Measuring Group-Level Psychological Properties (A Tribute to Larry James) Daniel A. Newman University of Illinois Daniel A. Newman, Ph.D. 1 Overview Group-Level Psychological Properties? 1. Psychological Climate Group-Level vs. Individual-Level Constructs 2. Aggregation Bias 3. Why we need rWG (Within-group agreement) Justifying Aggregation 4. rWG(J) for multi-item scales Agreement vs. Reliability 2 Overview Group-Level Psychological Properties? 1. Psychological Climate James & Jones (1974), Jones & James (1979), James & Sells (1981), James (1982), James et al. (1988), James & James (1989) 2. Aggregation Bias James (1982), James et al. (1980) 3. Why we need rWG (Within-group agreement) James (1982), James, Demaree, & Wolf (1984; 1993), George & James (1993) 4. rWG(J) for multi-item scales 3 James, Demaree, & Wolf (1984), LeBreton, James, & Lindell (2005) Overview Group-Level Psychological Properties? 1. Psychological Climate James & Jones (1974), Jones & James (1979), James & Sells (1981), James (1982), James et al. (1988), James & James (1989) 2. Aggregation Bias James (1982), James et al. (1980) 3. Why we need rWG (Within-group agreement) James (1982), James, Demaree, & Wolf (1984; 1993), George & James (1993) 4. rWG(J) for multi-item scales 4 James, Demaree, & Wolf (1984), LeBreton, James, & Lindell (2005) Quotes & Equations In summarizing Larry James’s contributions to Multilevel Theory, I’ll use a two-pronged approach: 1. Quotes 2. Equations 5 Quotes & Equations In summarizing Larry James’s contributions to Multilevel Theory, I’ll use a two-pronged approach: 1. Quotes 2. Equations rWG 1 (s x2j E2 ) 6 Levels of Analysis • In social science, hypothetical constructs reside at multiple levels of analysis (or levels of aggregation): – National Level: Culture – Organizational Level: Organizational Climate, CEO personality, Strategy – Team Level: Team efficacy, Norms, Leader style – Individual Level: Attitude, Personality, Job Performance, Psychological Climate 7 Levels of Analysis Organizational Group Individual 8 Levels of Analysis • Individuals are nested within Groups • Groups are nested within Organizations • One level can influence another – Group norms influence individual behavior – Individual behaviors aggregate to produce group/team performance 9 Psychological Climate • Psychological Climate – ‘the meaning an individual attaches to a work environment’ • Organizational Climate – ‘the aggregated meaning; i.e., the typical, average, or usual way people in a setting [work environment] describe it’ • Schneider (1981, pp. 4-5), as cited by James (1982) 10 Psychological Climate • Psychological Climate – individual level construct • Organizational Climate – group level construct 11 Psychological Climate • “… perceptual agreement implies a shared assignment of psychological meaning, from which it follows that an aggregate (mean) climate score provides the opportunity to describe an environment in psychological terms.” • “Furthermore, given perceptual agreement, I submit that a climate construct at the aggregate level is defined in precisely the same manner as it is at the individual level.” • James (1982, p. 221) 12 Psychological Climate Relationship between organizational climate and psychological climate: OC average(PC) • PC = psychological climate perception of person in a group • OC = organizational climate of the group 13 Psychological Climate Relationship between organizational climate and psychological climate: ng OC0 g PCpg ng p 1 • PCpg = psychological climate perception of person p in group g • OC0g = organizational climate in group g 14 Psychological Climate Relationship between organizational climate and psychological climate: PCpg OC0 g u pg • PCpg = psychological climate perception of person p in group g • OC0g = organizational climate in group g • upg = deviation of person p’s individual psych. climate perception from group g’s org. climate 15 Psychological Climate James & Jones (1974), reviewed 3 approaches to conceptualize & measure org. climate: 1) Org.-Level Attribute, Multiple Measures 2) Org.-Level Attribute, Perceptual Measures 3) Indiv.-Level Attribute, Perceptual Measures* * Introduced the term, “Psychological Climate” 16 James & Jones (1974) • “Returning to the perceptual definition of organizational climate, it would seem that the reliance on perceptual measurement may be interpreted as meaning that organizational climate includes not only descriptions of situational characteristics, but also individual differences in perceptions and attitudes. This is somewhat confusing if one wishes to employ organizational climate as an organizational attribute or main effect, since the use of perceptual measurement introduces variance which is a function of differences between individuals and is not necessarily descriptive of organizations or situations. Therefore, the accuracy and/or consensus of perception must be verified if accumulated perceptual organizational climate measures are used to describe organizational 17 attributes (Guion, 1973).” (p. 1103) Jones & James (1979) • “The [conceptual] argument for aggregating perceptually based climate scores (i.e., psychological climate scores) appears to rest heavily on three basic assumptions: first, that psychological climate scores describe perceived situations; second, that individuals exposed to the same set of situational conditions will describe these conditions in similar ways; and third, that aggregation will emphasize perceptual similarities and minimize individual differences. Based on this logic, it is generally presumed that empirically demonstrated agreement among different perceivers implies that these perceivers have experienced common situational conditions (Guion, 1973; Insel & Moos, 1974; James & Jones, 1974; Schneider, 1975a),” • (p. 206). 18 James & Jones (1974) • “Although this school of thought [from Schneider and others] assumes that situational and individual characteristics interact to produce a third set of perceptual, intervening variables, such an assumption does not mean that perceived climate is different from an individual attribute. Rather, the intervening variables are individual attributes which provide a bridge between the situation and behavior.” • (p. 1107) • So … “Psychological Climate” is born! 19 James (1982) • “current thinking in climate suggests that the unit of theory for climate, including organizational climate, is the individual, and the appropriate unit to select for observation is the individual. This thinking is based on the view that climate involves a set of macro perceptions that reflect how environments are cognitively represented in terms of their psychological meaning and significance to the individual.” • (p. 219) • So … measuring organizational climate (an org.-level attribute) involves an individuallevel true score (i.e., psychological climate). 20 James et al. (1988) • “Shared assignment of meaning justifies aggregation to a higher level of analysis (e.g., groups, subsystems, organizations) because it furnishes a way of relating a construct (PC) that is defined and operationalized at one level of analysis (the individual) to another form of the construct at a different level of analysis (e.g., group climate, subsystem climate, OC). Although the unit of analysis for the aggregate psychological variable is the situation (e.g., group, subsystem, organization), the definition and basic unit of theory remains psychological.” • (p. 130, from Organizations Do Not Cognize) 21 James & James (1989) General PC .85 Leader Support .86 Role Stress, Conflict, Ambiguity .77 .81 Job Autonomy, Challenge - PC = Cognitive evaluation of work environment - See James & Sells (1981), Jones & James (1979) Group Warmth & Cooperat. 22 Psychological Climate Psych. Climate Job Satisfaction /Affect - Reciprocal relationship between PC and Job Satis./Affect 23 - James & Tetrick (1986), James & James (1992) Psychological Climate Summary: • There is a group-level organizational reality (“the situation”) • That reality is reflected in individual-level, psychological perceptions • The individual-level psychological climate perceptions are a meaningful locus of theory • The individual perceptions can be aggregated to represent a group-level, psychological 24 property [if perceptions are shared] Aggregation Bias Aggregation – combining micro-level data so it can represent the macro-level (typically, by taking an average of micro-level responses) • The aggregate of individuals’ scores represents the group-level construct 25 Levels of Analysis Organizational Group Individual 26 Aggregation • Ecological fallacy – generalizing group-level (aggregate) results to the individual level – Because we know group collectivism is related to grouplevel cooperation, we inaccurately assume individual collectivism is related to individual cooperativeness. • Atomistic fallacy – generalizing individuallevel results to the group (aggregate) level – Because we know indiv. IQ is strongly related to indiv.level job performance, we inaccurately assume group IQ is strongly related to group performance. 27 Aggregation The Truth about Aggregates: • If the individual-level correlation between X and Y is rindiv. = .3, this does not imply that the group-level correlation between X and Y is rgroup = .3. • Likewise, if the group-level correlation between X and Y is rgroup = .3, this does not imply that the individual-level correlation between X and Y is rindiv. = .3. 28 Aggregation Direction of a correlation (+ or -) can change when we move from the individual level to the group level. Within-Group Correlation Between-Group Correlation Y X 29 Aggregation Example) Foreign birth & Illiteracy (Robinson, 1950). rindiv. = .12; rgroup(states) = -.53 Within-Group Correlation Between-Group Correlation Y X 30 Aggregation Total correlation is a combination of the individuallevel correlation and the group-level correlation. Within-Group Correlation Between-Group Correlation rwithin Y Total Correlation X rtotal rbetween 31 Aggregation • Total correlation is a combination of the individual-level (within) correlation and the group-level (between) correlation. rtotal f (rbetween, rwithin ) 32 Aggregation • Specifically, rtotal rbetween ( x y ) rwithin (1 )(1 ) 2 x 2 y • rtotal = overall X-Y correlation, ignoring group membership • rbetween = between-groups X-Y correlation • rwithin = within-groups X-Y correlation • x2 SSbetween SStotal (from ANOVA; DV= X, IV= group) [like R2; variance in X accounted for by group membership, then inflated by the 33 2 unreliability of group means; i.e., x ICC(1) / ICC(2) .] Aggregation • For example, suppose • rbetween = -.45 = between-groups X-Y correlation • rwithin = .20 = within-groups X-Y correlation 2 • x = .64 (from ANOVA; DV= X, IV= group) 2 • y = .81 (from ANOVA; DV= Y, IV= group) Then … rtotal rbetween ( x y ) rwithin (1 )(1 ) 2 x 2 y rtotal .45( .64 .81) .20 (1 .64)(1 .81) .27 34 Aggregation • For example, suppose • rbetween = -.45 = between-groups X-Y correlation • rwithin = .20 = within-groups X-Y correlation 2 • x = .64 (from ANOVA; DV= X, IV= group) 2 • y = .81 (from ANOVA; DV= Y, IV= group) Then … rtotal rbetween ( x y ) rwithin (1 )(1 ) 2 x 2 y rtotal .45( .64 .81) .20 (1 .64)(1 .81) .27 35 Aggregation Total correlation is a combination of the individuallevel correlation and the group-level correlation. Within-Group Correlation Between-Group Correlation rwithin Y Total Correlation X rtotal rbetween 36 Aggregation Implications: • Even if total correlation between X and Y (rtotal) is statistically significant, – rwithin might not be – rbetween might not be * Many studies in top journals report total relationships between variables, while ignoring nesting/ nonindependence (e.g., different groups, different jobs, different supervisors). Considering levels of 37 analysis could potentially change the results! Aggregation Implications: • So-called “aggregation bias” – when rbetween is larger than rtotal – Only occurs if rbetween happens to be larger than rwithin rtotal rbetween ( x y ) rwithin (1 )(1 ) 2 x 2 y 38 Aggregation Bias Implications: • Don’t look at rtotal to draw inferences about rwithin! • Don’t look at rtotal to draw inferences about rbetween! rtotal rbetween ( x y ) rwithin (1 )(1 ) 2 x 2 y • See James (1982) and James, Demaree, & Hater (1980), who applied similar formulae to estimate bias in both 2 and corr.’s between aggregated situational (OC) and individual 39 difference variables. Aggregation Bias Summary: • When we aggregate individual-level measures (e.g., psychological climate) to represent organizational attributes (e.g., organizational climate), then all the theoretical and empirical relationships can change. • Aggregation of the same measures can create a different construct! 40 Why We Need rWG • Justifying Aggregation • “… organizational climate is the overall meaning derived from the aggregation of individual perceptions of a work environment (i.e., the typical or average way people in an organization ascribe meaning to that organization) (James, 1982; Schneider, 1981). Thus, organizational climate can be viewed as the outcome of aggregating individuals’ psychological climates. The important caveat is that these psychological climates are shared in order to make the inference that an organizational climate exists.” • James et al. (2008, pp. 15-16) 41 Why We Need rWG Group-Level Consensus Constructs • In measuring group consensus constructs, agreement and reliability are tools used to justify aggregation of individual-level responses to the group level • Agreement and reliability help us gauge how well the average across individual responses represents the group. 42 Why We Need rWG Group-Level Consensus Constructs Organizational Climate (average) Psych. Climate, Person #1 Psych. Climate, Person #2 Psych. Climate, Person #3 43 Why We Need rWG Overview • Aggregation/Composition Models – Chan (1998) – Kozlowski & Klein (2000) • Agreement – rWG family of indices • Reliability – ICC(1) – ICC(2) See Bliese, 2000 44 Why We Need rWG • Aggregation/Composition Models – Chan (1998) – Kozlowski & Klein (2000) • Both typologies include consensus models – Use the mean of individual responses to represent the group-level construct – Assume isomorphism (James, 1982) – Require high within-group agreement 45 Why We Need rWG • Within-Group Agreement – degree to which ratings from individuals are interchangeable – Agreement-based tests reflect degree to which raters provide essentially the same rating – Three dominant indices designed to assess withingroup agreement: • James et al.’s (1984) rWG(J) * r • Lindell et al.’s (1999) WG ( J ) • Burke, Finkelstein, & Dusig’s (1999) AD index 46 George & James (1993) • “The key statistical test of the appropriateness of aggregation to the group level of analysis is that there is within-group agreement on the variable in question. If there is agreement within groups on the theorized group-level variable, then the aggregate may be used in subsequent analyses.” • … agreement within a group is not conditional on betweengroups differences. For example, in a scenario that Yammarino and Markham portray, in which all members in each group have the same moderately high score, both agreement and aggregation may be justified provided that aggregation to the group level was theoretically based. However, there would be no group effect inasmuch as the group means do not vary under these conditions.” 47 • (p. 799) Why We Need rWG • Within-Group Agreement – For single items: rWG 1 (s x2j E2 ) – s x2j = observed variance of single item – = theoretical null variance (represents “zero agreement”) 2 E – rWG = “1 - observed variance over expected variance” 48 Why We Need rWG Summary: • Under consensus composition models (with isomorphism across levels), within-group agreement is needed to justify aggregation. • Within-group agreement is even more essential than ICC(1) and ICC(2), both of which depend upon between-group variance. • Within-group agreement = shared psychological meaning! • rWG is the key to measuring group-level psychological properties! 49 rWG(J) for Multi-Item Scales rWG(J) is NOT the same as rWG! • rWG = for single items rWG 1 (s x2j E2 ) • rWG(J) = for multiple-item climate scale rWG ( J ) J [1 (s J [1 (s 2 xj 2 xj )] 2 E )] (s 2 E 2 xj ) 2 E 50 rWG(J) for Multi-Item Scales • Within-Group Agreement (James et al., 1984) – For multiple items: rWG ( J ) J [1 (s J [1 (s 2 xj 2 xj )] 2 E )] (s 2 E 2 xj ) 2 E – J = number of items – s x2 = mean of observed item-level variances j 2 – E = theoretical null variance (represents “zero agreement”) † Can be derived without Spearman-Brown (LeBreton et al., 2005) 51 rWG(J) for Multi-Item Scales • Three Issues with James et al.’s (1984) rWG(J) : 1) J = number of items (is rWG(J) an index of agreement, reliability, or both?) 2) s 2 xj = mean of observed item-level variances 2 3) E = theoretical null variance (represents “zero agreement”) (addressed by LeBreton & Senter, 2008) 52 James et al. (1993) • Describing whether rWG(J) is an index of agreement vs. reliability: • “Kozlowski and Hattrup are also correct in stating that our intention was to suggest a measure of agreement, and not consistency [reliability], and that rWG is an estimator of agreement. However, what cannot be done, at least not the way things are presently set up, is to follow Kozlowski and Hattrup's recommendation to sever all ties between interrater reliability and rWG and to treat rWG as strictly a measure of agreement with, in effect, no ties to classic measurement theory. It is not possible to follow this recommendation because rWG is currently derived in terms of classic measurement theory as an interchangeability (agreement) index of interrater reliability.” 53 • (p. 306) rWG(J) for Multi-Item Scales • Issues with James et al.’s (1984) rWG(J) : – J = number of items • What happens to rWG(J) as number of items (J) increases? rWG ( J ) J [1 (s J [1 (s 2 Xj 2 Xj )] 2 E )] (s 2 E 2 Xj ) 2 E 54 rWG(J) for Multi-Item Scales • Issues with James et al.’s (1984) rWG(J) : – J = number of items • What happens to rWG(J) as number of items (J) increases? rWG ( J ) J [1 (s J [1 (s 2 Xj 2 Xj )] 2 E )] (s 2 E 2 Xj ) 2 E 55 rWG(J) for Multi-Item Scales • Issues with James et al.’s (1984) rWG(J) : 1 0.9 James et al.'s rWG(J) 0.8 0.7 0.6 0.5 0.4 mean_itemvar = 0.2 0.3 mean_itemvar = 0.6 0.2 mean_itemvar = 1 mean_itemvar = 1.4 0.1 mean_itemvar = 1.8 0 1 3 7 Number of Items (J) 11 20 56 rWG(J) for Multi-Item Scales • Issues with James et al.’s (1984) rWG(J) : 1 rWG(J) = .7 0.9 James et al.'s rWG(J) 0.8 0.7 0.6 s x2 j 0.5 0.4 mean_itemvar = 0.2 0.3 mean_itemvar = 0.6 0.2 mean_itemvar = 1 mean_itemvar = 1.4 0.1 mean_itemvar = 1.8 J 0 1 3 7 Number of Items (J) 11 20 57 rWG(J) for Multi-Item Scales • Issues with James et al.’s (1984) rWG(J) : – To get a large rWG(J) (James et al., 1984), simply add more items to your scale!! – Even under near-maximal within-group variance, 2 s [ x = 1.8] rWG(J) = .7 when the scale has J = 20 items! j 58 rWG(J) for Multi-Item Scales • Issues with James et al.’s (1984) rWG(J) : – s x2 = mean of observed item-level variances j • What is it? • First calculate the within-group variance of each item, 2 • Then average these variances across items, s x j 59 s x2j rWG(J) for Multi-Item Scales • s x2 j = mean of observed item-level variances Compare s 2 xj vs. 2 x s (scale score variance): Scale score variance sx2 => • First calculate mean across items (i.e., scale score), x 2 • Then take the within-group variance of scale score, sx s s [ J ( J 1)] 2 xj • s 2 xj 2 x is almost always larger than s 2 x 60 rWG(J) for Multi-Item Scales • Why is s x2 j almost always larger than scale score variance sx2 ? Psych. Climate True Score Variance PC Item 1 d1 PC Item 2 d2 PC Item 3 d3 PC Item 4 d4 Item Unique 61 Variance rWG(J) for Multi-Item Scales • Why is s x2 j almost always larger than scale score variance sx2 ? Psych. Climate True Score Variance s 2 x s PC Item 1 d1 PC Item 2 d2 PC Item 3 d3 PC Item 4 d4 2 xj Item Unique 62 Variance rWG(J) for Multi-Item Scales • s x2 j = mean of observed item-level variances Compare s s 2 xj vs. 2 x s (scale score variance): 2 , Scale score variance => zooms in on true, construct-level x variance within-groups vs. s x2 j , Mean of observed item-level variances => includes true construct-level variance + item-specific variance s s [ J ( J 1)] 2 xj 2 x 63 rWG(J) for Multi-Item Scales • Issues with James et al.’s (1984) rWG(J) : – s x2 = mean of observed item-level variances j • It would be much clearer to just base withingroup agreement on the within-group variance in scale scores, s x2j rather than on the average of item-level within-group variances, s 2 . xj 64 rWG(J) for Multi-Item Scales • Issues with James et al.’s (1984) rWG(J) : – = theoretical null variance (represents “zero agreement”) 2 E 2 EU ( A2 1) 12 – E.g., Uniform null distribution – A = number of response options (e.g., A = 5 for a 5point Likert scale); 2 EU (52 1) 12 2 65 rWG(J) for Multi-Item Scales • Issues with James et al.’s (1984) rWG(J) : E2 = theoretical null variance – Can alternatively use a non-uniform expected null variance for rWG(J) (see James et al., 1984; LeBreton & Senter, 2008) • Normal null dist. • Skewed null dist. • Maximum null dist. (Brown & Hauenstein, 2005) 66 rWG(J) for Multi-Item Scales • Issues with James et al.’s (1984) rWG(J) : E2 = theoretical null variance – Can alternatively use an Average Deviation index (AD; average absolute value deviation from mean or median; Burke et al., 1999). • Less vulnerable to outliers • Still compared against arbitrary cutoff, AD < A/6 2 • Still includes item-specific variance (like s x j ) 67 rWG(J) for Multi-Item Scales Summary: • Whereas rWG is a great index of standardized within-group agreement, rWG(J) reflects 3 sources of variance: a) within-group variance in psych. climate/latent construct true scores (“shared meaning”), plus b) item-specific variance (in s x2 ), and c) number of items (J). j • It would be better to use an agreement index that homes in on (a) within-group variance in psych. climate/latent construct true scores 68 (“shared psychological meaning”). Within-Group Agreement • So what is the alternative? 69 Within-Group Agreement • What if we still want to assess within-group agreement (“shared psychological meaning”) with a multi-item climate scale? • First, conceptualize the degree of “shared psychological meaning” at the latent theoretical level (James, 1982; James et al., 1988), but use a format similar to rWG: (2psych.c limate) WG 1 2 E 70 Within-Group Agreement • WG does not increase as you add items to the climate scale (i.e., it is a pure parameter of within-group agreement, not reliability) WG 1 2 ( psych.c limate) 2 E 71 Within-Group Agreement • How well does each of the following withingroup agreement indices estimate WG? (“shared psychological meaning”) 1) James et al. (1984) rWG ( J ) J [1 (s X2 j E2 )] J [1 (s X2 j E2 )] (s X2 j E2 ) * 2 2 1 ( s 2) Lindell et al. (1999) rWG (J ) X E) j 2 2 r 1 ( s 3) Simple index: WG( ) x E) 72 Within-Group Agreement • Comparison of rWG(J), rWG(J)*, and rWG() 1 0.9 J =5 items, WG = .90 0.8 rWG index 0.7 0.6 PSI_WG 0.5 rWG(J) 0.4 rWG(J)* 0.3 rWG(alpha) 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 True Within-Group Agreement (WG) 1 Newman & Sin, 2008 73 Within-Group Agreement • Conclusions: 1) All within-group agreement indices are very strongly correlated. 2) rWG(J) can notably overestimate within group agreement, especially when rWG(J) > .7. 3) rWG() seems to offer a closer estimate of within group agreement (slight underestimate) 4) One could also directly estimate WG . 74 Within-Group Agreement • How well does each of the following withingroup agreement indices estimate WG? (“shared psychological meaning”) J =5 items, WG = .90 1) When WG = .60: rWG(J)= .75; rWG(J)*= .38, rWG() = .56 2) When WG = .65: rWG(J)= .81; rWG(J)*= .46, rWG() = .61 3) When WG = .70: rWG(J)= .85; rWG(J)*= .53, rWG() = .67 75 Overview Group-Level Psychological Properties? 1. Psychological Climate Group-Level vs. Individual-Level Constructs 2. Aggregation Bias 3. Why we need rWG (Within-group agreement) Justifying Aggregation 4. rWG(J) for multi-item scales Agreement vs. Reliability 76 Overview Group-Level Psychological Properties? 1. Psychological Climate Group-Level vs. Individual-Level Constructs 2. Aggregation Bias 3. Why we need rWG (Within-group agreement) Justifying Aggregation 4. rWG(J) for multi-item scales Agreement vs. Reliability 77 Overview Group-Level Psychological Properties? 1. Psychological Climate Group-Level vs. Individual-Level Constructs 2. Aggregation Bias 3. Why we need rWG (Within-group agreement) Justifying Aggregation 4. rWG(J) for multi-item scales Agreement vs. Reliability 78 Overview Group-Level Psychological Properties? 1. Psychological Climate Group-Level vs. Individual-Level Constructs 2. Aggregation Bias 3. Why we need rWG (Within-group agreement) Justifying Aggregation 4. rWG(J) for multi-item scales Agreement vs. Reliability 79 Overview Group-Level Psychological Properties? 1. Psychological Climate Group-Level vs. Individual-Level Constructs 2. Aggregation Bias 3. Why we need rWG (Within-group agreement) Justifying Aggregation 4. rWG(J) for multi-item scales Agreement vs. Reliability 80 Thank You Larry! OC (average) PC Person #1 PC Person #2 rWG 1 (s 2 xj PC Person #3 ) 81 2 E