Caffeine and Cognitive Performance: The Nonlinear Yerkes–Dodson Law

Ca�eine and Cognitive Performance: The NonlinearYerkes±Dodson Law

PAUL ANDREW WATTERS1�, FRANCES MARTIN2 and ZOLTAN SCHRETER2

1Physiological Laboratory, University of Cambridge, UK2Department of Psychology, University of Tasmania, Australia

This study presents a test of the Yerkes±Dodson Law (YDL; Yerkes and Dodson, 1908), which is understood topredict a negative quadratic relationship between arousal and performance (ìnverted-U' hypothesis), and a lowerlevel of arousal for optimal performance on more di�cult tasks than easier tasks (`task di�culty' hypothesis). Anumber of recent studies (e.g. Neiss, 1988) have questioned the validity of the YDL on several grounds: the confusionof theory and model; observed linear arousal±performance relationships; non-speci®c de®nitions of arousal; andpoor experimental design. A single-blind modi®ed version of Anderson's (1994) within-subjects study (N � 10) wasperformed, utilizing graded cortical arousal manipulations of ca�eine (100 mg cumulative dosages to a maximum of600 mg), and four tests of basic cognitive ability in the procedural alphanumerical domain (with counterbalancing ofdrug/placebo session and ordering of presentations of tasks). The ìnverted-U' hypothesis was supported in three outof four experimental conditions (easy and di�cult numerical, and di�cult alphabetical tasks; p < 0�05). No supportwas found for the task di�culty hypothesis. The results are discussed in terms of the emergence of nonlinearity inneural±cognitive interactions as a fundamental quality of drug±behaviour interactions. # 1997 by John Wiley &Sons, Ltd.

Hum. Psychopharmacol. Clin. Exp. 12: 249±257, 1997.No. of Figures: 2. No. of Tables: 3. No. of Refs: 34.

KEY WORDS Ð Yerkes±Dodson law; ca�eine; cortical arousal

INTRODUCTION

The signi®cance of nonlinearity in neural andcognitive function has received increasing attentionin recent years, as reliance on the general linearmodel as the basis for determining structuralrelationships between cognitive and behaviouralvariables has decreased. Whether at the basic levelof neural networks models of learning, where thesigmoidal activation of theoretical neurones under-lie the success of particular learning algorithms(Rumelhart and McClelland, 1986), or at thecognitive level, where it has been shown thathuman participants have the ability to predictchaotic sequences of numbers with a much higher

success rate than random sequences (Smithson,1996), nonlinearity appears to be an importantfunctional link between brain and behaviour. Oneof the oldest psychological laws, the Yerkes±Dodson Law (YDL; Yerkes and Dodson, 1908),has generated many decades of research, and in asense, its current status re¯ects broader divisionswithin psychology itself. The YDL is generallyinterpreted as predicting a negative quadraticrelationship between arousal and performance(the ìnverted-U' hypothesis), and that the optimallevel of arousal for a more di�cult task will belower than for an easier task (the `task di�culty'hypothesis).

Although Yerkes and Dodson (1908) originallydemonstrated these relationships empirically in thecontext of a learning experiment, the use of anonlinear arousal construct as an explanatoryvariable for human performance is a theoreticallyattractive notion for examining drug±behaviourrelationships. Indeed, the continuing popularityof the YDL can be attributed largely to its

�Correspondence to: Paul Watters, Physiological Laboratory,University of Cambridge, Downing Street, Cambridge CB23EG, UK. E-mail: [email protected].

Contract grant sponsor: CVCP/ORS,Contract grant sponsor: Cambridge Commonwealth Trust.Contract grant sponsor: Michael Foster Trust.Contract grant sponsor: Pembroke±Australia Society.

CCC 0885±6222/97/030249±09$17.50# 1997 by John Wiley & Sons, Ltd.

HUMAN PSYCHOPHARMACOLOGY, VOL. 12, 249±257 (1997)

employment in the concurrent development of the`general arousal' construct (e.g. Du�y, 1957;Malmo, 1957; Stennett, 1957) and its physiologicalexplanation in the reticular activating hypothesis(Morruzzi and Magoun, 1949; Lindsley, 1957).The YDL, expressed as an arousal±performancerelationship, has strongly in¯uenced the develop-ment of theories of attention (Easterbrook, 1959),personality (Eysenck, 1967), and cognition (Du�y,1972).

It is this interdependence of general relationshipand explanation which has given rise to some of thestrongest criticisms of the YDL in recent years,particularly since critics (e.g. Winton, 1987) havequestioned the basis for the use of a general arousalconstruct in an era when there is a greater know-ledge and appreciation of the cortical and physio-logical mechanisms underlying the complexinterrelationships between arousal and behaviour.Indeed, many modern studies investigating theYDL in the context of a particular theory ®ndsupport for aspects of the theory, but not for theLaw. For example, Humphreys and Revelle (1984)proposed an explanation of the YDL, in terms ofarousal-mediated attentional resource allocation,which was partially supported by data fromMatthews et al. (1990), but only to the extent thatarousal was linearly correlated with resourceutilization. Matthews et al. failed to ®nd thecharacteristic decrease in performance at highlevels of arousal. One problem with these recentstudies is that tests of the general relationshipspredicted by the YDL are confounded with tests ofparticular theories of cognition or behaviour, orwith explanations of the relationships in terms ofthose theories. This has led to a circular situation inwhich neither the YDL nor these theories can beindependently veri®ed or examined.

In addition, although many studies havereported a linear relationship between arousaland performance, there are critical questions inevaluating the experimental evidence, concerningthe relative levels, range, and number of arousalmanipulations performed, which must be takeninto account. For instance, at least three arousalmanipulations are required to test for the presenceof the ìnverted-U' relationship, but in an explora-tory study, many more would be required to ensuredata su�ciency requirements. It is not surprising,then, that many studies (e.g. Corteen, 1967;Bergstrom, 1970; Gould et al., 1987) have foundpositive linear relationships between perform-ance and arousal Ð it may be that their arousal

manipulations were simply not strong enough toelicit a decrease in performance. For example,Loke (1993) used a high ca�eine dosage (600 mg)which successfully elicited a decrease in cognitiveperformance.

A related issue concerns creating a probabilisticbias against ®nding the negative quadratic relation-ship by increasing the number of arousal manip-ulations in YDL studies (Revelle and Anderson,1992). The ®nding of a negative quadratic functionin studies which use only three arousal manipula-tions results in the observed linearity or nonlinear-ity being dependent on a single active degree offreedom. Therefore, increasing the number ofmanipulations results in an increased probabilityof failing to reject the null hypothesis of a lineararousal±performance. In addition, it is desirable toutilize the minimum scale of arousal manipulationpossible to ensure continuity of any observed e�ect,particularly where pharmacologically active sub-stances are utilized. By increasing the number ofactive degrees of freedom through many arousalmanipulations, and by observing the nonlinearityof arousal manipulations at a ®ner scale (in thiscase, a quadratic function), more reliable changesin performance as a function of arousal statesshould be observable, and should provide astatistically strong test of any observed e�ect.

On the basis of the evidence presented here, itcould be argued that the major confounding factorin YDL research is the de®nition of the explanatoryvariable, arousal, and the failure to explicitly de®neits mechanisms of action, and how it is manipu-lated in research designs. This arises from a basicproblem of de®ning arousal in psychophysiologicalresearch particularly with the decline of the generalarousal construct. The conceptualization ofarousal as an hypothetical construct that re¯ectsnonspeci®c physiological activation (e.g. Ander-son, 1994) has been criticized as biologicallyimplausible (Neiss, 1988). For example, the mea-sures of autonomic arousal utilized in tests of theYDL, such as heart rate and the Galvanic skinresponse, do not reliability correlate with measuresof cortical arousal, such as increased b activity(13±30 Hz) in the electroencephalogram (Stern-bach, 1960). This criticism re¯ects a weakness instudies where the authors appear to be confusedabout their arousal manipulation, yet rely on self-report measures of arousal which lack externalvalidity. For example, some studies do not use anarousal manipulation, employing self-reportmeasures to classify participants into arousal

# 1997 by John Wiley & Sons, Ltd. HUMAN PSYCHOPHARMACOLOGY, VOL. 12, 249±257 (1997)

250 P. A. WATTERS ET AL.

categories (e.g. Gould et al., 1987). This is afundamental error in experimental design whichinvolves inferential testing, since there is no way toestablish causal relationships if no manipulation isconducted. Finally, in studies which do conductarousal manipulations (e.g. Loke, 1990, 1993),there is failure to de®ne a direct measure of arousalwhich is functionally related to the manipulationutilized.

Recent tests of the YDL have utilized di�er-ential ca�eine (1,3,7-trimethylxanthine) doses asmonotonically-increasing arousal manipulations toprovide support for the inverted-U hypothesis(Revelle et al., 1976; Loke, 1990, 1993; Anderson,1994). Ca�eine is an alkaloid which is found inco�ee and other stimulant beverages. The humanresponse to its pharmacological action is nonadap-tive, that is, habituation to its stimulant e�ects doesnot generally occur (Graham, 1978). In-vivo humanstudies indicate that small doses (100±200 mg)appear to enhance cognitive performance, but thathigher levels may reduce performance below asubject's normal baseline (Svennson et al., 1980;Pons et al., 1988; Foreman et al., 1989). Ca�einemodulates cortical arousal through adenosineantagonism, by blocking stimulation of cAMPformation (Daly et al., 1981; Boulenger et al.,1986). Since adenosine produces e�ects opposite tothose of ca�eine, including downregulation of therate of catecholamine synthesis (Marangos et al.,1984), high levels of ca�eine result in a highly-aroused state that leads to the generally observedcognitive performance de®cits.

Since ca�eine has a long half-life in vivo,cumulative ca�eine doses at regular intervalsprovide one means of manipulating the explana-tory variable (arousal) in tests of the YDL in termsof a cortical mechanism. Anderson (1994) success-fully used this manipulation in a within-subjectsdesign, using ®ve graded ca�eine dosages, suggest-ing strong support for the ìnverted-U' hypothesisof the YDL, and in contrast to the ®nding ofMatthews et al. (1990) of a linear arousal±perform-ance relationship. Anderson's results emphasizethe importance of running participants in acounterbalanced, repeated-measures design, whereparticipants perform the same tasks in both controland drug conditions. Loke (1993) had previouslyestablished the upper limit of 600 mg of ca�eine asa reasonable dosage limit for observing its detri-mental e�ects on cognitive performance. Whilstthese studies have contributed to the validity of theYDL, a number of problems in these studies have

prompted critics (e.g. De�enbacher, 1994) toquestion the utility of further YDL research.Again, these recent studies have unfortunatelyconfounded tests of particular theories andexplanations of the inverted-U hypothesis of theYDL with tests of the general relationship.Anderson, for example, attempts to provide sup-port for the Eysenck model of diurnal-arousalrhythms interacting with personality type tomodulate cognitive performance. Loke primarilyaims to integrate an automaticity account ofcognitive performance with the predictions of theYDL, without ®rst establishing the validity ofeither the YDL or the theory in question Ð inparticular, presuming that estimating the frequencyof a particular word in a list after presentation ismore automatic than a free recall task. Although itis desirable to be able to explain the YDL in termsof cognitive processes and personality factors, andto use this as a basis for validating particulartheories of human behaviour, criticism against theYDL ®rstly needs to be addressed.

A further di�culty with previous studies is thatthe tasks used in these studies are those on whichperformance can be improved quite substantiallyby small amounts of practice. This is particularly aproblem in terms of the task di�culty hypothesis.For example, Anderson (1994) required all partici-pants to complete the easier task (letter cancella-tion) after the di�cult task (GRE verbal abilitytest), with no counterbalancing to eliminate ordere�ects. The letter cancellation task, which isessentially a perceptual pattern-matching task,di�ers substantially from the GRE verbal-scaletask not only in di�culty, but in the fact that it ispossibly testing two very di�erent abilities. Indeed,the GRE verbal task consists of three di�erentkinds of abilities, some of which draw on declara-tive knowledge (e.g. antonyms) rather than proced-ural knowledge (as tested in the letter cancellationtask), so there is possibly a lack of internal validityin the design. A potential solution to the problemexists in using simple tasks where practice e�ectscan be accounted for in terms of a monotonically-increasing component in the nonlinear regressionmodel, such that performance is a function of thearousal manipulation (negative quadratic), and ofpractice (linear).

This study attempted to replicate the ®ndings ofAnderson (1994), by testing the ìnverted-U' andtask di�culty hypotheses of the YDL in the contextof the methodological and theoretical issues out-lined above. Speci®cally, two simple procedural


CAFFEINE AND COGNITIVE PERFORMANCE 251

cognitive tasks, based around counting in alpha-numeric sequences were employed. No furtherinterpretation is made regarding the theoreticalsigni®cance of these tasks (unlike the tasks utilizedin previous studies to test particular theories), otherthan that they are as basic a test of cognitiveperformance that is possible, and that they testmultiple types of cognitive activity, that is, bothalphabetical and numerical. In addition, two levelsof task di�culty for each task were used, and weregraded in their di�culty, rather than being distinct,incomparable tasks. It was assumed that partici-pants would not greatly increase their countingabilities over the course of the experiment, althoughthe possibility of a small practice e�ect was antici-pated by the use of a combined linear and quadraticregression model. As the explanatory variable,cortical arousal was operationalized through sevengraded dosages of ca�eine (100 mg cumulativeincrements to a maximum of 600 mg), correspond-ing to twice the minimum number of manipulationsrequired for performing a quadratic ®t to the data.Participants performed all tasks under all condi-tions, thereby acting as their own controls. This, inconjunction with the large number of explanatoryvariable manipulations, implied that the power ofthe experiment would be high.

MATERIALS AND METHODS

Participants

Participants were 10 undergraduate Psychologystudents from the University of Tasmania, forwhom participation ful®lled a course requirement.Participants were screened for a number of riskfactors associated with the consumption ofca�eine, and were excluded if they had a historyof coronary heart disease, migraine headaches,psychoactive medication or were pregnant. Partici-pants were also excluded if they did not regularlyconsume ca�eine (at least one cup of co�ee or teaper day), and were free to withdraw from theexperiment at any time without penalty. Approvalfor the study was granted by the University ofTasmania Scienti®c Ethics Committee.

Design

The experiment had three within-subjects explana-tory variables: task type (counting and alpha-betical exercises with two levels of di�culty),treatment (drug or placebo), and session (eight

levels). The response variable was accuracy ofresponse in each task. Since the e�cacy of the taskdi�culty manipulation can only be determinedpost hoc, each task was initially treated in analysiswithout reference to di�culty.

Apparatus, instrumentation and materials

Ca�eine was administered in the form of `No Doze'tablets, containing 100 mg of ca�eine. Participantsused 50 ml of orange juice per tablet to assistdigestion. Vitamin B-complex tablets (25 mg) wereused as the placebo, because of their similarity inshape, colour and size to the ca�eine tablets.Ca�eine in tablet form is rapidly absorbed, andquickly crosses the blood±brain barrier (McCallet al., 1982). Trials and cumulative doses weretherefore spaced by 15-min intervals.

Procedure

Participants attended for two sessions. Uponarrival at their ®rst session, participants werescreened for the medical conditions outlined above,and signed a consent form which outlined the risksassociated with consumption of the maximumdosage of ca�eine (600 mg), and its equivalent incups of strongly brewed co�ee (three cups). Orderof drug and placebo sessions was counterbalanced,as was the order of presentation of the four tasks,and a single-blind procedure used to minimizeexpectancy e�ects of consuming large doses ofca�eine.

Each session consisted of eight trials of the fourtasks, with each task separated by a 10-s break(subjects were verbally instructed to relax after eachtask). The èasy numerical' (ENT) task requiredparticipants to count forward from an initial valueby a constant increment (e.g. `count forward bytwos from two'). The `di�cult numerical' (DNT)task required participants to count backward froman initial value by a constant increment (e.g. `countbackward from seven hundred by sevens'). Theèasy alphabetical' task (EAT) required partici-pants to generate an alphabetical sequence froman initial letter, with a particular alphabeticalincrement (e.g. `starting from h, go forward in thealphabet by two letters'). The `di�cult alpha-betical' (DAT) task required participants togenerate an alphabetical sequence from an initialletter, with a particular alphabetical decrement(e.g. `starting from z, go backward in the alphabetby two letters').



Alphabetical and numerical initial values weredi�erent for each trial, whilst the increments anddecrements were kept constant for each task. Eachtask lasted for 10 s, with participants instructed tovocalize their response through an intercom to theexperimenter. After each of the ®rst six trials werecompleted, participants were required to swallowa ca�eine tablet (drug condition) or vitaminB-complex tablet (placebo condition). After the®rst trial, subsequent trials were separated by15-min intervals from the time of the ca�eineingestion. After the second testing session wasconducted, participants were debriefed about thepurpose of the experiment, and were informed inwhich sessions they had received ca�eine.

RESULTS

Data was analysed as a function of session number(in the drug condition, corresponding to ca�einelevel), to test the ®rst statement of the YDL. Nocases had missing data. Figures 1 and 2 display themean performance measures (number of correctresponses) for the drug and placebo conditionsrespectively (Table 1 contains means and standarddeviations for performance for both conditions).

Regression equations of the form

F � b0 � b1G � b2G2 �1�

were ®tted using the SPSS curve-®tting program,where F represents level of performance, and Grepresents the session. Three tasks, ENT, DNRand DAT, had statistically signi®cant model ®ts forR: for ENT, F�2;77� � 3�21, p < 0�05; for DNT,F�2;77� � 3�59, p < 0�05; and for DAT, F�2;77� �3�83, p < 0�05 (Table 2).

EAT approached signi®cance, with F�2;77� �453�08, p � 0�052. Each regression model ®tted inthe drug condition had a signi®cantly negative G2,indicating the presence of an inverted-U relation-ship: for ENT, G2 � ÿ0�26, t�39� � ÿ2�50,p < 0�05; for DNT, G2 � ÿ0�83, t�39� � ÿ2�49,p < 0�01; for EAT G2 � ÿ0�11, t�39� � ÿ2�45,p < 0�05; for DAT, G2 � ÿ0�11, t�39� � ÿ2�67,p < 0�01 (Table 3).

No signi®cant inverted-U relationships werefound for the placebo condition, although ENT,HNT, and DAT, had statistically signi®cantmodel ®ts for R (Table 2), with neither thequadratic nor linear component alone beingsu�cient to reach statistical signi®cance as indi-vidual components (Table 3). The optimal level ofca�eine for performance in both conditions andin all levels of task di�culty occurred after theadministration of 400 mg of ca�eine (session 5),providing no support for the task di�cultyhypothesis.

Figure 1. Graph of mean performance data (number of correct responses) as afunction of sessions for the drug condition, for the ENT (èasy numerical'), DNT(`di�cult numerical'), EAT (èasy alphabetical') and DAT (`di�cult alphabetical')tasks



DISCUSSION

The inverted-U hypothesis of the YDL wassupported by signi®cantly negative quadratic com-ponents in regression models for ENT, DNTand DAT, where cognitive performance was theresponse variable, and the ca�eine dosage was the

explanatory variable. Every model in both theplacebo and drug conditions, except EAT, con-tained a signi®cant linear increase in performanceacross conditions, indicating a practice e�ect.It should be noted that while the quadraticcomponent of model ®ts for ENT, DNT, andDAT reached statistical signi®cance, the predictor

Figure 2. Graph of mean performance data (number of correct responses) as afunction of session for the placebo condition, for the ENT (èasy numerical'), DNT(`di�cult numerical'), EAT (èasy alphabetical') and DAT (`di�cult alphabetical') tasks

Table 1. Descriptive statistics for performance data, where `Drug (n)' denotes mean performance (number ofcorrect responses) on session n for each task in the drug condition, and `Placebo (n)' denotes mean performance onsession n for each task in the placebo condition, for the ENT (èasy numerical'), DNT (`di�cult numerical'), EAT(èasy alphabetical') and DAT (`di�cult alphabetical') tasks

Session ENT SD DNT SD EAT SD DAT SD

Drug (1) 10.40 3.50 3.10 1.45 7.20 1.93 1.90 1.91Drug (2) 12.70 4.92 3.50 1.27 8.10 2.08 2.50 1.35Drug (3) 13.10 3.73 3.80 1.03 8.10 2.02 3.20 2.57Drug (4) 13.90 4.51 4.10 1.85 8.50 1.90 3.40 1.27Drug (5) 14.90 4.36 4.30 1.16 9.00 1.41 3.50 1.35Drug (6) 13.70 4.72 4.30 1.70 8.30 1.70 3.60 2.32Drug (7) 11.40 4.25 4.00 1.33 7.10 2.69 2.50 1.78Drug (8) 11.90 5.04 3.30 1.34 7.30 2.26 2.50 1.35Placebo (1) 10.70 4.25 3.20 1.54 7.40 1.51 1.80 2.40Placebo (2) 11.50 4.30 2.80 1.23 6.80 2.10 2.60 2.37Placebo (3) 11.90 4.15 3.20 1.62 6.90 1.20 2.60 2.41Placebo (4) 12.60 4.62 3.60 1.51 8.00 2.11 2.20 1.81Placebo (5) 13.30 3.30 3.90 1.73 7.00 2.26 3.30 1.77Placebo (6) 12.70 2.79 4.30 1.57 7.90 2.33 3.40 2.17Placebo (7) 13.40 2.95 3.80 1.75 7.90 2.47 3.70 1.70Placebo (8) 15.40 3.98 4.70 1.89 8.30 1.83 3.70 2.21

SD, standard deviation.



variables could account for only 9 per cent of thevariability at most in the criterion variable.However, since this study is one of the few modernstudies to employ an arousal manipulation in aspeci®c domain, and which is of su�cient magni-tude to observe a decrease in performance at higharousal levels, (Loke, 1990; Anderson, 1994), theresults make a contribution to the growing body ofevidence supporting the validity of the YDL. Inaddition, the use of twice the arousal manipula-tions necessary to observe a quadratic e�ectincreased the degrees of freedom for testing therelationship, thereby reducing the variabilityaccounted for in the data. However, the fact thatthe relationship still existed under this maximalentropy approach indicates its robustness.

Analysis of the data was less encouraging for thetask di�culty hypothesis of the YDL. There waslittle evidence to suggest that more di�cult taskshave a lower threshold of cortical arousal foroptimal performance, with respect to the amountof ca�eine consumed. However, the signi®cance ofthe ìnverted-U' was generalizable across thealphabetical and numerical task domains, indicat-ing that the e�ect was not task-speci®c. Althoughthe task di�culty hypothesis was not supported,further studies employing more than two gradeddi�culty manipulations may succeed in elicitingthe predicted arousal±performance thresholds, inthe same way that using a large number of arousalmanipulations successfully revealed the predictednegative quadratic relationship. As Anderson(1994) previously observed, and as critics havepointed out (e.g. Neiss, 1988), it is quite di�cult tojustify the labelling of tasks as `di�cult' or èasy'.In this experiment, although the tasks were onlydi�erentiated by di�culty in a very basic way,participants may more quickly learn complex tasks

(such as counting backwards in the alphabet),rather than tasks which are simple, and which havebeen practiced for many years (such as countingforwards). This idea was supported by the practicee�ects which were accounted for in the regressionmodel, for which the inclusion of a practice e�ectterm was a novel contribution to YDL research,and may have more clearly separated variabilitydue to the arousal manipulation. Data fromprevious experiments, which have both supported

Table 2. R and signi®cance values for performance data in drug and placebo conditions (quadratic and linear ®t)for the ENT (èasy numerical'), DNT (`di�cult numerical'), EAT (èasy alphabetical') and DAT (`di�cultalphabetical') tasks

Task R SE F df p

ENT (Drug) 0.28 4.31 3.21 2,77 0.04�DNT (Drug) 0.30 1.37 3.59 2,77 0.03�EAT (Drug) 0.27 1.99 3.08 2,77 0.05DAT (Drug) 0.30 1.75 3.83 2,77 0.03�ENT (Placebo) 0.32 3.75 4.42 2,77 0.02�DNT (Placebo) 0.32 1.58 4.37 2,77 0.02�EAT (Placebo) 0.20 1.98 1.64 2,77 0.20DAT (Placebo) 0.29 2.06 6.98 2,77 0.01�

A criterion of p < 0�050 was applied to signi®cance levels, with signi®cant R values denoted by �.

Table 3. Regression coe�cients (quadratic and linear®t) and signi®cance values for ENT (èasy numerical'),DNT (`di�cult numerical'), EAT (èasy alphabetical')and DAT (`di�cult alphabetical') tasks (drug andplacebo conditions)

Task/model B SE B T pcomponent

ENT (Drug) G 2.44 0.97 2.53 0.01�ENT (Drug) G2 ÿ0�26 0.11 ÿ2�50 0.02�DNT (Drug) G 0.81 0.31 2.64 0.01�DNT (Drug) G2 ÿ0�83 0.03 ÿ2�49 0.01�EAT (Drug) G 1.03 0.45 2.31 0.02�EAT (Drug) G2 ÿ0�11 0.05 ÿ2�45 0.02�DAT (Drug) G 1.09 0.39 2.76 0.01�DAT (Drug) G2 ÿ0�11 0.04 ÿ2�67 0.01�ENT (Placebo) G 0.31 0.84 0.40 0.71ENT (Placebo) G2 0.03 0.09 0.28 0.78DNT (Placebo) G 0.13 0.36 0.35 0.72DNT (Placebo) G2 0.01 0.04 0.29 0.77EAT (Placebo) G ÿ0�11 0.45 ÿ0�26 0.80EAT (Placebo) G2 0.03 0.05 0.64 0.52DAT (Placebo) G 0.13 0.36 0.35 0.73DAT (Placebo) G2 0.01 0.04 0.29 0.77

A criterion of p < 0�050 was applied to signi®cance levels, withsigni®cant R values denoted by �. G represents the linearcomponent of the model, and G2 denotes the quadraticcomponent.



or rejected the YDL, should be re-analysed toinclude a practice e�ect term, only after which thenegative quadratic e�ect of the arousal manipula-tion on performance, as observed in this experi-ment, may appear.

Two clear conclusions may be drawn from thisstudy. Firstly, the replication of ®ndings ofprevious studies (Loke, 1990, 1993; Anderson,1994) is encouraging for a number of reasons,particularly the e�cacy of the cortical arousalmanipulation through ca�eine, and through theuse of within-subjects designs, and large numbersof explanatory variable manipulations. The suc-cessful demonstration of the ìnverted-U' e�ectusing this latter technique suggests that futureresearch employ the same strategy to test the taskdi�culty hypothesis, which was not supportedwith only two levels of the explanatory variable.Secondly, the role that nonlinearity plays in bothcognitive and neural systems is receiving increasedattention (see Wright and Liley (1996) for areview). It is therefore interesting to consider thatthe nonlinear YDL was constructed almost 100years ago, when a paradigm of linear analysis wasdominant. It is anticipated that the application ofnonlinear modelling to studies of drug±cognitionrelationships in the future will result in an enrichedunderstanding of the implications of YDL-likefunctions for theories of cognitive functioning.

ACKNOWLEDGEMENTS

The assistance of Walter S. Pritchard in thepreparation of this manuscript is gratefullyacknowledged. PAW is supported by the CVCP/ORS, Cambridge Commonwealth Trust, MichaelFoster Trust, and the Pembroke±Australia Society.

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