Human Schedule Performance with Hypothetical Monetary Reinforcement

Transcription

1 EUROPEAN JOURNAL OF BEHAVIOR ANALYSIS 2001, 2, NUMBER 2 (WINTER 2001)225 Human Schedule Performance with Hypothetical Monetary Reinforcement University College London, UK Experiments examined the effect of variable ratio (VR) and variable interval (VI) schedules between a response (an investment made in the context of a game) and an outcome (a return on the investment) on human response rates and judgments of the causal effectiveness of the response. In Experiment 1, the time between successive outcomes obtained on a VR schedule became the successive interval criterion for a yoked VI schedule. Response rates and ratings of causal efficacy were higher on the VR than the VI schedule. In Experiment 2, the number of responses required per outcome on a VR schedule was matched to that on a master VI 40-s schedule. Both response rate and the ratings of causal effectiveness were higher in the VR schedule. However, these findings only held when the cost of a response was relatively high, but not when it was low. Free-operant responding maintained by schedules of reinforcement is patterned in a highly reliable manner (see Ferster & Skinner, 1957; Zeiler, 1977, for reviews). For example, response rates obtained from rat and pigeon subjects are typically higher on a variable ratio (VR) schedule than they are on a variable interval (VI) schedule (Cole, 1994; Peele, Casey, & Silberberg, 1984; but see Baum, 1993). Such a response rate difference between the above two schedules also has been found in experiments using human subjects (e.g., Baxter & Schlinger, 1990; Mathews, Shimoff, Catania, & Sagvolden, 1977). However, there have been a number of reports in which human schedule performance has been found to be different from that displayed by nonhumans (see Lowe, 1979; Wearden, 1988). There are a number of potential factors underlying this apparent species difference. For example, there is the possibility that verbal rules influence human performance (e.g., Wearden & Shimp, 1985), and that the wider experience of human Some of these data were first presented during the Experimental Analysis of Behaviour Group Meeting, London, Thanks are due to Lisa A. Osborne for her support. Requests for reprints of this manuscript should be addressed to, Department of Psychology, University College London, Gower Street, London, WC1E 6BT, UK. p.reed@ucl.ac.uk 225 subjects with different contingencies prior to training, relative to the typically naive nonhuman subjects, both exert an effect on human performance (e.g., Wanchisen, Tatham, & Mooney, 1989). The current experiments examine an additional issue relating to human schedule performance. Wearden (1988) noted that many studies of human schedule performance use money as a reinforcer, but in many of these studies the level of monetary reward obtained may be insufficient to maintain typical nonhuman-like performance. This issue obviously is exacerbated when nonmonetary reinforcers are used with human subjects (see Navarick, 1985). Some studies, especially those concerned with choice behaviour in humans, have used hypothetical monetary reinforcers. Several of these studies have found that the performance exhibited by human subjects was similar to that exhibited by nonhumans under similar contingencies with food reinforcers (e.g., Rachlin, Raineri, & Cross, 1991). Although the patterns of choice behaviour generated by such reinforcers in humans do show similarities to the behaviour generated by food in nonhuman subjects, the effect of such hypothetical monetary reinforcers on rates and patterns of human schedule responding have rarely been explored.

2 226 Studies of human schedule performance which used hypothetical monetary reinforcers were conducted by Reed (1994, 1999). In these studies, subjects responded by making investments from a fund of hypothetical money, and they received a reinforcement (the addition of hypothetical money to their investment fund) according to various schedules of reinforcement. Although the subjects ratings of the causal effectiveness of such responses mirrored nonhuman response rates (i.e., the ratings were higher for VR than the VI schedules), in none of these studies did the response rate match that expected from nonhuman studies. The failure to obtain response rate differences in the studies reported by Reed (1994, 1999) may be explained by the weakness of the hypothetical monetary reinforcer (Wearden, 1988). The failure also may be attributable to the fact that in these studies only one, three to four minutes exposure was given to each schedule. It may be that such response rate differences in nonhumans do not usually emerge until a number of sessions have been experienced. This limited exposure to the contingencies is a criticism levelled at many studies of human schedule performance by Jacobs and Hackenberg (2000). Alternatively, it may be that the procedure is not capable of producing schedule-typical VR versus VI response rate differences in humans, or even that humans do not exhibit such differences with hypothetical reinforcers. A further issue meriting investigation is the nature of response made by humans during exposure to such schedules. In the studies of human schedule performance reported by Reed (1994, 1999), the recorded response was a press of a computer key. This is a response which can be performance at very high rates by human subjects without a great deal of effort. Reed (1994, 1999) showed that only when the response was made more costly, by adding a higher response cost contingency within the confines of the procedure (i.e., making each investment more expensive), was the above pattern of schedule-induced judgment obtained. In contrast, with low levels of investment cost, there was little nonhuman-like schedule control over performance. Thus, the present experiment sought to investigate whether human performance could be brought under schedule control using the hypothetical monetary procedure used by Reed (1994,1999), and also whether the response cost contingency plays some role in generating the results obtained from this procedure. EXPERIMENT 1 The first step in this analysis is to establish that, using the investment game procedure mentioned above, human performance on VR and VI schedules is similar to that of nonhumans. To this end, a yoking procedure was adopted that equated the number of outcomes per minute obtained on a master VR schedule and on a yoked VI schedule. Such a yoking procedure has been found to result in higher rates of response for VR compared to VI schedules in nonhumans (e.g., Mathews et al., 1977; Peele et al., 1984). If the procedure can generate nonhuman-like, schedule-typical response rates, then the response rates (as well as the subjects judgments of causal effectiveness) will be higher on the VR compared to the VI schedule. In order to explore the effect more fully, multiple exposures to each schedule were given in the present study. Additionally the present experiment examined the influence of the response cost on performance. In the experiments reported by Reed (1994, 1999), the relationship between judgment of causality and schedule of reinforcement was only found to hold if the cost of the investment was relatively large (i.e., 100), but not when it was nominal (i.e., 1). Both of these costs were employed in the present study to see if similar findings would be obtained in the multiple exposure procedure. Method Subjects Twenty human subjects were recruited (thirteen female and seven male). All subjects were volunteers recruited in the Department of Psychology, U.C.L., and none was paid for their participation. The subjects were all normally intellectually functioning, and had an age range of 18 to 45.

3 Human schedule performance 227 Apparatus The experiment was conducted in a room with the subject sitting at a table, on which was placed a BBC computer that controlled the video display screen (screen size 24 cm wide and 17 cm high) placed approximately 50 cm in front of the subject. The subjects could respond to the instructions given to them on the video screen via the computer keyboard in front of them. Procedure The subjects were divided into two groups of ten. One group would experience a high cost associated with a response, the other group a low cost associated with a response. All the subjects were presented with the following instructions. You have been given the job of testing the effectiveness of investments made in a number of countries. You must test how well your investments in these countries do and report back to the company that hired you. (Return). Your managing director has given you a sum of 5,000 to invest as you see fit. After a certain time the board will want a report on how well your investments have gone. They will want to know how effective an investment was in that country. (Return). You can make an investment by pressing the SPACE BAR of the computer. Each press will subtract 100 (or 1 for the low cost group) from your investment fund. You may, or may not, receive income from your investment. Should you receive income, 1500 will be added to your fund. (Return). You are free to make an investment at any time. However, due to the nature of the economies it is to your advantage to invest some of the time and not to invest some of the time. (Return). You will be involved in testing two different economies. The relationship between investment and returns will be constant within a particular country, but may well differ from country to country. (Return). After a period of time, you will be asked to report to the board on your activities. They will want to see a good return on your investment. The board will also want you to give an estimate of how effective an investment was in the country your are investigating. (Return). You will be required to give a rating on a scale of 0 to 100 on the success of your investments. Zero means that investments never made money, and 100 means that investments always produced a return - made money. (Return). After presentation of the instructions the subjects were exposed to two conditions. Each condition was clearly labelled by the words Country 1 or Country 2 which appeared at the bottom of the screen during exposure to that condition. For Group High, a response deducted 100 from the total displayed on the screen, for Group Low a response deducted 1 from the total displayed on the screen. For both groups, an outcome was registered by 1500 being added to the total displayed on the screen (along with the words Successful Investment, which were presented on the screen, for 2s, just below the fund total). In one condition (VR), subjects responded on a VR-10 (range 1-19) schedule. This schedule was chosen to be compatible with the previous research conducted on the effects of schedules on causal judgement described in the General Introduction. In the second condition (VI), subjects responded on a VI schedule in which the successive intervals required for an investment to produce a return were those obtained under the preceding VR schedule. That is, the VI schedule was yoked to the VR schedule with respect to the interreinforcement interval. Subjects performed a judgment of the causal effectiveness of the response (investment) after each condition had finished. At the end of each condition the subject was asked: How effective on a scale of 0 to 100 was an investment in this country? Each of the two conditions was experienced four times by the subjects. Each of the conditions was presented for four minutes. Although four minutes is a relatively short exposure period for schedule work, this exposure period was adopted both for comparison with previous research, and because pilot studies had indicated a fall in attentiveness in the subjects if the exposure period (and resultant experimental length) exceeded this length of time. Results and Discussion The mean rate of response to the space bar during each exposure to both contingencies, in both groups, is shown in the top panel of Figure 1. Inspection of these data for Group High shows that response rates increased over training

4 228 in both the VR and the VI conditions. Responses rates became higher in the VR compared to the VI condition by the end of training. Responding was faster in Group Low than in Group High, and it increased over the course of training. However, there was no clear difference between the VR and VI schedules for Group Low. An analysis of variance (ANOVA) with group (High versus Low) as a between-subject factor, and schedule (VR versus VI) and block as withinsubject factors, was conducted on these data. A rejection criterion of p < 0.05 was adopted for this and all subsequent analyses. This analysis revealed significant main effects of block, F(3,54) Figure 1. Results from Experiment 1. Top panel: Mean responses per min over the four exposures to each of the contingencies. Bottom panel: Mean ratings of the causal effectiveness of responses over the three exposures to each condition. VI = variable interval; VR = variable ratio. High = response cost of 100; Low = response cost of 1. = 9.24, and group, F(1,18) = 5.17, and a significant interaction between group and schedule, F(1,18) = There were no other significant main effects or interactions, all ps > To analyse further these data the mean rates for the VR and VI schedules, for both groups, were calculated across all the blocks. This revealed a mean rate per minute for Group High of 35.4 in the VR, and 24.9 for the VI, schedule. Analysis of the simple effect of schedule revealed that this difference was statistically significant, F(1,18) = For Group Low, the VR rate was 44.7 responses per minute, and the VI rate was 46.3 responses per minute. This difference was not statistically significant, F < 1. The mean judgements regarding the causal efficacy of the responses emitted during each exposure of the two contingencies are shown in the bottom panel of Figure 1. These ratings were higher in Group Low than in Group High. In the former group, the VI rating was slightly higher than the VR rating. On the contrary, in Group High, the VR rating was higher than that for the VI condition. A three-factor ANOVA (group x schedule x block) conducted on these data revealed a significant interaction between group and schedule, F(1,18) = There was a marginal main effect of group, F(1,18) = 4.30, 0.06 > p > No other main effects or interactions were significant, all ps > To analyse further these data the mean ratings for the VR and VI schedules, for both groups, were calculated across all the blocks. This revealed a mean rating for Group High of 40.1 on the VR schedule, and 30.3 for the VI schedule. Analysis of the simple effect of schedule revealed that this difference was statistically significant, F(1,18) = For Group Low, the mean VR rating was 46.6, and the mean VI rating was This difference was not statistically significant, p > The number of outcomes obtained per min was necessarily the same in both conditions, rising from 2.98 reinforcers per minute in Block 1, to 5.50 reinforcers per minute in Block 4, for Group Low; and from 1.94 reinforcers per minute in Block 1, to 4.95 reinforcers per minute in Block 4, for Group High. The number of outcomes per response in Group Low was 0.09 in the VI (mean from all four blocks) compared

5 Human schedule performance 229 to a mean of 0.10 outcomes per response in the VR condition. In Group High, the mean number of outcomes per response was 0.15 for the VI condition, compared to 0.10 in the VR condition. When the cost of a response was high, the response rates were higher on the VR schedule compared to a VI schedule with the same frequency of reinforcement. This effect appears to depend upon the use of multiple exposures to the schedule. As noted by Reed (1994, 1999), in the present study, response rates on the VR and VI schedules were similar to one another after only one exposure, but became different over the course of training. Such response rate differences between VR and VI schedules have previously been noted with human subjects performing for monetary reward (Mathews et al., 1977), but not with hypothetical money as a reinforcer. This finding suggests that the present procedure for generating schedules of reinforcement produces behaviour similar to that noted in previous investigations of free-operant schedules of reinforcement. The above pattern of response rate differences between the VR and VI schedules was not noted when the response cost was relatively small. For the group with a low response cost, there were no response rate differences between the schedules. There are many possible explanations for this apparent lack of typical schedule sensitivity. It could be that the present data represents asymptotic responding for humans on a VR-10 schedule under these low cost conditions. This would obscure any VR versus VI differences. It may be that the demand characteristics of the task with a trivial cost were to engage the subject. Alternatively, with this range of schedule and response cost parameters, it may be that the VR and VI schedules would produce similar rates of response in nonhumans (see Baum, 1993). Whatever the reason, this finding with respect to response rate fits with those concerning causal judgment and response cost reported by Reed (1999). Since the aim of this experiment was to assess the effect of the present procedure on response rates, it did not equate the numbers of outcomes per response on the VR and VI schedules. Thus, little can be said unequivocally about the effect of the schedule on ratings of causal efficacy produced on these schedules. Even given this, the ratings of response efficacy emitted on VR schedules were higher than those on the VI schedule for Group High, despite the probability of an outcome following a response being higher on the VI schedule. This suggests that something other than a simple statistical rule for judgements, as would be suggested by models such as presented by Allen (1980) is operating. It should be noted also that the efficacy judgements did tend to follow the subjects response rates; there were differences between the schedules in terms of judgements when there were differences in response rates (or vice versa, of course). EXPERIMENT 2 The second experiment sought to explore whether VR and VI schedules of reinforcement affect evaluations of the causal effectiveness of responses when the probability of an outcome following a response was equated on the two schedules. To this end, subjects first performed according to a VI schedule, the number of responses emitted for each successive outcome being the number required for each successive outcome in a subsequent VR condition. Method Subjects and Apparatus Twenty human subjects were recruited (fourteen female and six male). All subjects were volunteers, as described in Experiment 1. The subjects were normally intellectually functioning, and had an age range of 18 to 34. The apparatus was that described in Experiment 1. Procedure The subjects were divided into two groups of ten. One group would receive a high cost associated with a response, the other group a low cost associated with a response. All subjects were presented with the same instructions as described in Experiment 1. After witnessing the instructions, the subjects experienced the two different schedule conditions four times. In the first sched-

6 230 ule condition, subjects responded on a VI 40-s schedule (range 1-80s), and in the second schedule condition they responded on a yoked VR schedule. The value of the VI schedule was chosen to allow comparability with previous research on this topic. The value of the VR component was yoked to the number of responses emitted by the subject in the completion of the VI condition. Thus, if a subject emitted 10 responses during the first interval, and 5 responses during the second interval, set up by the VI condition; then the first ratio value in the next VR trial would be 10 responses, and the second would be 5 responses. The condition lasted until all of the reinforcers collected in the preceding VI condition had been collected in the yoked VR condition. Thus, the probability of a response being followed by an outcome was equated across the two conditions. The VI component lasted for 4 minutes, the VR component lasted until the subject had obtained all the investment returns available as a result of the yoking procedure (i.e. the number of outcomes were the same in the two conditions). After the yoked VR schedule, subjects experienced the master VI 40-s schedule a second time, and then a VR schedule with ratio values yoked to the second VI schedule condition. After this the subjects experienced another two exposures each to the VI and VR schedule conditions in alternation. Each schedule type was clearly signalled by the words Country 1 or Country 2 which remained visible during exposure to that condition. Subjects performed a judgment of the causal effectiveness of the response (investment) after each condition had finished. At the end of each condition the subject was asked: How effective on a scale of 0 to 100 was an investment in this country? The subjects were divided into two groups (n = 10). In Group High, each response subtracted 100 from the subjects total (i.e. 5000). In Group Low, each response subtracted 1 from the subjects total. All other aspects of the procedure were as described in Experiment 1. Results and Discussion The mean rate of response to the space bar during each exposure to each of the contingencies is shown in the top panel of Figure 2. Inspection of the data from Group High shows that response rates increased over training in the VR conditions, but did not change consistently in the VI condition. Response rates in Group Low increased over the course of training in both VR and VI conditions, but there was little difference between these rates. A three-factor ANOVA (group x schedule x block) revealed significant interactions between group and schedule, F(1,18) = 6.14, schedule and block, F(3,54) = 4.81, and between all three factors, F(3,54) = No main effect, or other interaction, was statistically significant, ps > To further analyze these data, the simple effect of schedule on each block, for each group, was calculated. For Group High, Figure 2. Results from Experiment 2. Top panel: Mean responses per min over the four exposures to each of the contingencies. Bottom panel: Mean ratings of the causal effectiveness of responses over the four exposures to each condition. VI = variable interval; VR = variable ratio. High = response cost of 100; Low = response cost of 1.

7 Human schedule performance 231 there was no difference between the response rates emitted on the two schedules on blocks 1 and 2, ps > However, response rates were significantly higher for the VR compared to the VI schedule on blocks 3 and 4, smallest F(1,67) = For Group Low, there were no significant differences between the response rates emitted during exposure to the VR and VI conditions on any exposure, ps > The mean judgements of causal efficacy of the responses during each exposure to both contingencies are shown in the bottom panel of Figure 2. Inspection of these data shows that for Group High ratings of the causal efficacy of responses were higher in the VR compared to the VI condition. There was little systematic difference between the schedules in Group Low. A three-factor ANOVA (group x schedule x block) revealed a significant main effect of schedule, F(1,18) = 13.81, and significant interactions between group and schedule, F(1,18) = 14.44, schedule and block, F(3,54) = 6.18, and between all three factors, F(3,54) = No main effects or other interactions proved statistically significant. As suggested by Howell (1997), following a three-way interaction, separate two-factor (schedule x block) ANOVAs were conducted for the two groups. The ANOVA for Group Low revealed only a significant interaction, F(3,27) = 9.98, between the factors. However, no simple effect analysis for schedule on any block proved statistically reliable, all ps > The two-factor ANOVA (schedule x block) for Group High revealed a significant main effect of schedule, F(1,9) = 21.13, but no other effect or the interaction was significant, ps > In the present experiment, when a difference was noted between the schedules in terms of response rates and judgements of causality, these scores were higher for the VR schedule compared to the VI schedule. With respect to the rates of response, these were higher when the cost was lower, as might be expected on the basis of conditioning experiments with nonhumans (e.g., Peele et al., 1984). However, the differences in response rate between the schedules may reflect, simply, differences in the rate at which reinforcement was obtained on the VR and VI schedules. For Group High, reinforcement was obtained at a higher rate on the VR than on the VI schedule. One finding obtained in the present study, that was not noted in Experiment 1, was the similarity of the response rates and causality judgements in the VR High condition and the rates obtained in the Low cost conditions. As noted above, reinforcement rate was not equated in the present study between the VR and VI conditions (whereas, it was in Experiment 1). This produced a greater rate of reinforcement in the VR High than the VI High condition, as noted above. This rate of reinforcement presumably elevated the response rate in the VR High relative to the VI High condition, and, in fact, made it equivalent to the Low cost conditions, on which the schedule did not exert such an influence on performance. Importantly, the pattern of results, especially those regarding causality judgments, is consistent with those data obtained in the present Experiment 1. However, this pattern of results (i.e., higher response rates and causality judgments for the VR schedule) only held when the cost of the response was relatively high. No difference in these scores were found in the group with a nominal response cost. This finding with respect to response cost replicates those reported by Reed (1994, 1999), and extends the results to a situation in which the subjects experienced multiple exposures to the schedules. GENERAL DISCUSSION The results of the preceding experiments indicate that human response rates and causality judgements are influenced in a consistent manner by the schedule of reinforcement employed. Moreover, response rates and causality judgments appear to be influenced by these schedules in a similar manner to one another, and in a similar manner to that noted for nonhuman response rates. Rates and judgments were higher on a VR schedule compared to a VI schedule. This above finding extends those reported by Reed (1999), who found that judgments, but not response rate, were effected by the schedule after one exposure. That the effect emerged with additional exposures to the schedules in the

8 232 present experiments suggests that the number of exposures to the schedule is a critical determinant of schedule-typical behaviour in humans, and that the use of hypothetical reinforcers with no intrinsic value can be used to generate such behaviour. However, the present experiments also demonstrate that the similarity of causal judgments and response rates to those generated in nonhumans apparently holds only when the cost of a response is high. When the cost of a response was marginal, patterns of response rate across VI and VR schedules did not appear to conform to that which would have been predicted on the basis of nonhuman studies (e.g., Ferster & Skinner, 1957). It may be that different processes are responsible for human performance on schedules where only negligible costs are associated with a response. This fact may explain the data from several reports, in which human response rates on schedules of reinforcement do not appear to match that noted for nonhumans. Experiments in which little difference has been noted between the response rates maintained by different schedules in human subjects, could reflect the relatively trivial nature of a response used in those experiments for the human subjects (see also Wearden, 1988). The reasons why the cost of responding is important are unclear. In the present studies, a reinforcer was delivered which was sufficient to generate schedule-appropriate behaviour under some conditions. Yet the behaviours observed was only controlled in a lawful manner by the schedule when there were also relatively high response costs added to the situation. There could be many possible causes of this effect. Perhaps the emission of a response is only salient when it costs the subject something; in the absence of a meaningful cost, there is no reason not to respond at asymptotic level, and this would obscure response rate differences. Alternatively, this may be one of those conditions under which VR and VI rates are similar to one another (see Baum, 1993). A schedule can only control behaviour differently from other schedules to the extent that its reinforcer contacts different behaviours. If the reinforcer is contacting similar behaviours in different schedules, then similar patterns and rates of response should be observed. Further speculation regrading this point should be reserved for further studies which are designed to address this issue specifically. Of course, there are limitations in the degree to which such work can be generalised from the present paradigm using humans to previous work with nonhumans. One of the driving forces behind the present experiments was to allow some comparison between human and nonhuman species with respect to their schedule-controlled performance. A difference between the experiments designed to investigate the species is that nonhumans typically have a much longer exposure time to schedules than did the human subjects in the present study. Perhaps future work could address this difference in exposure time. This difference might underlay the failure of the low cost conditions to control behaviour in the present study. A further problem is exactly how the cost of making a response in the present procedure can be equated, say, to the cost of a response to a rat pressing a lever? Although the answers to such issues ought to be sought, it should be noted that the present procedure did show that human performance under high cost conditions, despite the limited exposure to the schedules employed, did equate at a global level to that of nonhumans. It may be that a finer-grained analysis of the moment-to-moment probabilities of a response, on the various schedules employed, would reveal differences between the behaviour generated under the various experimental procedures. For example, would human subjects show the typical burst-pause pattern on VR schedules that nonhumans emit?; and, is there any equivalence in the human performance to the slight scalloping shown by nonhumans on some VI schedules? The results of the present studies, which show human sensitivity to schedules, raise a number of questions when contrasted with the recent demonstration of human schedule sensitivity by Raia, Shillingford, Miller, and Baier (2000). In the latter study, it was shown that several factors were implicated in generating human schedule sensitivity. These were that instructions should be minimal, responses should be shaped, and there should be a consummatory response present.

9 Human schedule performance 233 None of these factors were present in the present study. However, the two studies did share one feature, and that is the introduction of pauses into the behavioural stream. Raia et al., (2000) produced pausing by the introduction of a consummatory response, and in the present study, pauses were introduced by the explicit instruction to pause. The interruption of the behavioural stream, however it is produced, may allow the reinforcement of longer IRTs on VI schedules (the absence of pausing would not allow this long IRT reinforcement). This view is strengthened by the finding reported both by Raia et al., (2000) that VI rather than VR schedules are differentially affected by instructions, and by the present study (see also Reed, 1994), that it is the rating of the VI schedules that are altered by the introduction of costs (allowing lower responses rates and pauses to develop). This view, of course, has to be tested experimentally, but seems to be a possibility worth further analysis. Whatever the eventual resolution of these issues, it has been demonstrated that the present procedure is effective in generating schedule-typical performance in humans under some conditions. This may prove a useful tool in the future investigation of such performance, and may furnish answers to the above questions regarding human schedule controlled behaviour. REFERENCES Allan, L.G., (1980). A note on measurement of contingency between two binary variables in judgment tasks. Bulletin of the Psychonomic Society, 15, Baum, W.M. (1993). Performances on ratio and interval schedules of reinforcement: Data and theory. Journal of the Experimental Analysis of Behavior, 59, Baxter, G.A., & Schlinger, H. (1990). Performance of children under a multiple randomratio random-interval schedule of reinforcement. Journal of the Experimental Analysis of Behavior, 54, Cole, M.R. (1994). Response rate differences in variable-interval and variable-ratio schedules: An old problem revisited. Journal of the Experimental Analysis of Behavior, 61, Ferster, C.B., & Skinner, B.F. (1957). Schedules of reinforcement. New York: Appleton-Century- Crofts. Howell, D.C. (1997). Statistical methods for psychology. London: Duxbury Jacobs, E.A., & Hackenberg, T.D. (2000). Human performance on negative slope schedules of points exchangeable for money: A failure of molar maximization. Journal of the Experimental Analysis of Behavior, 73, Lowe, C.F. (1979). Determinants of human operant behavior. In M.D.Zeiler & P.Harzem (Eds.), Advances in analysis of behaviour (volume 1): Reinforcement and the organisation of behaviour (pp ) Chichester, UK: Wiley. Mathews, B.A., Shimoff, E., Catania, A.C., & Sagvolden, T. (1977). Unstructured human responding: Sensitivity to ratio and interval contingencies. Journal of the Experimental Analysis of Behavior, 27, Navarick, D.J. (1985). Choice in humans: Functional properties of reinforcers established by instruction. Behavioural Processes, 11, Peele, D.B., Casey, J., & Silberberg, A. (1984). Primacy of interresponse-time reinforcement in accounting for rates under variable-ratio and variable-interval schedules. Journal of Experimental Psychology: Animal Behavior Processes, 10, Rachlin, H.A., Raineri, A., & Cross, D. (1991). Subjective probability and delay. Journal of the Experimental Analysis of Behavior, 55, Raia, C.P., Shillingford, S.W., Miller, H.L., & Baier, P.S. (2000). Interaction of procedural factors in human performance on yoked schedules, Journal of the Experimental Analysis of Behavior, 74, Reed, P. (1994). Influence of the cost of responding on human causality judgments. Memory and Cognition, 22, Reed, P. (1999). Effect of perceived cost on judgments regarding the efficacy of investment. Journal of Economic Psychology, 20, Wanchisen, B.A., Tatham, T.A., & Mooney, S.E. (1989). Variable-ratio conditioning history produces high- and low-rate fixed interval performance in rats. Journal of the Experimental Analysis of Behavior, 52,

10 234 Wearden, J.H. (1988). Some neglected problems in the analysis of human operant behavior. In, G.Davey & C.Cullen (Eds.), Human operant conditioning and behavior modification (pp ). New York: John Wiley. Wearden, J.H., & Shimp, C.P. (1985). Local temporal patterning of operant behavior in hu- mans. Journal of the Experimental Analysis of Behavior, 44, Zeiler, M.D. (1977). Schedules of reinforcement. In W.K.Honig & J.E.R.Staddon (Eds.), A handbook of operant behavior. Englewood Cliffs, NJ: Prentice-Hall.