Social Science Research 42 (2013) 217–229

Contents lists available at SciVerse ScienceDirect

Social Science Research

journal homepage: www.elsevier .com/locate /ssresearch

Do magnitudes of difference on status characteristics matterfor small group inequalities?

David MelamedDepartment of Sociology, University of South Carolina, Columbia, SC 29208, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 1 March 2012Revised 20 August 2012Accepted 2 September 2012Available online 12 September 2012

Keywords:Expectation states theoryGraded status characteristicsInequalitySmall groupsStatusStratification

0049-089X/$ - see front matter � 2012 Elsevier Inchttp://dx.doi.org/10.1016/j.ssresearch.2012.09.001

E-mail address: melamed@mailbox.sc.edu

The theory of status characteristics and expectation states (SCT) explains how macro-leveldimensions of stratification and specific abilities come to organize small group processes.The theory argues that people generate expectation states for each other based on relativestandings on dimensions of stratification such that people with the more culturally valuedstates of the characteristics have higher expectations. Subsequently social influence, partic-ipation rates and evaluations of participation are purported to be directly related to expec-tation states. The result of this process is that large-scale inequalities are perpetuated insmall group interactions, and individuals higher on abilities receive systematic advantagesin small groups. SCT has received substantial experimental support for over 40 years. How-ever, the theory assumes that only states of relatively high and relatively low matter. Thatis, the theory and its applications assume that the magnitude of difference separating indi-viduals on a dimension of stratification or ability is irrelevant. Recently, though, extensionsto both the theory and its mathematics have been introduced that allow the magnitude ofdifference to be incorporated into the theory’s predictions, supposedly yielding more pre-cise predictions. This paper offers an experimental test of these procedures, showing thatincluding the magnitude of difference into the theoretical predictions yields more preciseestimates that explain more status-based inequalities.

� 2012 Elsevier Inc. All rights reserved.

1. Introduction

The link between macro-level social structures and micro-level inequalities has received much attention from social the-orists (e.g., Berger et al., 1977; Blau, 1977; Coleman, 1986; Fiske, 2000; Kohn and Schooler, 1983; Lawler et al., 1993; Ridge-way, 1991). At the macro level American society is stratified, for example, by race (Massey, 2007) and sex (Bielby, 2001), andsmall group interactions tend to also be stratified by race (Lovaglia et al., 1998; Steele and Aronson, 1995) and sex (Ridge-way, 2011; Wagner and Berger, 1998). The expectation states theories explain how characteristics around which macro-levelinequalities exist (e.g., race and sex), and other factors such as effort and ability, combine to create small group inequalitiesin reward distributions, participation rates, and social influence (Berger et al., 1977, 1998). That is, the expectation statestheories provide one mechanism linking macro-level structures to small group inequalities.

The expectation states theories argue that initial inequalities in small collective task-oriented groups are a function ofstatus beliefs, such that individuals with the more socially valued states of status characteristics are predicted to participatemore and be more influential over the group. Here, a status characteristic refers to an attribute of an individual with widelyheld cultural beliefs that attach greater value and competence to one state of the attribute than to another (Correll andRidgeway, 2003). Race, sex, age, beauty, education and other factors may each function as status characteristics. For theexpectation states theories, differences on status characteristics are not the only means to the formation of inequalities:

. All rights reserved.

218 D. Melamed / Social Science Research 42 (2013) 217–229

differences in socially valued rewards (Berger et al., 1998) and differential contributions to the group (Fisek et al., 1991) canalso create small group inequalities. Collectively, the expectation states theories argue that relative differences on statuscharacteristics, ability, effort, and valued rewards may each lead to small group inequalities such that individuals that arehigher in status, try harder, are more able, or have more valued rewards are more influential, participate more and receivemore rewards from a distribution of valued goods.

Applications of the expectation states theories, however, rely on an ‘‘ordinal comparison hypothesis,’’ which treats all sta-tus differences as having only two states: relatively high and relatively low (Balkwell, 2001; Berger et al., 1980).1 However,there is no theoretical or methodological reason to ignore the magnitude of difference between individuals on a graded statuscharacteristic, or a status characteristic with more than two ordered states. Indeed research shows that models which includethe additional information contained in graded status characteristics explain more status-based inequalities than models thattreat all status differences as having only two states (Foddy and Smithson, 1996; Melamed, 2011). Recently, procedures havebeen developed that include the magnitude of difference on a graded characteristic into the existing mathematical structureof the expectation states theories (Fisek, 2009; Melamed, 2011). The aim of this paper is to present the results of an experimentthat systematically varied a graded status characteristic, which show that procedures that include graded conceptions of statusexplain more status-based inequalities and also fit the experimental data better than models based on the ordinal comparisonhypothesis.

In what follows, I review the logic of status characteristics theory, the expectation states theory that is relevant to theexperimental setting. I then review the extant literature on graded status processes within the expectation states tradition.I present an experimental investigation of graded status processes, the results of which indicate the utility of procedures formodeling graded status characteristics. I conclude with a discussion of how the procedures reviewed in this paper are con-sistent with the emerging social neuroscience literature on status processes, a comparison and discussion of the ways tomodel graded status characteristics and the implications of this research for applications of the expectation states theories.

2. Status characteristics theory

Inspired by the work of (Bales (1950), Bales and Slater, 1955) and other research showing that status characteristics af-fected social influence (e.g., Strodtbeck and Mann, 1956), Berger and colleagues (1966, 1972, 1977) developed a general the-oretical account for why the attributes of individuals in a group might result in one person having more opportunities toparticipate and also being more influential. This theory is SCT. The theory states that in situations where actors are collec-tively oriented and working towards the completion of a valued task, any status-valued attribute that differentiates groupmembers will become salient and affect the status hierarchy of the group. The logic of theory dictates that in collective taskgroups, people size-up the potential contributions of the others they are working with. One dimension of evaluation of futuretask related contributions is relative standings on status characteristics. The theory does not assume that people consciouslymake use of status characteristics to generate expectations for task contributions; rather the theory simply assumes thatbehavior will unfold as if they did.

Despite the relevance of differentiating status characteristics, the theory argues that all salient status characteristics willbenefit those higher in status unless the characteristics are directly disassociated from the task (Berger et al., 1977; Moore,1968). If a group is working on a mathematical task, for example, and sex differentiates the group members, then the ‘‘bur-den of proof’’ falls on showing that sex is not relevant to the task, implying that individuals with the more socially preferablestate of the characteristic (i.e., men) will participate more and be more influential than individuals with the less socially pref-erable state (i.e., women). Once salient, the strength of a status characteristic is dictated by how relevant it is to the groups’task (Balkwell, 1991a; Berger et al., 1976, 1992). The effect of math ability when a group is working on a math-related task isstronger than the effect of sex or race. Research shows that multiple, even conflicting, status characteristics combine to forma global composite measure of relative status (Berger et al., 1992). This composite measure of status is referred to as an‘‘aggregate expectation state,’’ which indicates an individual’s status rank relative to another person in the group. The theoryargues that power and prestige behaviors (e.g., participation or social influence) are a direct continuous function of expec-tation states (for a formal presentation of the theory, please see: Berger et al., 1977, pp. 107–130; Kalkhoff and Thye, 2006,pp. 221–222; Webster et al., 2004, pp. 742–743).

The logic of status characteristics theory has received substantial empirical support (for reviews, please see: Berger et al.,1980; Berger and Webster, 2006). However, when generating estimates of aggregate expectation states, the theory assumesthat only relatively high and relatively low states of status characteristics matter for status-based inequalities in power andprestige behaviors. This assumption has worked well for explaining status-based inequalities in experimental settings, par-ticularly since the models that are used were developed to account for the standardized experimental setting (Berger et al.,1977, pp. 122–161), which either uses categorical status distinctions (e.g., level of schooling) or induces categorical thinkingabout potentially quantitative status characteristics (e.g., Berger and Fisek, 1970, p. 295). However, in experiments with dif-ferent initial conditions (as in below) and, more importantly, non-experimental settings, magnitudes of difference on statuscharacteristics are often salient. Some research has shown that including magnitudes of difference into SCT models leads tobetter representations of the data generating mechanism of status-based inequalities (Foddy and Smithson, 1996; Melamed,

1 As Berger et al. (1980, p. 482) point out, individuals can have the same state of a characteristic, but then it does not differentiate the actors.

D. Melamed / Social Science Research 42 (2013) 217–229 219

2011). Consequently, below I review the literature on graded status characteristics, highlighting two recent procedures formodeling graded status characteristics within the expectation states tradition.

3. Graded status characteristics

Before delving into the literature on graded status characteristics, I point out that no conception of graded status char-acteristics assumes that people consciously process the magnitude of difference on a graded status characteristic. The liter-ature on social cognition suggests that people are cognitive misers that only process vital pieces of information about thesocial situation (Fiske and Taylor, 2008). In line with this view, conceptions of graded status characteristics assume thatbehavior will unfold as if people process this information. This assumption is parallel to the standard SCT assumption thatpeople do not consciously generate expectation states based on any number of salient status characteristics. To assume thatpeople consciously process their relative ranks on several status characteristics, separate out their positive ranks and processthem, then separate out their negative ranks and process them, to combine them into a composite measure of status is a veryunrealistic assumption indeed. Likewise, assuming that people consciously process magnitudes of difference on graded sta-tus characteristics is similarly unrealistic.

Some theorists have made progress towards incorporating graded characteristics (e.g., general intelligence or occupa-tional prestige) into SCT (Driskell and Mullen, 1990; Fisek, 2009; Foddy and Smithson, 1996; Melamed, 2012; Shelly,1998). Foddy and Smithson (1996) conducted an experiment in the standardized experimental setting for SCT researchwhere they randomly assigned subjects scores on a quantitative characteristic. This enabled them to compare finely gradeddifferences in ability to categorical states of high versus low. They found that modeling graded differences between two ac-tors explained more variation in influence than a simple dichotomy (c.f., Balkwell, 2001). In their concluding remarks, theyclaimed: ‘‘These results are sufficient to warrant considerations about including graded ability levels and differences in de-grees of ability into the SCT framework’’ (151).

Recently Fisek (2009) has developed a method for modeling graded status characteristics. Drawing from the theory of sta-tus cues (Fisek et al., 2005), he argued that status cue gestalts, or the entirety of information that can be used to infer states ofa status characteristic, can be distinguished into two categories- strong and weak. Strong cue gestalts indicate that an actorindeed possesses the relevant status element; weak cue gestalts indicate that an actor is expected to possess the relevantstatus element. This subtle distinction between strong and weak cue gestalts is theorized to produce a different cognitiveprocess for actors in collective task situations. Specifically, weak cue gestalts are argued to be less relevant to task outcomesthan are strong cue gestalts. Therefore, subtle differences on graded characteristics can be modeled slightly differently thanobvious status distinctions such that a status that is relevant through weak cue gestalts is predicted to have less of an effecton observable inequalities in task groups than a status that is relevant through strong cue gestalts. This approach was thefirst to open the door to the a priori modeling of graded status characteristics within the expectation states tradition (seeAppendix A for how this procedure yields a priori estimates).

A second procedure for the a priori modeling of graded status characteristics has also been introduced by Melamed (2011;Melamed and Walker, 2010). Primarily motivated to increase the accuracy of estimates drawn from the expectation statetheories for an application to issues of justice, Melamed’s (2012) procedure converts the magnitude of difference betweenindividuals on a graded characteristic into the area under an assumed functional form (e.g., the normal or gamma distribu-tion) which is then incorporated into the existing mathematical structure of the expectation state theories. This proceduresyields continuous estimates of expectation states that take on a range of values around a given level of relevance for thegraded characteristic. Specifically, relatively large magnitudes of difference on graded characteristics lead to stronger pre-dicted effects and relatively small magnitudes of difference on graded characteristics lead to weaker predicted effects thanthe ordinal comparison hypothesis.2 Furthermore, graded characteristics can be assumed to follow any functional form, whichallows for ordinal and continuous status differentiation (see Appendix A for how this procedure yields a priori estimates). Theresults of observational studies suggest that Melamed’s (2011, 2012) procedure explains more variation and has a better fit tothe data than estimates of expectation states drawn using the ordinal comparison hypothesis.

The Fisek (2009) procedure has yet to be empirically evaluated, and the Melamed (2011) procedure has only been appliedto observational studies. This paper presents the results from a controlled laboratory study that manipulated a single gradedstatus characteristic. The experiment was conducted to compare the above conceptions of graded status characteristics tothe ordinal comparison hypothesis in order to evaluate the extent to which these conceptions explain more status-basedinequalities in collective task groups. The expectation, or prediction, is that because the above conceptions of graded statuscharacteristics contain more information about the status differences in the groups, that they should both fit the experimen-tal data better and explain more variation in small group inequalities. Consequently, below I describe the experimental pro-cedures and results, which show that both procedures fit the data better than the model based on the ordinal comparisonhypothesis, and that they fit about equally well. I then conclude with a comparison and discussion of the procedures, andthe implications of this research for applications of the expectation state theories to real-world situations.

2 The notion of ‘‘salience’’ is problematized when status differences are treated continuously. Is an IQ difference of two points, for example, to be considered astatus difference? On the one hand, subtle status differences, such as a two point difference in IQ, may not become salient; on the other hand, the effect wouldbe so small that its effects would likely be indistinguishable (i.e., because the status weight would be trivial). The benefits of a truly continuous notion of statuswill likely not be found in situations of minimal difference, as in this example, but rather in situations where many states of a single characteristic are salient.

220 D. Melamed / Social Science Research 42 (2013) 217–229

4. Method

A single factor experimental design is well suited to evaluate the extent to which the graded characteristics estimationprocedures are a better approximation of status-based inequalities than the ordinal comparison hypothesis. The experimentwas run in a computer mediated version of the standardized experimental setting (SES) for tests of status characteristics the-ory (Berger et al., 1977, pp. 43–48; Berger, 2007; Kalkhoff and Thye, 2006). In general the SES requires that four conditionsare met: (1) The SES requires that the participants do not meet, so that a status hierarchy may be ‘‘created.’’ That is, it isimportant that non-manipulated characteristics, such as ethnicity and beauty, are not salient to the participants in orderto ensure that the manipulated characteristic is the only factor driving the observed inequalities. (2) The SES requires aset of standard instructions for ensuring that the initial conditions of the theory are met (e.g., that the participants are bothtask and collectively oriented). (3) The SES requires the use of a binary choice task to manipulate relative status of the par-ticipant and their purported partner. And, (4) the SES also requires the use of a standard measure of social influence (e.g., thenumber of trials that the participant behaviorally rejects influence attempts from their partner).

5. Design and subjects

The SES uses a binary choice task to manipulate the status of participants relative to their partners. Six different levels ofrelative status constituted the status manipulation. In two of the conditions, the participant (P) and the partner (O) were dif-ferentiated as much as possible. In the remaining four conditions, P and O were differentiated as little as possible, at bothends of the distribution of the manipulation (see below). One hundred twenty undergraduate students were randomly as-signed to the six conditions.3

Not all of the data from the one hundred twenty participants was analyzable data. Data was excluded for one of the fol-lowing reasons: (1) failure to recall the number of trials used to manipulate status (i.e., manipulation checks), (2) disbelief ofthe deception involved in the experiment (either disbelief that they were working with a partner or disbelief that the task forthe experiment was valid), and (3) blatant lack of collective orientation or task orientation. The first exclusion criterion wascompletely objective: at the end of the study, the computer program asked participants how many trials they got correct inphase one, and they were also asked how many trials their partner got correct in phase one. If the participant reported anumber different from the one that was reported to them in that condition, then the participant failed the manipulationcheck and was excluded from the analyses. Post-experimental interviews were the only way to assess belief in experimentaldeception and the extent to which the participants were collective and task oriented. Participants were asked if they believedin the task (contrast sensitivity) and that they were working with a partner. Further, participants were asked if they weremotivated to get each trial correct and if they used the information provided from their partner in phase two. As a resultof all three exclusion criteria seventeen of the 120 cases (14%) were identified as problematic. The problematic cases werere-run in random order.4 Sex was not controlled by design as both female and male participants were randomly assigned acrossconditions.

6. Procedures

Participants were escorted to isolated rooms and were informed that they would be working with a partner over a com-puter network in a two phase experiment. In reality they did not work with a partner; the computer program simulated thebehavior of a fictitious partner in order to control those behaviors. Participants did not meet or see each other to avoid non-manipulated status characteristics, such as beauty (Webster and Driskell, 1983), from becoming salient. They were told thatthey would be working at an individual task in the first phase and that they would then work over a computer network witha partner on a collective task. After this initial introduction to the study the remainder of the session was computermediated.

The instructions addressed three important aspects of the experiment. First, participants were informed that they wouldbe paid for their performance in the experiment. Specifically, they were told that the minimum they could earn was $6.00.They were told that they could earn an additional $.25 for each trial that they got correct in phase two and $.25 for each trialthat their partner got correct in phase two. The earnings were used to motivate participants to be both task and collectivelyoriented; making the amount they earned contingent on their performance should increase task orientation and makingthem dependent on their partner should increase collective orientation. Research has shown that subtle protocol variations,such as performance-based pay, can lead to systematic changes in SCT results (Kalkhoff and Thye, 2006). This change wasmade to the SES in order to maximize task and collective orientation, and may be why fewer of the cases had to be re-run than normal (see Ridgeway and Correll, 2006 for similar procedures).

3 There were 32 males and 105 females. Of the 17 cases that were redone, 5 of them were males and 12 of them were females; given the marginals, this iswithin sampling variability, indicating that sex does not have an effect on having to redo a case (v2

ð1Þ = .4, p = .53). Among the 120 cases that are analyzed, menwere not systematically assigned to any of the conditions (v2

ð5Þ = 1.7, p = .89). Moreover, in the regression models reported below, a dummy variable for sex isnot significant (results available from the author upon request).

4 Upon redoing one of the cases, the wrong condition number was entered into the experimental program; as such there are 21 cases in condition 1, 19 casesin condition 3, and 20 cases each in the other four conditions.

D. Melamed / Social Science Research 42 (2013) 217–229 221

Second, the instructions introduced the task for the experiment, contrast sensitivity. Contrast sensitivity was described asa relatively new ability that is not associated with other abilities such as mathematical or verbal skills. Participants wereshown two rectangular images,

each composed of smaller black and white areas, and were asked to select which of the two images contained the mostwhite area. They were told that ‘‘the difference in the amount of white area is sometimes quite small,’’ and that they wouldtherefore ‘‘probably find that some of the pictures . . . are very difficult [to judge].’’ Participants were then told that peoplewith high contrast sensitivity consistently choose more correct answers than people with low or average contrast sensitivity,and that people with high levels of contrast sensitivity may not be aware of how it is that they choose the correct answer.Nonetheless, they were informed that there is a correct answer to each trial and that the test in phase one, which was de-signed for student populations, is designed to measure the presence of contrast sensitivity ability. In reality, contrast sensi-tivity is not a real ability and there is no correct answer (Moore, 1968).

Third, the instructions were used to create the initial conditions of SCT. The instructions described the team portion of theexperiment as a ‘‘critical choice’’ situation in which taking others’ opinions into consideration leads to an increased likeli-hood of making a correct decision. It was stressed to the participants that they work as a team because ‘‘exchanging infor-mation with others often leads to more correct decisions than an individual could make working alone.’’ This portion of theinstructions was intended to increase participants’ collective orientation.

Phase one of the experiment consisted of a practice trial with on-screen instructions followed by 25 trials of contrast sen-sitivity problems. Participants were given ten seconds to decide which of two images contained the most white area, afterwhich they were unable to make a choice for that trial. After phase one, the participant’s and partner’s (fictitious) scores werereported to the participant constituting the experimental manipulation.

Phase two of the experiment also consisted of 25 trials of contrast sensitivity problems. In phase two, participants weregiven ten seconds to make their initial opinions as to which of two images contained the most white area. Then they wereshown their partner’s initial opinion, given ten more seconds to study the images, and were asked for their final opinions.Once the ten seconds were up, the participants were no longer eligible to make a choice for that trial. On 20 predeterminedtrials the partner’s initial decision was different from the participant’s initial decision. The proportion of trials that the par-ticipant rejects this influence attempt from the partner is the main outcome; that is, the proportion of twenty trials that theparticipant stays with her own initial opinion, despite receiving information that the partner disagrees with her initial opin-ion, is the outcome (referred to as P(s) for proportion of stay responses). After phase two, participants completed a brief ques-tionnaire and then they were debriefed.

7. Manipulation

The participant’s score and the partner’s score in phase one were used to manipulate status. Traditionally the scores arereported with a rule-of-thumb interpretation that induces thinking about contrast sensitivity as if it is a discrete ability withstates that are poor, average, and superior (e.g., Berger and Fisek, 1970, p. 295). For example, if twenty trials are used tomanipulate status, participants might be told that a score of zero to ten represents a poor performance and a relative lackof ability, a score of eleven to fifteen represents an average performance, and a score of sixteen or more represents a superiorperformance. Given that I want to evaluate the extent to which participants make use of more finely graded distinctions thanthe above mentioned three categories, the phase one scores were reported as whole numbers without reference to any cat-egorical interpretation of that score. Fig. 1 visually represents the distribution that was used for the manipulation.

There are three important aspects of the distribution of contrast sensitivity scores. First, it induces thinking about contrastsensitivity as a continuously distributed ability rather than a discrete ability with three ordered states. Second, the distribu-tion visually represents that the ability is centered about fourteen. Third, the distribution visually represents that the stan-dard deviation is three, indicating that as scores move farther away from fourteen they become less likely. Again, I do notassume that the participants consciously processed this distributional information; I just assume that behavior will unfoldas if they did.

Manipulating contrast sensitivity in phase one and then measuring influence using the same characteristic in phase twoserves a distinct purpose. Once contrast sensitivity is manipulated, it is the only salient status characteristic since theparticipants did not meet or even see one another before the study. In this case, contrast sensitivity is the most relevant

5 8 11 14 17 20 23

Fig. 1. The distribution that was used to manipulate contrast sensitivity ability.

Table 1Summary of the Phase I Scores used to manipulate status.

Condition P’s Phase I Score O’s Phase I Score

1 23 52 5 233 23 194 9 55 19 236 5 9

222 D. Melamed / Social Science Research 42 (2013) 217–229

characteristic to solving contrast sensitivity problems (i.e., it is the ‘‘instrumental task characteristic’’). This is analogous tomath ability being the only salient characteristic in a group that is working on a linear algebra problem, except that I canmanipulate contrast sensitivity ability. Although other characteristics may factor into participation rates and influence, con-trast sensitivity ability is the characteristic that is predicted to have the largest effect. Since it is the most relevant charac-teristic, the effect sizes of status on social influence should be the largest, allowing the graded characteristic procedures themost variation to explain.

Only two screens varied across the conditions of the experiment. The first showed the participant her and her partner’sscore in raw form beneath the distribution that is presented in Fig. 1. On the second screen, participants were told that ‘‘thatthe national average on the contrast sensitivity test is 14. . . [and that] most people will score relatively close to 14. Increas-ingly smaller or larger scores around 14 are increasingly unlikely.’’ Depending on the condition, the participant’s and thepartner’s percentile scores were also reported to the participant (see note 5).

The specific values that were used to manipulate status were selected to maximize the likelihood of observing a gradedstatus difference in the P(s) scores (i.e., a strong manipulation). Table 1 presents the phase one scores that were used tomanipulate status. The first two conditions created a very large status difference between the participant and their partner.In the very high status condition, the participant was told that she got 23 out of 25 trials correct in phase one, and she wastold that her partner got 5 out of 25 trials correct. In the very low status condition, the scores and corresponding percentileswere reversed, telling the participant she got 5 correct while the partner got 23 correct. The scores, 23 and 5, correspond toplus and minus three standard deviations, respectively. The other four conditions induced relatively small status differencesbetween the participant and her partner at both ends of the distribution of contrast sensitivity ability. In the high status,small difference conditions the participant was told that she got either 9 or 23 correct and that her partner got either 5or 19 correct. In the low status, small difference conditions the participant was told that she got either 5 or 19 correctand that her partner got either 9 or 23 correct. In all four of the small difference conditions, four trials separated the scoresof the participant from the partner.5

I used contrast sensitivity because it states could be manipulated. A real-world example of this process might entail occu-pational prestige. Conditions 1 and 2 are analogous to a physician working with a short order cook, where the physicianholds an extremely high state of occupational prestige and a short order cook holds an extremely low state of occupationalprestige. Conditions 3 and 5 are analogous to a physician working with a lawyer, and conditions 4 and 6 are analogous to ashort order cook working with a welder. In both of the latter sets of occupations subtle differences in occupational prestigedifferentiates the individuals (Bose and Rossi, 1983).

8. Predicting social influence

Tests of SCT using the standardized experimental setting often use a two-step procedure to evaluate the predictions. Thefirst step is to estimate a linear probability model, regressing the proportion of stay responses (P(s)) on the estimated statusdifference between P and O. Here is a typical linear probability model: P(s) = m + q(ep � eo) + e, where m (the constant) refersto a baseline propensity to reject influence attempts, q (the slope) refers to a parameter that captures idiosyncrasies of themanipulation and other systematic effects, e refers to a vector of errors, and ep � eo refers to P’s expectation advantage over O(Berger et al., 1977, pp. 136–144). The expectation advantage is calculated a priori based on the graph-theoretic representa-tion of the theory (e.g., Berger et al., 1977). In words, the graphic representation models salient status characteristics andtheir relevance such that more relevant characteristics have shorter paths in the graphic representation, and less relevantcharacteristics have longer paths in the graphic representation. Subsequently, functions of the path lengths in the graphicrepresentation are taken to estimate P’s and O’s expectation state values (Balkwell, 1991a; Berger et al., 1977; Fisek et al.,1992). Subtracting O’s expectation state value from P’s leads to the expectation advantage of P over O (see Appendix A forthe computations of all of the expectation advantages used to generate the predictions).

Assuming the ordinal comparison hypothesis, the estimates of P’s expectation advantage over O are the same for condi-tions 1, 3 and 5. The estimates are also the same for conditions 2, 4, and 6. In conditions 1, 3, and 5 the participant is rela-tively high in status and the magnitude of difference is irrelevant. In conditions 2, 4, and 6 the participant is relatively low in

5 A score of 23 is at the 99th percentile, a score of 19 is at the 95th percentile, a score of 9 is at the 5th percentile and a score of 5 is at the 1st percentile. Thesepercentiles were reported to the participants. Post-experimental interviews during pre-testing suggested that participants understood the percentile scores.

D. Melamed / Social Science Research 42 (2013) 217–229 223

status and, again, the magnitude of difference is irrelevant. That is, under the ordinal comparison hypothesis, there are onlytwo values for P’s expectation advantage over O. With either the Fisek (2009) or the Melamed (2011) conceptions of gradedstatus characteristics there are four values for P’s expectation advantage over O. In both cases there is a single estimate of theexpectation advantage for conditions 1 and 2, conditions 3 and 4 have the same estimate, and conditions 5 and 6 have thesame estimate. Using the Fisek procedure, conditions 3–6 could be argued to constitute weak cue gestalts, making the path-lengths longer and the effects weaker. These conditions constitute weak cue gestalts because the difference between the par-ticipants is indicative that both the relatively high and the relatively low status person are ‘‘expected to possess the relevantstatus element’’ (Fisek et al., 2005, p. 86). Conditions 1 and 2 constitute clear strong status cue gestalts – the participants arelargely differentiated on contrast sensitivity ability. However, in conditions 3–6 there is a small but noticeable difference inthe scores that operate through weak cue gestalts.

Likewise, using the Melamed (2011) procedure leads to four estimates of P’s expectation advantage over O. The distribu-tional information contained in Fig. 1 is the reason for the separate estimates. In condition one, there is a certain area underthe curve separating P and O and this information is used as a weight to generate the expectation advantage. Because thenormal distribution is symmetrical, in condition two the same weight is used, but in this condition P has the negatively eval-uated state of contrast sensitivity (i.e., the expectation advantage for condition two is the opposite of the expectation advan-tage for condition one). Conditions three and four have the same estimates of the expectation advantage because of thesymmetry of the distribution of contrast sensitivity scores: the same area is under the curve between scores of 23 and 19as the area under the curve between scores of 9 and 5. Conditions five and six have the same areas under the curve as con-ditions three and four, except that P has the negatively evaluated state of contrast sensitivity ability in these conditions. Thatis, the expectation advantages in conditions five and six are the opposite of the expectation advantages in conditions threeand four.

Once the expectation advantages are computed, the linear probability models can be estimated. Then the second step of atypical analysis is to estimate a Chi-squared goodness-of-fit test comparing the predicted P(s) values from the linear prob-ability model to the observed values. This is often done using (Balkwell’s (1991b), note 3) computational formula, but canalso be estimated using a conventional Pearson Chi-squared test (Agresti, 2002, p. 78). With respect to the predictions,the results are relevant at both steps of the analysis. When estimating the linear probability models, the graded conceptionsof status characteristics should explain more variation in stay responses than the ordinal comparison hypothesis estimates.When computing the goodness-of-fit statistics, the graded conceptions should fit the data better than the ordinal compar-ison conceptions.

9. Results

Table 2 presents the observed proportion of stay responses (P(s)) and the sample sizes for the six conditions in the exper-iment. The results are in the predicted directions. The mean P(s) values for the three high status conditions (1, 3 and 4) arehigher than the mean P(s) values in the low status conditions (2, 5 and 6). These results follow from the logic of the ordinalcomparison hypothesis. More precise predictions follow from the logic of graded status characteristics, which predicts higherP(s) values in condition one than in conditions three and four. Although the participant is high status in each of these con-ditions, she is very high status in condition one. Results of Mann–Whitney U tests (see Gibbons, 1993) confirm that the P(s) incondition one is higher than conditions three (U = 2.38, p = .009) and four (U = 2.87, p = .002). The logic of graded status char-acteristics also predicts lower P(s) values in condition two than in conditions five and six. In condition two the participant isvery low in status relative to her partner, but in conditions five and six the participant is only marginally lower than herpartner. Results from Mann–Whitney U tests suggest that the P(s) for condition two is less than the P(s) for condition six(U = 2.62, p = .004), but not less than the P(s) for condition five (U = .76, p = .224). Thus three of the four more specific pre-dictions have been supported by the data. To discern the broader trends in the data, though, I now turn to assessing ex-plained variance and global model fit.

The first step of the analysis is to regress the P(s) values on the three sets of expectation advantages (see Appendix A).Table 3 presents a summary of these models. Two things from Table 3 warrant attention. First, the Fisek (2009) and the Mel-amed (2011) approaches to modeling graded status characteristics explain the exact same amount of the variation in theproportions of stay responses. Second, both conceptions of graded status characteristics explain an additional 5.3% of the var-iation in stay responses beyond that which is explained by the model based on the ordinal comparison hypothesis estimates

Table 2Observed P(s) scores and sample sizes by conditions.

Condition P(s) N

1 (23 � 5) .765 212 (5 � 23 .250 203 (23 � 19) .661 194 (9 � 5) .599 205 (19 � 23) .307 206 (5 � 9) .440 20

Table 3Summary of results from regressing P(s) on three estimates of expectation advantages.

Ordinal comparison hypothesis Fisek (2009) estimates Melamed (2011) estimates

M (Std. error) .505*** .504*** .503***

(.019) (.018) (.018)Q (Std. error) .115*** .166*** .136***

(.013) (.016) (.013)R-squared .411 .464 .464

*** p < .001.

Table 4Observed cell counts of stay responses and trials influenced.

Condition Defer to partner Stay response

1 (23 � 5) 96 3112 (5 � 23 286 973 (23 � 19) 125 2464 (9 � 5) 142 2515 (19 � 23) 277 1096 (5 � 9) 220 172

Table 5Predicted cell counts and chi-squared values for the ordinal comparison model.

Condition Predicted counts Residuals v2 Components

Defer to partner Stay response Defer to partner Stay response Defer to partner Stay response

1 (23,5) 131.66 275.34 �35.66 35.66 9.66 4.622 (5,23) 255.58 127.42 30.42 �30.42 3.62 7.263 (23,19) 120.02 250.98 4.98 �4.98 .21 .104 (9,5) 127.14 265.86 14.86 �14.86 1.74 .835 (19,23) 257.58 128.42 19.42 �19.42 1.46 2.946 (5,9) 261.58 130.42 �41.58 41.58 6.61 13.26

v2 = 52.31

224 D. Melamed / Social Science Research 42 (2013) 217–229

of the expectation advantage. Thus, the a priori procedures for including graded characteristics explain more variation in so-cial influence; I now turn to the issue of model fit.

Table 4 presents the observed cell counts of stay responses and trials in which the participant deferred to the partner (thecomplement of stay responses) by experimental conditions.6 Table 5 presents the predicted cell counts based on the ordinalcomparison hypothesis version of the expectation advantages, the residuals between the observed cell counts and the expectedcell counts, and the Chi-squared components. The results indicate that the model does not fit the data (v2

ð10Þ ¼ 52:31;p < :001).The Chi-squared components indicate that the largest breakdown in fit is that there are fewer stay responses in condition 6 thanexpected under the model. Likewise, the Chi-squared components indicate that the second largest reason the model does not fitis that there are fewer trials in condition 1 in which the participants defer to their partner than expected.

Table 6 presents predicted cell counts from the model using Fisek’s (2009) conception of graded status characteristics toestimate the expectation advantages. The results of this model also suggest that it does not fit the data(v2ð10Þ ¼ 21:81; p ¼ :016), but the estimated Chi-squared statistic is substantially smaller than the Chi-squared for the ordinal

comparison hypothesis model. For the Fisek model, the Chi-squared components indicate that the largest breakdown in fitoccurs because fewer participants stayed with their initial opinions in condition 5 than predicted by the model. Likewise, thesecond largest breakdown in fit occurs in condition 6, but for the opposite reason: the model predicts fewer stay responsesthan were actually observed. Finally, Table 7 presents predicted cell counts from the model using Melamed’s (2011) concep-tion of graded status characteristics to estimate the expectation advantages. This model does not fit the data either(v2ð10Þ ¼ 25:32; p ¼ :005), but, again, it has a substantially smaller Chi-squared value than the model estimated under the

ordinal comparison hypothesis. Here the Chi-squared components indicate that condition 5 is the most problematic, withthe model predicting fewer stay responses and more deference trials than were observed.

Unfortunately the models based on conceptions of graded status characteristics are not nested in the model based on theordinal comparison hypothesis. All three models use a similar logic to generate estimates of the expectation advantages, but

6 Recall, if the participants did not make a final decision within ten seconds, they were unable to make a final choice. This is why the trials in Table 4 do notsum to factors of 20.

Table 6Predicted cell counts and chi-squared values for the Fisek model of graded characteristics.

Condition Predicted counts Residuals v2 Components

Defer to partner Stay response Defer to partner Stay response Defer to partner Stay response

1 (23,5) 100.90 306.10 �4.90 4.90 .24 .082 (5,23) 285.22 97.78 .78 �.78 .00 .013 (23,19) 133.67 237.33 �8.67 8.67 .56 .324 (9,5) 141.60 251.40 .40 �.40 .00 .005 (19,23) 244.11 141.89 32.89 �32.89 4.43 7.636 (5,9) 247.90 144.10 �27.90 27.90 3.14 5.40

v2 = 21.81

Table 7Predicted cell counts and chi-squared values for the Melamed model of graded characteristics.

Condition Predicted counts Residuals v2 Components

Defer to partner Stay response Defer to partner Stay response Defer to partner Stay response

1 (23,5) 94.46 312.54 1.54 �1.54 .02 .012 (5,23) 291.50 91.50 �5.50 5.50 .10 .333 (23,19) 140.02 230.98 �15.02 15.02 1.61 .984 (9,5) 148.32 244.68 �6.32 6.32 .27 .165 (19,23) 237.74 148.26 39.26 �39.26 6.48 10.406 (5,9) 241.43 150.57 �21.43 21.43 1.90 3.05

v2 = 25.32

D. Melamed / Social Science Research 42 (2013) 217–229 225

they all use two parameters estimated from the data (i.e., m and q) leaving no degrees of freedom with which to estimate atest of nested models. Consequently, evaluating the extent to which the graded models fit better than the ordinal model can-not be estimated using a simple test of full and constrained models (see e.g., Agresti, 2002; Powers and Xie, 2000). Rather, Inow turn to a test for non-nested contingency tables to evaluate the extent to which the estimates drawn from the gradedconceptions of status characteristics fit better than the ordinal comparison hypothesis model. Specifically I use a test for non-nested contingency tables that (Weakliem (1992), p. 161) calls the C test. The C test requires three steps: (1) Estimate thepredicted cell counts under two different models, and let f refer to the cell counts under the null model and let g refer tothe cell counts under the alternative model; (2) define a variable h = g � f, and then regress y � f on h using 1/f as a weight7

(where y refers to the observed cell counts); and, (3) Divide the coefficient for h by its standard error to obtain the C-statistic.8

The first C test that I estimated treats the model that uses the ordinal comparison hypothesis to estimate the expectationadvantages as the null and the model that uses Fisek’s (2009) conception of graded characteristics to estimate the expecta-tion advantages as the alternative. The results indicate that the estimates of expectation advantages based on Fisek’s gradedcharacteristics procedure fits the data better than estimates of expectation advantages based on the ordinal comparisonhypothesis (C = 3.776, p = .003). The second C test that I estimated uses the same null model, but uses Melamed’s (2011) con-ception of graded characteristics to estimate the expectation advantages for the alternative model. Again, the results indicatethat the estimates of expectation advantages based on Melamed’s graded characteristics procedure fits the data better thanestimates of expectation advantages based on the ordinal comparison hypothesis (C = 3.625, p = .004). Furthermore, treatingeither the Fisek model or the Melamed model as the null and using the other one as the alternative does not lead to a sig-nificant C test, indicating that they both fit the data equally well, at least within sampling variability.

In summary, the results from the experiment support the predictions. Both conceptions of graded status characteristicsexplain more variation in social influence than the ordinal comparison hypothesis. Unfortunately, none of the regressionmodels fit the data in a chi-squared sense, but the results of the C tests indicate that the models based on the graded statuscharacteristics fit the data significantly better than the model based on the ordinal comparison hypothesis.

10. Discussion

SCT predicts and explains such behaviors as social influence, participation, and evaluations of task-related contributions.Improving upon the formalisms of SCT by developing the means to include the additional information contained in gradedstatus characteristics increases the precision of predictions and explains more status-based inequalities. The graded charac-teristic procedures are not only applicable to SCT, but to the entire family of expectation state theories. Reward expectations

7 Here is the matrix solution to the estimated weighted coefficient: b = (XTWX)�1XTWY (Neter et al., 1996, p. 409), where X is a vector of h values (i.e., thereis no intercept), Y refers to the vector y � f, and W refers to a diagonal matrix with values 1/f on the diagonal.

8 I point out that all of the relevant information to compute the C statistics reported below is provided in Tables 4–7.

226 D. Melamed / Social Science Research 42 (2013) 217–229

theory (Berger et al., 1998), for example, argues that status differences lead to different reward expectations, which shapeanticipations of reward allocations. Procedures for graded status characteristics increase estimates of reward expectations,which aid in predicting perceptions of just rewards (Melamed, 2012). And as Jasso (1980) notes, the distribution of just re-wards is associated with factors such as societal stability and the likelihood of a revolution.

The results of the experiment described herein indicate that relative two-state comparisons of status differences are notsufficient to explain status-based inequalities. The results also suggest that modeling graded status characteristics is not suf-ficient to explain the status-based inequalities found in these data. However, modeling graded status characteristics doeslead to a significant improvement in model fit. By offering SCT a means to model graded status characteristics, the Fisek(2009) and the Melamed (2011) procedures increase the precision of models drawn from SCT. Consequently, SCT can betterpredict and ameliorate status-based inequalities.

The procedures developed by Fisek (2009) and Melamed (2011) are also consistent with the emerging social neuroscienceliterature on status processes (see Chiao (2010) for a review). Research in this area shows that social status is processed inthe same region of the brain as continuous dimensions, such as numerical estimations and estimates of size (Chiao et al.,2009). This research also shows that there is greater neural activity when processing close status comparisons relative tofar status comparisons, and the evidence suggests that this is not due to task difficulty, but is instead due to a ‘‘genuinereflection of internal representations for knowledge of social status hierarchy’’ (Chiao et al., 2009, p. 362). According tothe social neuroscience literature, then, status is processed in the same region of the brain as other continuous dimensions(Pinel et al., 2004), which implies that magnitudes of difference on status characteristics are neurologically processed, andthe results of the experiment reported herein shows the behavioral consequences of this process effect.

The Fisek (2009) model of graded status characteristics is a substantial advance for SCT. This procedure was the first tomodel graded status characteristics a priori within the existing mathematical structure of SCT. By modeling strong and weakcue gestalts, a characteristic may take on many levels of relevance, which indicates the relative strength of the characteristic.The procedure worked well for generating predictions for the experiment, particularly since there were only four status dif-ferences to model.9 In general, the procedure should work well in settings in which status differences can take on a discrete setof differences based on status cues, the question remains as to how to define the threshold whereby a weak cue gestalt becomesa strong one.

The Melamed (2011) model of graded status characteristics is also a substantial advance for SCT, allowing continuous andprecise predictions to be generated based on any number of graded and ungraded status characteristics. This framework isvery general, allowing analysts to assume any functional form on a graded status characteristic. This procedure also workedwell for generating predictions for the experiment, especially since the distributional information on contrast sensitivity wasprovided to the experimental participants.

Together, the Fisek (2009) and the Melamed (2011) conceptions of graded status characteristics offer analysts a menu ofprocedures with which to model collective task situations. That is, the procedures complement one another, and dependingon the salient information in a collective task group, can be used in isolation or even in conjunction. If an analyst can assume,for example, that characteristic a is salient, but this assumption is based on situational cues and subtleties, then character-istic a may best be modeled using the Fisek procedure. On the other hand, if characteristic b is salient and an analyst canassume that participants know specific states of the characteristic and roughly how it is distributed, then b may best be mod-eled by the Melamed procedure. If characteristics a and b are both salient, there is no reason that both procedures cannot beused together to estimate the expectation advantage.

Both procedures are quite flexible in the sense that they can both model multiple graded and/or ungraded status char-acteristics. Under the ordinal comparison hypothesis, the aggregation of multiple characteristics is done by combining func-tions of the paths from the graphic representation (see Eq (A1)–(A3). With the Fisek (2009) procedure, paths may simplybecome longer (as a result of weak cue gestalts), which does not change the computations. With the Melamed (2011) pro-cedure, each graded path may be computed, and then combined with other paths in the standard way. Furthermore, it doesnot matter if the characteristics are specific or diffuse status characteristics. In the present study, both procedures were usedto estimate the effects of a graded specific status characteristic. Quantitative diffuse status characteristics, such as IQ, age oroccupational prestige, may also be modeled as such.10

Adjudicating between the two procedures may prove difficult. It is unlikely that any combination of dyads will enablediscernible effect sizes. A more likely scenario in which the two procedures would be discernible is a situation where manyindividuals are differentiated by different states of a quantitative status characteristic. Then Melamed’s (2011) procedurecould draw relational estimates for every dyad in the larger group, which becomes important in the computation of expec-tation standings (Fisek et al., 1991). Recent research has extended SCT beyond the dyad (e.g., Kalkhoff et al., 2010), and moreresearch is needed in this area. As SCT moves in this direction, though, the ability to model several states of a status char-acteristic (rather than simply high and low states) will prove useful and may shed further light on this issue.

The Fisek (2009) and the Melamed (2011) procedures are also relevant to status interventions in applications of SCT. Re-search on status interventions shows that creating the positively evaluated state of a characteristic can offset the negativeconsequences of negatively evaluated states of characteristics (Cohen and Lotan, 1995) and that interventions of this sort

9 Conditions 3 and 4 had the same predictions, and so did conditions 5 and 6.10 See Melamed (2012) for an application that treats age and occupational prestige as normally distributed continuous characteristics and education as an

ordinally distributed characteristic.

Fig. A1. Graphic representation of the experimental situation. — = Possession relation, –– = dimensionality relation and ---- = relevance relation.

D. Melamed / Social Science Research 42 (2013) 217–229 227

persist to new task groups (Markovsky et al., 1984). Procedures that better represent the construct ‘‘expectation states’’ canbe used to more precisely estimate the amount of status disadvantage to overcome.

In summary, this paper reviewed two procedures for modeling graded status characteristics within the expectation statestradition. The results of an experiment were reported that shows that the graded characteristics procedures explain morevariation and fit the data better than the conventional two-state conception of social status. It was argued that the two pro-cedures should be used based on the amount of information that analysts can assume is salient in a collective task group.Finally, the procedures may aid in applications of SCT by better specifying the amount of status disadvantage to be overcome.

Acknowledgments

I thank Joseph Berger, Scott R. Eliason, M. Hamit Fis�ek, Will Kalkhoff, Linda D. Molm and Henry A. Walker for valuablefeedback and discussions pertaining to this manuscript. I also thank Ronald L. Breiger (DTRA Grant #HDTRA1-10-1-0017)and Linda Molm (NSF Grant #SES0814317) for their support. An earlier version of this paper was presented at the 2011 An-nual Meeting of the American Sociological Association in Las Vegas, NV. This research was supported by the National ScienceFoundation (SES-1029068) and the mathematical sociology section of American Sociological Association.

Appendix A. Estimating expectation advantages

The graphic representation of SCT visually represents the elements and relations found in the theory’s logical core. Thestatus situation found in the experiment is represented in Fig. A1. The participant (P) and her partner (O) are linked to dif-ferentially evaluated states of the instrumental task characteristic (C�) by the possession relation.11 The oppositely evaluatedstates of the instrumental task characteristic are linked by the dimensionality relation. Each of the states of the instrumentaltask characteristic is linked to a like-signed state of the task outcome (T) through the relevance relation, indicating that possess-ing the positively evaluated state of the instrumental task characteristic is supposed to lead to contributions toward task suc-cess, and that possessing the negatively evaluated state of the instrumental task characteristic is supposed to lead tocontributions toward task failure. The paths in the graphic representation have valences. All relations are positive, except forthe dimensionality relation, which is negative. The sign of the path is the product of the outcome state (either positive (T(+))or negative (T(�))) and the sign of the path (either positive or negative through the dimensionality relation). Thus P has a positivetwo-path (P � C�(+) � T(+)) and a positive three-path through the dimensionality bond (P � C�(+) � (�)C�(�) � T(�)). Graphic repre-sentations are necessarily symmetrical, implying that O has a negative two-path and a negative three-path (for more on theconstruction of graphic representations, please see: Berger et al., 1977, pp. 100–113).

Experimental evidence suggests that behavior in collective task groups unfolds as if individuals generate a positive subsetof status information, a negative subset of status information, and then combine the two subsets into an aggregate expec-tation state value (Berger et al., 1992). The equations for these two subsets are given in Eqs. (A1) and (A2). In (A1) and (A2), xrefers to a single individual in the graphic representation, f(i) refers to a function of a path of length i and f(n) refers to the nthor final path function. Eq. (A3) represents the aggregate expectation state value for actor x. Presently there are three ways toestimate the path functions (Balkwell, 1991a; Berger et al., 1977; Fisek et al., 1992). I focus on Fisek et al.’s (1992) path func-tion equations, but all three can be used to generate expectation advantages with the ordinal comparison hypothesis, oreither conception of graded status characteristics. Eq. (A4) presents the Fisek et al. path function equation in its general form.

11 Theon a ma

eþx ¼ ½1� ð1� f ðiÞÞ � � � ð1� f ðnÞÞ� ðA1Þ

e�x ¼ �½1� ð1� f ðiÞÞ � � � ð1� f ðnÞÞ� ðA2Þ

ex ¼ eþx þ e�x ðA3Þ

f ðiÞ ¼ 1� e�2:6182�i ðA4Þ

instrumental task characteristic is a specific status characteristic that is the ability which relays competence at the groups’ task. If the group is workingth problem, for example, then mathematics ability is the instrumental task characteristic.

Fig. A2. Graphic representation of the conditions in the experiment requiring weak cue gestalts. — = Possession relation, –– = dimensionality relation and----- = relevance relation.

228 D. Melamed / Social Science Research 42 (2013) 217–229

Using Eq. (A4), we can generate the path functions from the graphic representation presented in Fig. A1. In Fig. A1, P has apositive two-path and a positive three-path. Substituting 2 for i in Eq. (A4) yields .632 and substituting 3 for i yields .317.12

Thus P’s positive subset is [1 � (1 � .632)(1 � .317)] = .749, and because P has no negative paths, P’s negative subset is 0. There-fore P’s aggregate expectation state value is .749. Through symmetry, the exact opposite is true for O, who has an aggregateexpectation state value of �.749. P’s expectation advantage is found by subtracting O’s aggregate expectation state value fromP’s aggregate expectation state value. Thus in conditions 1, 3, and 4 P’s expectation advantage is 1.498, and in conditions 2, 5,and 6 it is �1.498 (i.e., �.749 � .749).

For the Fisek (2009) conception of graded status characteristics, the same estimates of P’s expectation advantage are com-puted for conditions 1 and 2, which are the conditions that constitute strong cue gestalts. For the conditions warrantingweak cue gestalts, the graphic representations of these conditions is presented in Fig. A2 (see Fisek et al., 2005, p. 89). Notethat where P had a positive two-path and a positive three-path before, P now has a positive three-path and a positive four-path. It is important to point out that weak cue gestalts need not be symmetrical. It may be the case that P definitely has thepositively evaluated state of a characteristic (through a strong cue gestalt), but O may have the negatively evaluated state(through a weak cue gestalt). However, because of the relatively small difference between P’s contrast sensitivity scoreand O’s contrast sensitivity score in conditions 3–6, I argue that this characteristic operates through weak cue gestalts forboth actors. Thus, substituting a 3 for i in Eq. (A4) yields .317 and substituting a 4 for i yields .136, which when plugged intothe positive subset equation yields .410. Since P has no negative status information in conditions 3 and 4, P’s aggregateexpectation state value is .410. Through symmetry, O’s expectation state value is �.410, making P’s expectation advantageover O .820. P’s expectation advantage in conditions 3 and 4 is .820, and in conditions 5 and 6 it is �.820.

For the Melamed (2011) conception of graded status characteristics the graphic representation does not change for any ofthe conditions. Rather, Melamed developed a new set of path function equations which explicitly incorporate the magnitudeof difference between interactants on the graded characteristic. Eq. (A5) presents Melamed’s equation for graded path func-tions within the context of Fisek et al.’s (1992) original path function equations, where f(ig) refers to the path function for agraded status characteristic, zp and zo refer to standardized scores on the quantitative status characteristic, and U refers to acumulative distribution function.13

12 See13 The

standar

f ðigÞ ¼ 1� e� 2:168ð3�ðiþ½2�2� ½Ufzpg�Ufzog��ÞÞ½ � ðA5Þ

In condition 1, P had a contrast sensitivity score of 23 and O had a 5. Considering that contrast sensitivity is normally dis-tributed with a standard deviation of 3, the area separating P and O is .997. Substituting .997 for [U{zp} �U{zo}] and 2 for iyields .926, and then using the same weight with 3 for i yields .630. P’s positive subset is then[1 � (1 � .926)(1 � .630)] = .973, and P’s negative subset is 0. Therefore P’s aggregate expectation state is .973 and, throughsymmetry, O’s expectation state value is �.973. So P’s expectation advantage in condition 1 is 1.946, and it is �1.946 in con-dition 2. In conditions 3 and 4, the graded characteristics weight (i.e., [U{zp} �U{zo}]) is the same because the normal dis-tribution is symmetrical. In these conditions the weight, or the area separating P and O, is .046. Using this weight and solvingfor the two-path yields .341 and then solving for the three-path yields .147. P’s positive subset in conditions 3 and 4 is then[1 � (1 � .341)(1 � .147] = .438. Again, P has no negative status information in conditions 3 and 4 so P’s aggregate expecta-tion state value is .438 and O’s is �.438. Therefore P’s expectation advantage is .876 in conditions 3 and 4, and through sym-metry, it is �.876 in conditions 5 and 6. The estimated expectation advantages reported in this appendix may be used inconjunction with the regression models in Table 3 to generate the predicted P(s) values for the six conditions.

References

Agresti, Alan, 2002. Categorical Data Analysis. Wiley, Hoboken, NJ.Bales, Robert F., 1950. Interaction Process Analysis: A Method for the Study of Small Groups. Addison-Wesley, Cambridge, MA.Bales, Robert F., Slater, Philip, 1955. Role differentiation in small decision making groups. In: Parsons, T., Bales, R.F. (Eds.), Family, Socialization, and

Interaction Process. The Free Press, Glencoe, IL, pp. 259–306.Balkwell, James W., 1991a. Status characteristics and social interaction. Advances in Group Processes 8, 135–176.Balkwell, James.W., 1991b. From expectations to behaviors: an improved postulate for expectation states theory. American Sociological Review 56, 355–

369.

the author’s website for an excel workbook that does all of these calculations.oretically any cumulative distribution function (CDF) could be used. Melamed (2012) analyzed continuous status characteristics using the CDF for thed unit normal distribution and also analyzed ordinal status characteristics using the cumulative mass function.

D. Melamed / Social Science Research 42 (2013) 217–229 229

Balkwell, James, 2001. How do actors in task-oriented situations process finely graded differences in ability? Sociological Focus 34 (1), 97–115.Berger, Joseph, 2007. The standardized experimental situation in expectation states research: notes on history, uses, and special features. In: Webster, M.,

Sell, J. (Eds.), Laboratory Experiments in the Social Sciences. Elsevier, New York, pp. 353–378.Berger, Joseph, Fisek, Hamit, 1970. Consistent and inconsistent status characteristics and the determinations of power and prestige orders. Sociometry 33

(3), 287–304.Berger, Joseph, Webster, Murray, 2006. Expectations, status, and behavior. In: Burke, P. (Ed.), Contemporary Social Psychological Theories. Stanford

University Press, Palo Alto, CA.Berger, Joseph, Zelditch, Morris, Cohen, Bernard, 1966. Status characteristics and expectation states. In: Berger, J., Zelditch, M., Anderson, B. (Eds.),

Sociological Theories in Progress, vol. 1. Houghton Mifflin, Boston, pp. 29–46.Berger, Joseph, Cohen, Bernard, Zelditch, Morris, 1972. Status characteristics and social interaction. American Sociological Review 37, 241–255.Berger, Joseph, Hamit Fisek, M., Freese, Lee, 1976. Paths of relevance and the determination of power and prestige orders. Pacific Sociological Review 19, 45–

62.Berger, Joseph, Hamit Fisek, M., Norman, Robert, Zelditch Jr., Morris, 1977. Status Characteristics and Social Interaction: An Expectations States Approach.

Elsevier, New York.Berger, Joseph, Rosenholtz, Susan, Zelditch Jr., Morris, 1980. Status organizing processes. Annual Review of Sociology 6, 479–508.Berger, Joseph, Balkwell, James, Norman, Robert, Smith, Roy, 1992. Status inconsistency in task situations: a test of four status processes principles.

American Sociological Review 57 (6), 843–855.Berger, Joseph, Hamit Fisek, M., Norman, Robert, Wagner, David, 1998. Formation of reward expectations in status situations. In: Berger, J., Zelditch, M.

(Eds.), Status, Power, and Legitimacy. Transaction Publishers, New Brunswick, NJ, pp. 121–153.Bielby, William, 2001. The structure and process of sex segregation. In: Grusky, D. (Ed.), Social Stratification in Sociological Perspective. Westview, Boulder,

CO, pp. 703–713.Blau, Peter, 1977. Inequality and Heterogeneity. Free Press, New York.Bose, Christine E., Rossi, Peter H., 1983. Gender and jobs: prestige standings of occupations as affected by gender. American Sociological Review 48, 316–

330.Chiao, Joan Y., 2010. Neural basis of social status hierarchy across species. Current Opinion in Neurobiology 20, 803–809.Chiao, Joan Y., Harada, Tokiko, Oby, Emily R., Li, Zhang, Parrish, Todd, Bridge, Donna J., 2009. Neural representations of social status hierarchy in human

inferior parietal cortex. Neuropsychologia 47, 354–363.Cohen, Elizabeth, Lotan, Rachel, 1995. Producing equal-status interaction in the heterogeneous classroom. American Educational Research Journal 32 (1),

99–120.Coleman, James, 1986. Social theory, social research, and a theory of action. American Journal of Sociology 91 (6), 1309–1335.Correll, Shelley, Ridgeway, Cecilia, 2003. Expectation states theory. In: Delamater, J. (Ed.), Handbook of Social Psychology. Kluwer, New York.Driskell, James, Mullen, Brian, 1990. Status, expectations, and behavior: a meta-analytic review and test of the theory. Personality and Social Psychology

Bulletin 16, 541–553.Fisek, Hamit, 2009. Status cues, standards for competence, and graded characteristics. In: Paper Presented at the Annual Meeting of the American

Sociological Association, August, San Francisco, CA.Fisek, Hamit, Berger, Joseph, Norman, Robert, 1991. Participation in heterogeneous and homogeneous groups: a theoretical integration. American Journal of

Sociology 97 (1), 114–142.Fisek, Hamit, Norman, Robert, Nelson-Kilger, Max, 1992. Status characteristics and expectations states theory: a priori model parameters and test. Journal of

Mathematical Sociology 16, 285–303.Fisek, Hamit, Berger, Joseph, Norman, Robert, 2005. Status cues and the formation of expectations. Social Science Research 34 (1), 80–102.Fiske, Susan T., 2000. Stereotyping, prejudice, and discrimination at the seam between the centuries: evolution, culture, mind, and brain. European Journal

of Social Psychology 30, 299–322.Fiske, Susan T., Taylor, Shelley, 2008. Social Cognition: From Brains to Culture. McGraw-Hill, New York.Foddy, Margaret, Smithson, Michael, 1996. Relative ability, paths of relevance, and influence in task-oriented groups. Social Psychology Quarterly 59 (2),

140–153.Gibbons, Jean D., 1993. Nonparametric Statistics: An Introduction. Sage, Thousand Oaks, CA.Jasso, Guillermina., 1980. A new theory of distributive justice. American Sociological Review 45, 3–32.Kalkhoff, William, Thye, Shane, 2006. Expectation states theory and research. Sociological Methods and Research 35 (2), 219–249.Kalkhoff, William, Friedkin, Noah, Johnsen, Eugene, 2010. Status, networks and opinions: a modular integration of two theories. In: Thye, S. (Ed.), Advances

in Group Processes. JAI Press, New York, pp. 1–38.Kohn, Melvin L., Schooler, Carmi, 1983. Work and Personality. Ablex, Norwood, NJ.Lawler, Edward, Ridgeway, Cecilia, Markovsky, Barry, 1993. Stuctural social psychology and the micro- macro problem. Sociological Theory 11 (3), 268–290.Lovaglia, Michael, Lucas, Jeff, Houser, John, Thye, Shane, Markovsky, Barry, 1998. Status processes and mental ability test scores. American Journal of

Sociology 104 (1), 195–228.Markovsky, Barry, Smith, LeRoy, F., Berger, Joseph, 1984. Do status interventions persist. American Sociological Review 49, 373–382.Massey, Douglas, 2007. Categorically Unequal: The American Stratification System. Sage, Thousand Oaks, CA.Melamed, David, Walker, Henry A., 2010. Graded status characteristics and expectation states. In: Paper Presented at the 22nd Annual Group Processes

Conference, August, Atlanta, GA.Melamed, David, 2011. Graded status characteristics and expectation states. In: Thye, S., Lawler, E. (Eds.), Advances in Group Processes. Emerald Group,

Cambridge, MA, pp. 1–31.Melamed, David, 2012. Deriving equity from expectations: a cross-cultural evaluation. Social Science Research 41 (1), 170–181.Moore, James, 1968. Status and influence in small group interactions. Sociometry 31, 47–63.Neter, John, Kutner, Michael, Nachtsheim, Christopher, Wasserman, William, 1996. Applied Linear Statistical Models. McGraw Hill, New York.Pinel, Phillippe, Piazza, Manuela, Le Bihan, Denis, Dehaene, Stanislas, 2004. Distributed and overlapping cerebral representations of number, size, and

luminance during comparative judgements. Neuron 41, 983–993.Powers, Daniel A., Xie, Yu, 2000. Statistical Methods for Categorical Data Analysis. Academic Press, San Diego, CA.Ridgeway, Cecilia, 1991. The social construction of status value: gender and other nominal characteristics. Social Forces 70, 367–386.Ridgeway, Cecilia, 2011. Framed by Gender: How Gender Inequality Persists in the Modern World. Oxford University Press, New York.Ridgeway, Cecilia L., Correll, Shelley J., 2006. Consensus and the creation of status beliefs. Social Forces 85 (1), 431–453.Shelly, Robert, 1998. Some developments in expectation states theory: graduated expectations? Advances in Group Processes 15, 41–57.Steele, Claude, Aronson, Joshua, 1995. Stereotype threat and the intellectual test performance of African Americans. Journal of Personality and Social

Psychology 69 (5), 797–811.Strodtbeck, Fred, Mann, Richard, 1956. Sex role differentiation in jury deliberations. Sociometry 19 (1), 3–11.Wagner, David, Berger, Joseph, 1998. Gender and interpersonal task behavior: status expectation accounts. In: Berger, J., Zelditch, M. (Eds.), Status, Power

and Legitimacy: Strategies and Theories. Transaction, New Brunswick, NJ, pp. 229–261.Weakliem, David L., 1992. Comparing non-nested models for contingency tables. Sociological Methodology 22, 147–178.Webster, Murray, Driskell, James E., 1983. Beauty as status. American Journal of Sociology 89 (1), 140–165.Webster, Murray, Whitmeyer, Joseph, Rashotte, Lisa Slattery, 2004. Status claims, performance expectations, and inequality in groups. Social Science

Research 33, 724–745.