim solution. By using a theoretical model to develop dependent measures, one can rationally relate these measures (i.e., the parameters of the model) to the salient aspects of the experimental situation. Historical evidence indicates that this type of approach will utlimately be more productive than the present empirical approach. However, the development of a valid theoretical model appears to be a challenging endeavor and an acceptable theoretical solution may not be available for a number of years.

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It is possible that the present interim approach might also be applied to areas other than discrimination learning. Several investigators (e.g., Lockhart & Murdock, 1970; Banks, 1970) have recently examined TSD applications to recall and recognition memory data. The operating characteristics of the present RI measure seem to be more appropriate for their data analysis than the traditional TSD measures since the response bias in these situations probably reflects guessing bias more than perceptual bias. It may be worthwhile to investigate the potential utility of the SI and RI measures in the retention paradigm. REFERENCES BANKS, W. P. Signal detection theory and human memory. Psychological Bulletin, 1970, 74, 81-99. COLLIVER, J. A. Signal detection analysis of differential rabbit eyelid conditioning as a function of cue separation and relative frequency of cue presentation. Unpublished doctoral dissertation, Northwestern University, 1970. COLLIVER, J. A. “Confidence rating” analysis on response amplitude scores of cIassicaI discrimination conditioning data. Psychological Reports, 1973, 32, 79-84. DONALDSON, W., & GLATHE, H. Signal detection analysis of recall and recognition memory. Canadian Journal of Psychology, 1970, 24, 42-56. EGAN, J. P., & CLARKE, F. R. Psychophysics and signal detection. In J. B. Sidowski (Ed.), Experimental Methods and lnstmcmentation in Psychology. New York: McGraw-Hill, 1966. Pp. 211-246. FREY, P. W. Differential rabbit eyelid conditioning as a function of age, interstimulus interval, and cue similarity. Journul of Experimental Psychology, 1969, 81, 326333. FREY, P. W., & SHELDON, DEBRA R. Effect of food deprivation on differential eyelid conditioning in New Zealand white and American Dutch rabbits. Psychonomic Science, 1970, 20, 23-25. GREEN, D. M., & SWETS, J. A. Signal Detection Theory and Psychophysics. New York: Wiley, 1966. GRIER, J. B. Nonparametric indexes for sensitivity and bias: Computing formulas. Psychological Bulletin, 1971, 75, 424429. HILLYARD, S. A., SQUIFW, K. C., BAUER, J. W., & LINDSAY, P. H. Evoked potential correlates of auditory signal detection. Science, 1971, 172, 1357-1360. Hones, W. Non-parametric index of response bias for use in detection and rccognition experiments. Psychological Bulktin, 1970, 74, 351354. KRANTZ, D. H. Threshold theories of signal detection. Psych&gical Reoicw, 1969, 76, 308-334. LOCKHART, R. S., & MURDOCK, B. B., JR. Memory and theory of signal detection. Psychological Bulletin, 1970, 74, 100-109. LUCE, R. D. Indiuidual Choice Behavior. New York: Wiley, 1959. MURDOCK, B. B., JR. Signal detection theory and short term memory. ~oumcl of Experimental Psychology, 1965, 70, 433447. POLLACK, R., & NORMAN, D. A. A non-parametric analysis of recognition experiments. Psychonomic Science, 1964, 1, 125-126. RICHARDS, B. L., & THORNTON, C. L. Quantitative methods of calculating the d of

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signal detection theory. Educational and Psychological Measurement, 1970, 30, 855-859. RILLING, M., & MCDIARMID, C. Signal detection in fixed-ratio schedules. Science, 1965, 148, 526-527. SUBOSKI, M. D. The analysis of classical discrimination conditioning experiments. Psychological Bulletin, 1967, 68, 235-242. (Received

May

19,

1972)