Michael H. Birnbaum

Michael H. Birnbaum
California State University, Fullerton | CSUF · Department of Psychology

PhD

About

154
Publications
38,232
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Introduction
I study mathematical models of behavior with an emphasis on models of judgment and decision making and on methodology. I do empirical research, testing implications of models to evaluate their status as descriptions of behavior. I am currently working with various true and error models of probabilistic response. These models are both descriptive and useful as models for the analysis of data; that is, they are analogous to signal detection theory, factor analysis, or analysis of variance.
Additional affiliations
January 2012 - present
January 1986 - present
Education
August 1968 - June 1972
University of California, Los Angeles
Field of study
  • Mathematical Psychology

Publications

Publications (154)
Preprint
First order stochastic dominance is a core principle of rational decision making. Given two lotteries, A and B, if the probability of winning x or more in lottery A is greater than or equal to the same probability in lottery B for all x, and is strictly greater for at least one x, the decision maker should always prefer lottery A over lottery B. Vi...
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This article describes Advanced Training Institutes (ATIs) and workshops on psychological experimentation conducted via the Internet. These programs, conducted since 2002, presented instruction that evolved over the decades to reflect changes in Web-based methods and techniques. The need for instruction in the methods and methodology of Web-based r...
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This chapter reviews experiments testing theories of how people make choices between risky prospects, gambles in which the consequences and their probabilities are specified. When people prefer a small amount of cash to the expected value of a gamble, they are said to be risk averse. The St. Petersburg paradox is an extreme case of risk aversion in...
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Third generation prospect theory (Schmidt et al. J Risk Uncertain 36:203–223, 2008) is a theory of choices and of judgments of highest buying and lowest selling prices of risky prospects, i.e., of willingness to pay (WTP) and willingness to accept (WTA). The gap between WTP and WTA is sometimes called the “endowment effect” and was previously calle...
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This paper presents an experimental test of several independence conditions implied by expected utility and alternative models. We perform a repeated choice experiment and fit an error model that allows us to discriminate between true violations of independence and those that can be attributed to errors. In order to investigate the role of event sp...
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Judges assigned values to gambles from viewpoints of buyers (willingness to pay) and sellers (willingness to accept). Consistent with previous results, selling prices exceed buying prices, and these two judgments are not monotonically related to each other. There are systematic violations of consequence monotonicity when the consequence of zero is...
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Transitivity is the assumption that if a person prefers A to B and B to C, then that person should prefer A to C. This article explores a paradigm in which Birnbaum, Patton and Lott (1999) thought people might be systematically intransitive. Many undergraduates choose C = ($96, .85; $90, .05; $12, .10) over A = ($96, .9; $14, .05; $12, .05), violat...
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This paper reports results from a repeated experiment on decision making under risk where subjects must address the same choice problems in several rounds. We investigate how behavior changes in the course of the experiment. The design focuses on choice problems allowing for direct tests of independence and coalescing. We show that inconsistencies...
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Six experiments compared 4 classes of decision-making models that make different predictions for tests of 3 diagnostic behavioral properties. These properties are transitivity of preference, recycling of intransitivity, and restricted branch independence. Two experiments tested decisions based on advice from friends, a situation in which majority r...
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A psychological explanation consists of a set of premises postulated to account for the occurrence of some behavioral phenomenon. This paper contends that an explanation should satisfy at least five philosophical criteria: (1) The explanation must be deductive; that is, it should be possible to deduce the occurrence to be explained from the premise...
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Birnbaum (2011) criticized tests of transitivity that are based entirely on binary choice proportions. When assumptions of independence and stationarity (iid) of choice responses are violated, choice proportions could lead to wrong conclusions. Birnbaum (2012a) proposed two statistics (correlation and variance of preference reversals) to test iid,...
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Football outcomes are often used to illustrate violations of transitivity because, if team A beats team B, and if team B beats team C, there is no guarantee that team C will not beat team A. In the Big Ten Conference, every team played every other team in 1983, providing a complete test of transitivity of the football teams. The conference was very...
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Three experiments tested if individuals show violations of transitivity in choices between risky gambles in linked designs. The binary gambles varied in the probability to win the higher (better) prize, the value of the higher prize, and the value of the lower prize. Each design varied two factors, with the third fixed. Designs are linked by using...
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Individual true and error theory assumes that responses by the same person to the same choice problem within a block of trials are based on the same true preferences but may show preference reversals due to random error. Between blocks, a person{}'s true preferences may differ or stay the same. This theory is illustrated with studies testing two cr...
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This paper develops tests of independence and stationarity in choice data collected with small samples. The method builds on the approach of Smith and Batchelder (2008). The technique is intended to distinguish cases where a person is systematically changing ``true'' preferences (from one group of trials to another) from cases in which a person is...
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This article focuses on the design of Internet-based experiments. It discusses the five criteria of a theory, betweenversus within-subject designs, representative design, and systextual design. The results of psychological experiments can and do depend on the experimental designs used to establish causal effects. For example, the effect of a variab...
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Whereas some people regard models of risky decision making as if they were statistical summaries of data collected for some other purpose, I think of models as theories that can be tested by experiments. I argue that comparing theories by means of global indices of fit is not a fruitful way to evaluate theories of risky decision making. I argue ins...
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This article contrasts 2 approaches to analyzing transitivity of preference and other behavioral properties in choice data. The approach of Regenwetter, Dana, and Davis-Stober (see record 2011-00732-003) assumes that on each choice, a decision maker samples randomly from a mixture of preference orders to determine whether A is preferred to B. In co...
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Recently proposed models of risky choice imply systematic violations of transitivity of preference. This study explored whether people show the predicted intransitivity of the two models proposed to account for the certainty effect in Allais paradoxes. In order to distinguish “true” violations from those produced by “error,” a model was fit in whic...
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Three new properties are devised to test a family of lexicographic semiorder models of risky decision making. Lexicographic semiorder models imply priority dominance, the principle that when an attribute with priority determines a choice, no variation of other attributes can overcome that preference. Attribute integration tests whether two changes...
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This paper tests Birnbaum’s (2004) theory that the constant consequence paradoxes of Allais are due to violations of coalescing, the assumption that when two branches lead to the same consequence, they can be combined by adding their probabilities. Rank dependent utility and cumulative prospect theory imply that the Allais paradoxes are due to viol...
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Recent research reported evidence that contradicts cumulative prospect theory and the priority heuristic. The same body of research also violates two editing principles of original prospect theory: cancellation (the principle that people delete any attribute that is the same in both alternatives before deciding between them) and combination (the pr...
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During the last 25 years, prospect theory and its successor, cumulative prospect theory, replaced expected utility as the dominant descriptive theories of risky decision making. Although these models account for the original Allais paradoxes, 11 new paradoxes show where prospect theories lead to self-contradiction or systematic false predictions. T...
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Previous tests of cumulative prospect theory (CPT) and of the priority heuristic (PH) found evidence contradicting these two models of risky decision making. However, those tests were criticized because they had characteristics that might ``trigger'' use of other heuristics. This paper presents new tests that avoid those characteristics. Expected v...
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Several models of decision-making imply systematic violations of transitivity of preference. Our experiments explored whether people show patterns of intransitivity predicted by regret theory and majority rule. To distinguish “true” violations from those produced by “error,” a model was fit in which each choice can have a different error rate and e...
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E. Brandstätter, G. Gigerenzer, and R. Hertwig (2006) contended that their priority heuristic, a type of lexicographic semiorder model, is more accurate than cumulative prospect theory (CPT) or transfer of attention exchange (TAX) models in describing risky decisions. However, there are 4 problems with their argument. First, their heuristic is not...
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This paper tests a behavioral property called dimension integration. The test evaluates models, such as lexicographic semi-orders and the priority heuristic, which assume that a person uses only one dimension at a time. It provides a way to compare such models against those that assume a person combines information from different dimensions. The te...
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E. Brandstätter, G. Gigerenzer, and R. Hertwig (see record 2006-04733-008) displayed a correlation between the accuracy of the priority heuristic and expected value (EV). From this correlation, they argued that people use two processes to choose between gambles: First, they act as if they compute ratios of EV and choose the gamble with the higher...
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A classic paper by Tversky (Tversky, A. (1969). Intransitivity of preferences. Psychological Review, 76, 31–48.) reported that some people systematically violated transitivity of preference when choosing between specially constructed risky gambles. This conclusion remained controversial because his statistical analysis did not allow each participan...
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Abstract This experiment tested two behavioral properties of risky decision making, gain-loss separability and coalescing. Cumulative prospect theory (CPT) implies both properties, but the transfer of attention exchange model (TAX) violates both. Original prospect theory satisfies gain-loss separability but may or may,not satisfy coalescing, depend...
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Four experiments with 1391 participants compared descriptive models of risky decision making. The first replicated and extended evidence refuting cumulative prospect theory (CPT) as an explanation of Allais paradoxes. The second and third experiments used a new design to unconfound tests of upper and lower coalescing, which allows tests of branch-s...
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Three experiments tested behavioral properties of risky decision making. In the first, 433 participants received different formats for display of gambles. Within each of three formats, five “new paradoxes” that violate cumulative prospect theory (CPT) were tested. Despite suggestions that theories might be descriptive with these procedures, all fiv...
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Recently proposed models of risky choice imply systematic violations of transitivity of preference. Five studies explored whether people show patterns of intransitivity predicted by four descriptive models. To distinguish “true” violations from those produced by “error,” a model was fit in which each choice can have a different error rate and each...
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The customizable PHP script Generic HTML Form Processor is intended to assist researchers and students in quickly setting up surveys and experiments that can be administered via the Web. This script relieves researchers from the burdens of writing new CGI scripts and building databases for each Web study. Generic HTML Form Processor processes any s...
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This paper tests new "independence" properties to compare three models of risky decision making. According to the rank-affected multiplicative (RAM) weights model, all three properties should be satisfied; according to the transfer of attention exchange (TAX) model, two should be satisfied and one can be violated. However, according to cumulative p...
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Five descriptive models of risky decision making are tested in this article, including four quantitative models and one heuristic account. Seven studies with 1802 participants were conducted to compare accuracy of predictions to new tests of first order stochastic dominance. Although the heuristic model was a contender in previous studies, it can b...
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Four studies with 3440 participants investigated four new paradoxes that refute rank-dependent utility and cumulative prospect theories of risky decision making. All four paradoxes can be interpreted as violations of coalescing, the assumption that branches leading to the same consequence can be combined by adding their probabilities. These studies...
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The common consequence paradox of Allais can be decomposed into three simpler principles: transitivity, coalescing, and restricted branch independence. Different theories attribute such paradoxes to violations of restricted branch independence only, to coalescing only, or to both. This study separates tests of these two properties in order to compa...
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The common consequence paradox of Allais can be decomposed into three simpler principles: transitivity, coalescing, and restricted branch independence. Different theories attribute such paradoxes to violations of restricted branch independence only, to coalescing only. or to both. This Study separates tests of these two properties in order to compa...
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Advantages and disadvantages of Web and lab research are reviewed. Via the World Wide Web, one can efficiently recruit large, heterogeneous samples quickly, recruit specialized samples (people with rare characteristics), and standardize procedures, making studies easy to replicate. Alternative programming techniques (procedures for data collection)...
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The Internet is a new medium of communication, and as such it may create new types of social relationships, communication styles, and social behaviors. Social psychology may contribute to understanding characteristics and dynamics of Internet use. There are now several reviews of the psychology of the Internet, a topic that will not be treated in t...
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JavaScript programs can be used to control Web experiments. This technique is illustrated by an experiment that tested the effects of advice on performance in the classic probability-learning paradigm. Previous research reported that people tested via the Web or in the lab tended to match the probabilities of their responses to the probabilities th...
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ited only to students. Perhaps students do not understand probability or misunderstand the task for some other reason. I wanted to test people holding doctorate degrees who had read at least one book or scientific article on decision making. 1 California State University, Fullerton and Decision Research Center, Fullerton, USA. E--mail: mbirnbaum@fu...
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Publisher Summary This chapter provides case studies of experiential choices in laboratory that have violated implications deduced from these ideology. One of the things that decision scientists have not yet decided is how to represent the processes by which individuals make decisions when confronted with the simplest kinds of choices involving ris...
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SurveyWiz and factorWiz are Web pages that act as wizards to create HTML forms that enable one to collect data via the Web. SurveyWiz allows the user to enter survey questions or personality test items with a mixture of text boxes and scales of radio buttons. One can add demographic questions of age, sex, education, and nationality with the push of...
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In between-subjects (BS) designs, different groups may be asked to make judgments on numerical rating scales. According to judgment theory, judgments obtained BS are not an ordinal scale of subjective value. This article illustrates how BS designs can lead to strange conclusions: When different groups judge the subjective size of numbers, 9 is judg...
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This article reviews recent findings that violate a broad class of descriptive theories of decision making. A new study compared 1,224 participants tested via the Internet and 124 undergraduates tested in the laboratory. Both samples confirmed systematic violations of stochastic dominance and cumulative independence; new tests also found violations...
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This study tests between two modern theories of decision making. Rank- and sign-dependent utility (RSDU) models, including cumulative prospect theory (CPT), imply stochastic dominance and two cumulative independence conditions. Configural weight models, with parameters estimated in previous research, predict systematic violations of these propertie...
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The purpose of this chapter is to compare the descriptive adequacy of alternative theories of decision making. The common consequence paradox of Allais, which is evidence against expected utility theory, can be interpreted as a joint test of branch independence (a weaker version of Savage’s axiom), coalescing (equal outcomes can be combined by addi...
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This study tested branch independence, a key property distinguishing nonconfigural from configural theories of decision making. Sixty undergraduates judged buying and selling prices of 168 lotteries composed of 2 or 4 equally likely outcomes, ( x, y, z, v). Branch independence requires that ( x, y, z, v) is judged higher than ( x′, y′, z, v) whenev...
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Judges evaluated buying and selling prices of hypothetical investments, based on the previous price of each investment and estimates of the investment's future value given by advisors of varied expertise. Effect of a source's estimate varied in proportion to the source's expertise, and it varied inversely with the number and expertise of other sour...
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Choices between gambles show systematic violations of stochastic dominance. For example, most people choose ($6, .05; $91, .03; $99, .92) over ($6, .02; $8, .03; $99, .95), violating dominance. Choices also violate two cumulative independence conditions: (1) If S = (z, r; x, p; y, q) ? R = (z, r; x', p; y', q) then S? = (x', r; y, p + q) ? R? = (x'...
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Judges made choices and rated strengths of preference between gambles composed of 50–50 chances to receive either of 2 monetary outcomes (x, y). Others judged how much they would pay to play their chosen gamble rather than the other gamble. Judged strengths of preference violated interval independence, because they depended on the value of a common...
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Branch independence is weaker than Savage's "sure thing" principle. It requires that judgments of gambles with a com- mon outcome produced by the same probability-event must not re- verse order when that common outcome is changed. Subjects judged 168 gambles from viewpoints of both buyer (highest buying price) and seller (lowest selling price). Jud...
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This paper investigates two behavioral properties of choices between gambles: branch independence and distribution independence. Branch independence is the assumption that probability-outcome branches that are identical in two gambles being compared should have no effect on preference order. In the test of distribution independence, two middle outc...
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Branch Independence is weaker than Savage's independence axiom; it holds that if two gambles have a common outcome for an event of known probability, the value of that common outcome should have no effect on the preference order induced by other probability-outcome branches. Systematic violations of branch independence were obtained in two experime...
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The dominance principle states that one should prefer the option with consequences that are at least as good as those of other options for any state of the world. When applied to judged prices of gambles, the dominance principle requires that increasing one or more outcomes of a gamble should increase the judged price of the gamble, with everything...
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This article investigates choices between gambles and amounts of money to explore two issues in decision making. First, in recent studies, judgments of the values of gambles violated monotonicity (dominance), yet choices between the same gambles satisfied monotonicity, producing reversals of preference. This experiment tested whether certainty equi...
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Descriptive theories of decision making are constrained by the need to explain the following behavioral phenomena: risk aversion, gambling, purchases of insurance, investment, the paradoxes of Allais and Ellsberg, intransitivity of preference, irregularities of choice, preference reversals, risk judgments, violations of branch independence, the dif...
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In order to investigate derived scales for the utility, or subjective value of money, subjects were instructed to perform four tasks: in two tasks, they judged “ratios” and “differences” of strengths of preference for monetary amounts; in two other tasks, they judged the values of gambles from buyer's or seller's points of view. The two arrays of d...
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Systematically different preference orders are obtained when different procedures are used to elicit preferences for gambles. Three new experiments found different preference orders with attractiveness ratings, risk ratings, buying prices, selling prices, avoidance prices, and strength-of-preference judgments. Preference reversals persisted even wh...
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Ss judged the values of lotteries from 3 points of view: the highest price that a buyer should pay, the lowest price that a seller should accept, and the "fair" price. The rank order of judgments changed as a function of point of view. Data also showed violations of branch independence and monotonicity (dominance). These findings pose difficulties...
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This paper examines theories of impression formation which represent stimulus information as distributions on subjective dimensions rather than points along a continuum. These theories explain why unfavorable information often overrides favorable information. Subjects were asked to imagine hypothetical persons described by single adjectives or adje...
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Three experiments were conducted to investigate contextual effects and response mode effects (e.g., preference reversals) in risky decision making. Judgments of the worth of binary gambles were examined using two different contexts (positively and negatively skewed distributions of expected values) and two different response modes (attractiveness r...
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People judged both the attractiveness and risk of lotteries to win or lose money. The lotteries were designed to test whether risk and attractiveness judgments show systematic deviations from the simple sum of probability-by-utility-products analogous to (S)EU theory. Our results led to an alternative combination rule for probability and outcome in...
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The dominance principle states that the judged price of gamble A should be equal to or greater than the judged price of gamble B whenever A's outcomes are equal to or better than the corresponding outcomes of B, holding everything else constant. Subjects often violate the dominance principle by assigning a higher price to a gamble with some probabi...
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This paper evaluates models and measurements of the stress induced by life changes to determine whether a single scale can explain several different phenomena, including Judg- ments of "ratios" and "differences" as well as "combi- nations." Judgments of "ratios" and "differences" were found to be approximately monotonically related, suggesting that...
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When psychologists study human judgments of probability, judged probabilities unfortunately do not conform to the equations of probability theory. Because probability theory offers such a convenient and compelling structure for discussing beliefs about ambiguous and uncertain events, many scholars have found it disturbing to think that humans might...
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This study investigated the processes that underlie estimates of relative frequency. Ss performed 4 tasks using the same stimuli (squares containing black and white dots); they judged "percentages" of white dots, "percentages" of black dots, "ratios" of black dots to white dots, and "differences" between the number of black and white dots. Results...