Reciprocal Relationships Between Collective Efficacy

Group Dynamics: Theory, Research, and Practice 2004, Vol. 8, No. 3, 182–195

Copyright 2004 by the Educational Publishing Foundation 1089-2699/04/$12.00 DOI: 10.1037/1089-2699.8.3.182

Reciprocal Relationships Between Collective Efficacy and Team Performance in Women’s Ice Hockey Nicholas D. Myers, Craig A. Payment, and Deborah L. Feltz

This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

Michigan State University This study examined reciprocal relationships between collective efficacy and team performance over a season of competition in women’s intercollegiate ice hockey within weekends where the opponent was constant for 2 games. Collective efficacy beliefs within 12 teams were assessed prior to both games for at least 7 weekends. Team performance indexes produced an overall measure of performance for each game. The average influence of Saturday collective efficacy on Saturday performance was moderate and positive after controlling for Friday performance. The average influence of Friday performance on Saturday collective efficacy was small and positive after removing the influence of Friday collective efficacy from Friday performance.

In many organizational settings, such as business, military, and sport, individuals perform in teams requiring them to work together to reach their common goals. How well these teams perform is a function of the interactive and coordinative dynamics of their members (Bandura, 1997). Teams also vary in the belief of their collective and coordinative capabilities to reach their goals. Bandura (1986) proposed collective efficacy as the construct to refer to people’s judgments of group capabilities. He defined collective efficacy as “a group’s shared belief in their conjoint capabilities to organize and execute the courses of action required to produce given levels of attainments” (Bandura, 1997, p. 476). According to Bandura (1986, 1997) and others (Lindsley, Brass, & Thomas, 1995; Mischel & Northcraft, 1997), teams with high collective efficacy should outperform and persist longer in the face of obstacles than teams with low collective efficacy. In turn, organizations that have a record of successful perfor-

Nicholas D. Myers, Craig A. Payment, and Deborah L. Feltz, Department of Kinesiology, Michigan State University. This research was supported in part by a grant from Michigan State University, College of Education In-House Grant Program. We would like to acknowledge Kimberly Maier for her assistance with the hierarchical models used and Christy Duffy for her work on data entry. Correspondence concerning this article should be addressed to Deborah L. Feltz, Department of Kinesiology, Michigan State University, 138 IM Sports Circle, East Lansing, MI 48824. E-mail: [email protected]

mance should have a strong sense of collective efficacy among their members. Likewise, as Eden (1990) noted in his description of selffulfilling prophecies in organizations, a serious performance failure—such as the Challenger space shuttle disaster of the National Aeronautics and Space Administration— can decrease the collective efficacy of the organization’s members, which in turn can influence subsequent failures. Many of the types of teams in organizations resemble athletic teams, whose members frequently change and who must respond to a wide variety of competitors or changes in game conditions. The sporting environment provides a salient context in which to study the relationships between collective efficacy and team performance. Sports teams are intact, dynamic groups with common identities, goals, and objectives. They have a structured pattern of interaction, they perform meaningful tasks, and their performance outcomes are unambiguous. In any group, although collective efficacy is a group’s shared belief, it still reflects individuals’ perceptions of the team’s capabilities (Bandura, 1997). Bandura recommended two approaches for deriving single estimates of a team’s collective efficacy from individual team members. The first approach involves assessing each team member’s belief in his or her personal capabilities to perform within the group (i.e., self-efficacy) and then aggregating these individual measures to the team level. We refer to this estimate of collective efficacy as aggre-

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gated self-efficacy. The second approach involves assessing each team member’s belief in the team’s capabilities as a whole and then aggregating these individual measures to the team level. We refer to this estimate of collective efficacy as aggregated collective efficacy. Bandura contended that aggregated collective efficacy will be more predictive of team performance than aggregated self-efficacy when the group task is highly interdependent. Empirical studies in sport psychology have supported this claim (Feltz & Lirgg, 1998; Myers, Feltz, & Short, 2004). Zaccaro, Blair, Peterson, and Zazanis (1995) were more explicit than Bandura was in incorporating the coordinative and integrative aspects of collective efficacy in their definition of the construct. They defined collective efficacy as “a sense of collective competence shared among members when allocating, coordinating, and integrating their resources as a successful, concerted response to specific situational demands” (Zacccaro et al., 1995, p. 309). Various definitions of collective efficacy have contributed to multiple approaches to the measurement of the construct (Maddux, 1999). Measurement methods that are somewhat different from the two approaches advocated for by Bandura have included aggregated collective efficacy based on Zaccaro et al.’s definition of the construct (Paskevich, Brawley, Dorsch, & Widmeyer, 1999) and single measures obtained from group discussion (Gibson, Randel, & Earley, 2000). There is no evidence that a single measure of collective efficacy derived from group discussion or an aggregated measure of collective efficacy based on Zaccaro et al.’s definition predicts performance significantly better than either of the approaches advocated for by Bandura. For these reasons, and because empirical evidence supports the use of aggregated collective efficacy measures as opposed to aggregated self-efficacy measures, we used the aggregated collective efficacy measurement method suggested by Bandura (1997) in this study. Relationships between collective efficacy and group performance should be maximized when the group task is highly interdependent (Gully, Incalcaterra, Joshi, & Beaubien, 2002). Interdependence has been conceptualized as being defined by task, goal, and outcome interdependencies (Campion, Papper, & Medsker, 1996). Task interdependence refers to the degree of

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task-driven interactions among team members (Shea & Guzzo, 1987). Goal interdependence refers to the interconnections among group members implied by the goals that direct collective performance and efforts (Saavedra, Earley, & Van Dyne, 1993). Outcome interdependence refers to the existence of consequences and outcomes that are shared by team members (Shea & Guzzo, 1987). Ideally, team members in ice hockey work on interdependent tasks (e.g., execute a game plan), have interdependent goals (e.g., score goals), and experience interdependent consequences for their performance (e.g., receive praise from the coaching staff). Collective efficacy beliefs are hypothesized to exert a positive influence on subsequent and proximal group performances (Bandura, 1997). Hodges and Carron (1992) and Lichacz and Partington (1996) used lab tasks and found that teams with high collective efficacy outperformed and persisted longer than did teams with low collective efficacy and that failure resulted in lower collective efficacy on successive trials. Feltz and Lirgg (1998) examined the influence of collective efficacy on team performance in men’s ice hockey. They surveyed six teams within 24 hr prior to 32 competitions for 16 weekends. Teams played the same opponent within a weekend. They reported that collective efficacy was a positive predictor of team performance within teams. Myers et al. (2004) examined the influence of collective efficacy on team performance in American football. They surveyed 10 teams within 24 hr prior to eight competitions over eight consecutive weekends. They reported that collective efficacy was a positive predictor of team performance within teams, which replicated the findings of Feltz and Lirgg. They also extended the findings of Feltz and Lirgg by providing evidence that collective efficacy was a positive predictor of team performance within weeks and across teams. A limitation of these studies was that the influence of previous performance was not controlled for statistically, and thus the effects of collective efficacy may have been inflated. The influence that efficacy beliefs exert on performance has not always been positive in the literature. Vancouver and his colleagues (Vancouver, Thompson, Tischner, & Putka, 2002; Vancouver, Thompson, & Williams, 2001) reported a weak and negative effect of self-efficacy on individual performance in studies that


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used intraindividual designs. They interpreted the findings in relation to perceptual control theory (PCT; Powers, 1973), suggesting that elevated self-efficacy can result in decreased performance because an individual may become overconfident and allocate less resources to a task that is repeated across time.1 In reviewing the studies by Vancouver et al., Bandura and Locke (2003) contended that there were conceptual problems (e.g., self-efficacy is not a part of PCT), methodological problems (e.g., the lab task did not permit progressive changes in selfefficacy and performance across time), and interpretative problems (e.g., the results have little generalizability for nontrivial tasks) in the pair of studies that limit confidence in the results and the conclusions. Bandura and Locke (2003) concluded that “converging evidence from diverse methodological and analytic strategies verifies that self-efficacy and personal goals enhance motivation and performance attainments” (p. 87). Collective efficacy is hypothesized to be influenced by events and experiences similar to those that influence self-efficacy (Bandura, 1997; George & Feltz, 1995). As with selfefficacy, Bandura posited that mastery experiences of the group exert the most powerful influence on subsequent collective efficacy. Feltz and Lirgg (1998) reported that previous game outcome was a positive predictor of subsequent collective efficacy across games and teams. Watson, Chemers, and Preiser (2001) found that team-level predictors of collective efficacy in collegiate basketball included group size, past performance, and confident leadership. Myers et al. (2004) reported that previous performance was a negative predictor of subsequent collective efficacy within teams. The direction of this last finding opposed previous research and theory. The authors speculated that the negative relationship was probably spurious and due to design limitations in the study (i.e., temporal disparity between previous performance and subsequent collective efficacy, and that the opponent was not constant). Limitations of these studies were that the influence of previous performance on subsequent collective efficacy within teams when the opponent was constant was not explored and that the influence of previous collective efficacy was not controlled for statistically.

The first purpose of this study was to examine the influence of Saturday collective efficacy on Saturday performance after statistically controlling for Friday performance within teams. Our hypothesis was that Saturday collective efficacy would positively influence Saturday performance after statistically controlling for Friday performance. Supporting this hypothesis would extend the findings of Feltz and Lirgg (1998) and Myers et al. (2004) in that neither study statistically controlled for previous performance, and would provide additional evidence to the majority of research that suggests a positive influence of efficacy beliefs on performance across time (Bandura & Locke, 2003). The second purpose of our study was to examine the influence of Friday performance on Saturday collective efficacy after removing the influence of Friday collective efficacy from Friday performance within teams. Our hypothesis was that Friday performance would positively influence Saturday collective efficacy after removing the influence of Friday collective efficacy from Friday performance. Supporting this hypothesis would extend the literature by statistically controlling for previous collective efficacy; would extend the findings of Feltz and Lirgg (1998), because they provided evidence for a positive relationship only across games and teams; and would oppose the findings of Myers et al. (2004), because they reported a negative relationship between previous performance and subsequent collective efficacy within teams.

Method Sample Schedules of all the teams (N ⫽ 51) that participated in the 2002–2003 women’s collegiate ice hockey season in the United States were reviewed to determine which teams had a schedule that fit the design of the study (i.e., consecutive games against a constant opponent for at least five weekends). All such teams (N ⫽ 28) were contacted by the researchers to encour1 Efficacy beliefs can be considered situation-specific confidence (Feltz & Chase, 1998). Thus, in the remainder of this article we occasionally use the terms efficacy and confidence interchangeably, except when considering a particular construct.


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age participation in the study, and 16 teams agreed to participate, but only 12 teams submitted usable data for at least five weekends (range ⫽ 7–12). Teams that did not submit usable data for at least five weekends were dropped. Data were unusable when efficacy information was not returned for both games. Across the 12 teams that submitted an adequate amount of usable data, 234 games (117 weekends) fit the study design. Usable data were submitted for 216 of these games. Of the 12 teams that were retained, 7 were from Division III and 5 were from Division I. At the athlete level, participants were 243 intercollegiate ice hockey players from 12 different universities (M ⫽ 20.25 athletes per team). Within teams the number of participants varied from 15 to 24. Across the 216 games from which usable data were collected, there were 3,509 observations (M ⫽ 16.25 athletelevel observations per game). However, observations from athletes who indicated that they would be unable to play in an identified game were dropped (n ⫽ 42, or 1% of the data). Thus, across the 216 games there were 3,467 athletelevel observations.

Procedure Permission was obtained from the institutional review board and the 12 head coaches prior to data collection. An explanation of the study was presented to each team by the head coach. Informed consent was obtained from all athletes. Athletes were guaranteed confidentiality for their responses. Questionnaires were completed within 24 hr before each game. Games were held on consecutive days, and the opponent was constant within a weekend. On each team, an identified trainer or team manager administered the questionnaires for all games. Completed questionnaires were returned to the trainer or team manager, who mailed the returns to the researchers after each weekend. Trainers or team managers who successfully followed through over the entire season were given a $60 honorarium.

Measures Team performance. Performance indicators were obtained from a Web site that compiles college hockey statistics (http://www

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.collegehockeystats.com). The sport information director at each institution was responsible for submitting the data after each game. Indicators used in this study were similar to those used by Feltz and Lirgg (1998) and included (a) goal difference (number of goals for a participating team minus the number of goals for their opponent), (b) shots on goal difference (number of shots on goal for a participating team minus the number of goals for their opponent), (c) percentage of shots stopped, (d) scoring percentage (number of goals scored divided by the number of shots taken), and (e) percentage of penalties killed (number of penalty situations where the team held the opponent scoreless divided by the total number of penalty situations). Collective efficacy. The questionnaire that was used in the Feltz and Lirgg (1998) study was reviewed with the head coach of a women’s intercollegiate ice hockey team at a major university in the Midwest. One of the items, “outcheck the opponent,” was deleted, because checking is not allowed in women’s ice hockey. The final questionnaire contained seven items that assessed the degree of confidence that an athlete had in her team’s ability to perform significant game competencies against the upcoming opponent: (a) beat the opposing team, (b) outskate the opposing team, (c) goaltender can outperform the opposing goaltender, (d) outshoot the opposing team, (e) bounce back from performing poorly against the opposing team, (f) score power play goals against the opposing team, and (g) kill penalties against the opposing team.2 Ratings were made on an 11point rating scale ranging from 0 (cannot do at all) to 10 (certain can do). Participants were also asked demographic questions such as their injury status (i.e., “Do you have an injury that will keep you from playing in the upcoming game?”).

2 Judgments about performance accomplishments are not outcome expectations. As Bandura (1997) clearly articulated, “a performance is an accomplishment; an outcome is something that flows from it. In short, an outcome is the consequence of a performance, not the performance itself” (pp. 22–23). Performance accomplishments can take the form of letter grades in academia or a final game score in sports (Feltz & Lirgg, 2001).

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Table 1 Descriptive Statistics for Logit-Based Collective Efficacy and the Team Performance Scores


FRICE

FRITP

SATCE

SATTP

Team

n

M

SD

M

SD

n

M

SD

M

SD

Team A Team B Team C Team D Team E Team F Team G Team H Team I Team J Team K Team L Across teams

8 9 8 11 7 10 8 12 7 10 9 9 108

2.87 3.74 0.92 3.09 4.80 3.33 2.33 2.25 2.07 2.88 4.01 3.02 2.94

1.47 1.04 1.20 1.29 0.88 1.30 0.31 1.09 1.08 0.91 1.64 2.23 1.52

0.81 ⫺0.29 ⫺0.86 ⫺0.70 ⫺0.15 1.25 0.59 ⫺0.29 ⫺0.37 0.26 0.71 0.18 0.09

0.81 0.73 1.23 0.75 1.05 0.77 0.62 0.84 0.36 0.79 0.92 1.04 1.02

8 9 8 11 7 10 8 12 7 10 9 9 108

3.84 3.90 1.45 2.84 4.98 4.18 3.12 2.82 1.98 3.21 4.31 3.48 3.33

1.47 0.88 1.66 1.48 1.04 1.55 0.69 1.66 1.00 1.21 1.66 2.05 1.64

0.03 ⫺0.47 ⫺0.72 ⫺0.60 ⫺0.34 1.08 0.05 ⫺0.34 ⫺0.14 0.30 0.71 0.05 ⫺0.03

0.98 0.47 0.92 1.05 0.48 0.68 0.82 0.69 0.53 0.55 1.10 0.91 0.92

Note. FRICE ⫽ Friday collective efficacy; FRITP ⫽ Friday performance; SATCE ⫽ Saturday collective efficacy; SATTP ⫽ Saturday performance.

Treatment of the Data Principal-components analysis (PCA) was performed on the performance indicators and on the collective efficacy items. In both cases PCA was reasonable because the goal was to reduce the data to a single measure and to produce a composite score for each game (Fabrigar, Wegener, MacCallum, & Stahan, 1999).3 Prior to performing the PCAs, we noted that both sets of data were nested within games and that games were nested within teams. In both cases this dependency was tolerable because PCA is a descriptive rather than an inferential technique (Elliot & Wexler, 1994; Kivlighan & Tarrant, 2001), because there was no compelling reason to believe that the structure of team performance or collective efficacy would be substantively variant across the season, and because pooling the game-level indicators was desirable to maximize sample size (Tabachnick & Fidell, 2001). Decisions regarding component retention were guided by a conceptual understanding of the construct of interest, Kaiser’s criteria (Kaiser, 1960), the scree plot (Catell, 1966), and the number and magnitude of component loadings (Stevens, 1996). Team performance. The initial PCA extracted a majority of the total variance of the performance indicators (range of extracted communalities ⫽ .66 –.96). The principal component was above the lower asymptote (eigen-

value ⫽ 2.75), was reliably measured (range of loadings ⫽ .55–.96), accounted for 55% of the total variance, and was interpretable (i.e., as “performance”). The eigenvalue for the next unaccepted component was 1.08. Composite scores were computed for the principal component and were used as the performance scores in subsequent analyses (see Table 1). Cronbach’s alpha for the set of indicators was .78. Collective efficacy. Data were calibrated to the Rasch Rating Scale Model (RSM; Andrich, 1978) using Winsteps (Wright & Linacre, 1998). Rasch models are a family of one-parameter item response theory (IRT) measurement models. IRT is an alternative to true score test (TST) theory and is well suited to analyze rating scale data (Wright & Masters, 1982). The RSM describes the probability that a specific athlete (n) will rate a particular item (i) using a specific rating scale category (x). The log-odds equation for this probability, log (Px / Px - 1) ⫽ ␤n – ␦i – ␶x, contains three parameters: (a) athlete’s collective efficacy (␤n), (b) item’s difficulty (␦i), and (c) category threshold (␶x), the threshold between two adjacent rating scale categories. 3 Exploratory factor analyses (EFA) cannot be performed by Winsteps. In this study, when a PCA was performed, an unrotated EFA was also performed using SPSS. In each case, the factor/component structures were similar between the PCA and the EFA.


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Calibration of the data to this model resulted in a collective efficacy estimate for every observation. Estimates were reported on a single linear continuum in logistic ratio units (logits). A logit is the natural logarithm of an odds event. Because the data in this study were polytomous, odds were defined by the likelihood of assigning a rating in one category versus the odds of assigning a rating in the next lower category. The initial PCA extracted a majority of the total variance of the collective efficacy items (range of extracted communalities ⫽ .65–.85). The Rasch component was above the lower asymptote (eigenvalue ⫽ 5.26), was reliably measured (range of loadings ⫽ .80 –.92), accounted for 75% of the total variance, and was interpretable (i.e., as “collective efficacy”). The eigenvalue for the next unaccepted component was 0.52. The reliability-of-separation coefficient, which is analogous to Cronbach’s alpha in TST theory, for the set of items was .81. Consensus. As recommended by Moritz and Watson (1998), degree of consensus in the athlete-level collective efficacy responses was determined prior to aggregating the data. Raw scores, not logit-based measures, were used in determining consensus because the number of categories on the original rating scale is considered in the computation of the within-team agreement index (James, Demaree, & Wolf, 1984). Interrater agreement indices (rwg) estimated the degree of within-team consensus on the athlete-level collective efficacies prior to each game. Although cogent arguments have been put forth to question the validity of the rwg statistic as a measure of interrater reliability (Schmidt & Hunter, 1989), arguments of a similar magnitude have defended the use of this statistic as a measure of interrater agreement (James, Demaree, & Wolf, 1993). We interpreted rwg estimates as indicators of interrater agreement. Estimates of rwg were computed assuming no response bias and continuous data (James et al., 1984). No response bias was assumed because the observed negative skew for the raw score collective efficacy distribution matched the expected distribution (Feltz & Chase, 1998). A continuous distribution was assumed because the likelihood of respondents treating an 11category structure as discrete is low (Zhu, Updyke, & Lewandowski, 1997). The continuous assumption results in a conservative computa-

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tion of rwg estimates (James et al., 1984). A high degree of consensus was observed for athletelevel collective efficacies within each team and across all games (M ⫽ .87, SD ⫽ .13). Thus, aggregating athlete-level collective efficacies provided a reasonable estimate of a team’s collective efficacy. Hence, the logit-based athletelevel collective efficacies were aggregated within each team for each game (see Table 1). The distribution of collective efficacy scores. Across games, the mean and standard deviation for the collective efficacy raw scores were 8.44 and 1.17. The distribution of these scores was significantly negatively skewed (z ⫽ ⫺8.65). The raw scores in this study showed a similar restriction in range as were found by Feltz and Lirgg (1998) and Myers et al. (2004). However, unlike the aforementioned studies, which applied linear transformations to the raw scores to help normalize efficacy distributions, in this study the efficacy data were subjected to the RSM, which stretched extreme scores further apart via a nonlinear transformation of raw scores to a logit scale (Smith, 2000). The distribution of the logit-based collective efficacy measures was not significantly skewed (z ⫽ 0.33). Forming final measures. Bandura (1997) contended that behavior does not cause behavior. Rather, the magnitude of the correlation between sequential behaviors is attributable to the degree of commonality of their respective determinants. To avoid “statistical overcontrol” when modeling the influence of previous performance on subsequent performance, one should remove common determinants from previous performance prior to entering it as a predictor of subsequent performance (Wood & Bandura, 1989; Wood, Bandura, & Bailey, 1990). Accordingly, the influence of Friday collective efficacy was removed from Friday performance prior to entering Friday performance as a predictor of Saturday performance. This same “adjusted” Friday performance measure was used as the predictor of Saturday collective efficacy. Using the adjusted measure provided a conservative test of the influence of Friday performance on Saturday collective efficacy. Because the metrics for the variables of interest included logit-based collective efficacy measures, adjusted composite scores for Friday performance, and composite scores for Saturday performance, all of the variables were standard-


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ized to improve interpretation. Thus, the betas in the subsequent analyses were standardized. From this point forward, adjusted Friday performance is referred to as Friday performance. Addressing dependency. Dependent data increase the probability of committing a Type I error if the groupings are ignored (Barcikowski, 1981). The data were dependent in this study because there were repeated measures within teams. Hierarchical linear modeling (HLM) is well suited to handle dependent data. Growth modeling is an application of HLM that is designed to handle repeated measures because it addresses the time-series relationships among the variables. Linear growth models for both of the hypotheses were explored in HLM5 (Raudenbush, Bryk, Cheong, & Congdon, 2000). Linear growth models, as opposed to more complex models (e.g., quadratic, cubic), were reasonable because a relatively small number of within-team observations (range ⫽ 7–12 weekends) were collected (Raudenbush & Bryk, 2002). Model building consisted of at least three steps to test both hypotheses. First, an unconditional model was imposed: Level 1: Yti ⫽ ␲0i ⫹ eti, where

␲0i was the mean of the dependent variable of interest for team i eti was the residual for team i. Level 2: ␲1i ⫽ ␤00 ⫹ r0i, where

␤00 was the average team mean of the dependent variable of interest r0i was the unique effect of team i on the average team mean. Of particular interest in this model were the variance of eti, or the within-team variance (␴2), and the variance of r0i, or the between-teams variance (␶00). These two variances were used to estimate the intraclass correlation (ICC ⫽ ␶00 / [␶00 ⫹ ␴2]) of the dependent variable of interest. Second, an unconditional no-intercept linear growth model was imposed: Level 1: Yti ⫽ ␲1iati ⫹ eti, where

␲1i was the growth rate in the dependent variable of interest from one weekend to

the next over the data collection period for team i ati was the time-ordering variable where ati ⫽ weekend number minus 7 eti was the residual for team i. Level 2: ␲1i ⫽ ␤10 ⫹ r1i, where

␤10 was the average growth rate in the dependent variable of interest across teams r1i was the unique effect of team i on the average growth rate in the dependent variable of interest from one weekend to the next over the data collection period. This model was appropriate because the intercept was not meaningful (i.e., the average Saturday performance at Weekend 7), and dropping it increased model parsimony. The timeordering variable, ati, was specified to equal weekend number minus 7, because all teams submitted data for at least 7 weekends. Of particular interest in this model were ␤10 and the variance of r1i (␶11). ␶11 was the variance of the estimated growth rates in the dependent variables of interest (i.e., ␲1i values) around the average growth rate for the dependent variable of interest (i.e., ␤10). The probability of a Type I error was .05 for all hypothesis tests, and the magnitudes of the standardized betas were interpreted according to Cohen’s guidelines (1988). Third, a conditional growth model was imposed where time-varying covariates (i.e., game level) were added. To test the first hypothesis, we entered Friday performance and Saturday collective efficacy as predictors of Saturday performance. To test the second hypothesis, we entered Friday performance as a predictor of Saturday collective efficacy. The model below is interpreted as it was for the first hypothesis. Level 1: SATTPti ⫽ ␲1iati ⫹ ␲2iFRITP ⫹ ␲3iSATCE ⫹ eti, where

␲1i was the growth rate in Saturday performance for team i ati was the time-ordering variable, where ati ⫽ weekend number minus 7 ␲2iFRITP was the effect of Friday performance for team i ␲3iSATCE was the effect of Saturday collective efficacy for team i


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eti was the residual for team i. Level 2: ␲1i ⫽ ␤10 ⫹ r1i ␲2i ⫽ ␤20 ⫹ r2i ␲3i ⫽ ␤30 ⫹ r3i, where ␤10 was the average growth rate in Saturday performance across teams r1i was the unique effect of team i on the average growth rate in Saturday performance ␤20 was the average effect of Friday performance across teams r2i was the unique effect of team i on the average effect of Friday performance ␤30 was the average effect of Saturday collective efficacy across teams r3i was the unique effect of team i on the average effect of Saturday collective efficacy. In both models, division (0 ⫽ Division III, 1 ⫽ Division I) was entered as a Level 2 predictor to ensure that none of the slopes varied according to division. Model estimation and fit. Final parameters were estimated via restricted maximum likelihood, and differences in model fit were examined via full maximum likelihood estimation (Raudenbush & Bryk, 2002). Relative fit of nested models was evaluated using a likelihood ratio chi-square statistic (␹2LR ⫽ G2simple – G2complex), where G2 was the deviance value for the model in question. The ␹2LR statistic is distributed with degrees of freedom equal to the difference between the number of parameters in the nested models (McCullagh & Nelder, 1990). Because the ␹2LR statistic is sensitive to sample size, the consistent Akaike information criterion (CAIC; Bozdogan, 1987) was also considered. The CAIC (G2 ⫽ [–2 ⫻ Ln(L)] ⫹ p[1 ⫹ Ln(n)], where L ⫽ likelihood of the data given the model, p ⫽ the number of parameters in the model, and n ⫽ the number of observations in the data set) depicts the fit of the model in question relative to the number of parameters estimated (Wicherts & Dolan, 2004). Reliability estimates. Point reliability estimates in HLM describe how reliable, on average, the slopes are on the basis of computing ordinary least square regressions separately for each team. A reliability estimate is provided in

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HLM by averaging the individual team estimates. Raudenbush and Bryk (2002) suggest, as a guideline, that the point reliability estimate should be greater than .05. Slopes that do not meet this heuristic are candidates to be fixed across groups.

Results Influence of Saturday Collective Efficacy on Saturday Performance After Controlling for Friday Performance Table 2 summarizes the relevant growth models. The ICC for Saturday performance was .26, which suggested that 74% of the variance in Saturday performance was due to within-team differences. Fit indexes for the unconditional growth model were G2 ⫽ 298.45 and CAIC ⫽ 308.90. The average growth rate in Saturday performance from one weekend to the next across teams (␤10 ⫽ ⫺.01) was not significantly different from zero, t(11) ⫽ ⫺0.14, p ⫽ .89, in the unconditional growth model. The point reliability estimate for these slopes was .67. The variance of the team-level growth rates (i.e., ␶11) around ␤10 was significantly greater than zero, ␹2(11, N ⫽ 12) ⫽ 32.95, p ⬍ .01. Thus, we inferred that although the average growth rate was not significantly different from zero, growth rates were significantly different within teams and should remain random in subsequent models. Findings regarding these growth rates remained relatively stable across subsequent models and are not discussed further. Friday performance and Saturday collective efficacy were added as game-level predictors in the initial conditional growth model (see Table 2). This model appeared to fit the data better than the unconditional growth model, ␹2(7, N ⫽ 12) ⫽ 56.57, p ⬍ .01, CAIC ⫽ 276.73, and explained an additional 43% of the within-team variance in Saturday performance. The average influence of Friday performance was small and positive (␤20 ⫽ .13) and approached statistical significance, t(11) ⫽ 1.82, p ⫽ .10. The point reliability estimate for these slopes was .04. The variance of the team-level effects (i.e., ␶22) around ␤20 was not significantly greater than zero, ␹2(11, N ⫽ 12) ⫽ 10.11, p ⫽ .52. Thus, we inferred that the average effect of Friday performance was small and positive, had a low reliability, was similar within teams, and should

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Table 2 Hierarchical Growth Models in Which Saturday Performance Was the Dependent Variable Estimates of fixed effects


Model

Coefficient

SE

t

df

p

⫺0.01

0.04

⫺0.14

11

.89

⫺0.01 0.13 0.56

0.03 0.07 0.11

⫺0.43 1.82 4.99

11 11 11

.68 .10 ⬍.01

⫺0.01 0.14 0.56

0.03 0.07 0.11

⫺0.41 1.95 5.06

11 105 11

.69 .05 ⬍.01

Unconditional growth model Linear growth rate (␤10) Conditional growth model Linear growth rate (␤10) Friday performance (␤20) Saturday collective efficacy (␤30) Respecified conditional growth model Linear growth rate (␤10) Friday performance (␤20) Saturday collective efficacy (␤30)

Estimates of variance components for random effects

Unconditional growth model Between-team residuals (r1i) Within-team residuals (eti) Conditional growth model Between-team residuals (r1i) Between-team residuals (r2i) Between-team residuals (r3i) Within-team residuals (eti) Respecified conditional growth model Between-team residuals (r1i) Between-team residuals (r3i) Within-team residuals (eti)

␹2

p

SD

Variance

df

0.11 0.91

0.01 0.83

11

33

0.08 0.05 0.26 0.69

0.01 0.003 0.07 0.47

11 11 11

22.3 10.1 19.3

.02 .52 .06

0.08 0.26 0.69

0.01 0.07 0.47

11 11

21.7 16.9

.03 .11

be fixed in a respecified model. The average influence of Saturday collective efficacy was moderate and positive (␤30 ⫽ .56) and was statistically significant, t(11) ⫽ 4.99, p ⬍ .01. The point reliability estimate for these slopes was .40. The variance of the team-level effects (i.e., ␶33) around ␤30 approached statistical significance, ␹2(11, N ⫽ 12) ⫽ 19.27, p ⫽ .06. Thus, we inferred that although the average effect of Saturday collective efficacy was moderate and positive, this effect was somewhat different within teams and should remain random in a respecified model. Findings regarding the influence of Saturday collective efficacy remained relatively stable across subsequent models and are not discussed further. None of the slopes varied according to division. The effect of Friday performance was fixed across teams in the respecified conditional growth model (see Table 2). Conceptually, this model assumed that the influence of Friday per-

⬍.01

formance on Saturday performance was similar within teams. The respecified model appeared to fit the data at least as well as the initial conditional growth model, ␹2(3, N ⫽ 12) ⫽ 0.17, p ⫽ .98, CAIC ⫽ 266.45. The influence of Friday performance on Saturday performance across games remained small and positive (␤20 ⫽ .14) but more closely approached statistical significance, t(105) ⫽ 1.95, p ⫽ .051, owing to the increased degrees of freedom.

Influence of Friday Performance on Saturday Collective Efficacy After Removing the Influence of Friday Collective Efficacy From Friday Performance Table 3 summarizes the relevant growth models. The ICC for collective efficacy prior to

COLLECTIVE EFFICACY

191

Table 3 Hierarchical Growth Models in Which Saturday Collective Efficacy Was the Dependent Variable Estimates of fixed effects


Model

Coefficient

SE

t

df

p

0.01

0.04

0.20

11

.84

0.01 0.25

0.04 0.09

0.34 2.79

11 11

.74 .02

0.01 0.23

0.04 0.09

0.35 2.68

11 106

.73 ⬍.01

Unconditional growth model Linear growth rate (␤10) Conditional growth model Linear growth rate (␤10) Friday performance (␤20) Respecified conditional growth model Linear growth rate (␤10) Friday performance (␤20)

Estimates of variance components for random effects

Unconditional growth model Between-team residuals (r1i) Within-team residuals (eti) Conditional growth model Between-team residuals (r1i) Between-team residuals (r2i) Within-team residuals (eti) Respecified conditional growth model Between-team residuals (r1i) Within-team residuals (eti)

␹2

p

SD

Variance

df

0.12 0.89

0.01 0.79

11

40

⬍.01

0.13 0.11 0.85

0.02 0.01 0.72

11 11

44.6 3.46

⬍.01 .98

0.12 0.86

0.01 0.74

11

41

⬍.01

Saturday performance was .25, which suggested that 75% of the variance in collective efficacy prior to Saturday performance was due to within-team differences. Fit indexes for the unconditional growth model were G2 ⫽ 295.13 and CAIC ⫽ 305.58. The average growth rate in Saturday collective efficacy from one weekend to the next over the data collection period across teams (␤10 ⫽ .01) was not significantly different from zero, t(11) ⫽ 0.20, p ⫽ .84, in the unconditional growth model. The point reliability estimate for these slopes was .75. The variance of the team-level growth rates (i.e., ␶11) around ␤10 was significantly greater than zero, ␹2(11, N ⫽ 12) ⫽ 39.95, p ⬍ .01. Thus, we inferred that although the average growth rate was not significantly different from zero, growth rates were significantly different within teams and should remain random in subsequent models. Findings regarding these growth rates remained relatively stable across subsequent models and are not discussed further. Friday performance was added as a gamelevel predictor of Saturday collective efficacy in the initial conditional growth model (see Table

3). This model appeared to fit the data at least as well as the unconditional growth model, ␹2(3, N ⫽ 12) ⫽ 8.54, p ⫽ .04, CAIC ⫽ 307.50, and explained an additional 9% of the within-team variance in Saturday performance. The average influence of Friday performance was small and positive (␤20 ⫽ .25) and was statistically significant, t(11) ⫽ 2.79, p ⫽ .02. The point reliability estimate for these slopes was .11. The variance of the team-level effects (i.e., ␶22) around ␤20 was not significantly greater than zero, ␹2(11, N ⫽ 12) ⫽ 3.46, p ⫽ .98. Thus, we inferred that the average effect of Friday performance was small and positive, was similar within teams, and should be fixed in a respecified model. Neither of the slopes varied according to division. The effect of Friday performance on Saturday collective efficacy was fixed across teams in the respecified conditional growth model (see Table 3). Conceptually, this model assumed that the influence of Friday performance on Saturday collective efficacy was similar within teams. The respecified model appeared to fit the data as well as the initial conditional growth

192


model, ␹2(2, N ⫽ 12) ⫽ 1.47, p ⫽ .48, CAIC ⫽ 302.00. The influence of Friday performance across games remained small and positive (␤20 ⫽ .23) and statistically significant, t(102) ⫽ 2.68, p ⬍ .01.


Discussion Our findings suggest that the average influence of Saturday collective efficacy on Saturday performance is moderate and positive after statistically controlling for Friday performance. Additionally, the average influence of Friday performance on Saturday collective efficacy is small and positive after removing the influence of Friday collective efficacy from Friday performance. These findings, as well as aspects of the methodologies implemented that produced these findings, advance the literature on the relationships between collective efficacy and team performance in several ways. First, although previous studies (Feltz & Lirgg, 1998; Myers et al., 2004) have reported a positive relationship between collective efficacy and subsequent performance within teams, neither of these studies controlled for the effect of previous performance. Our finding is meaningful in that coaches are not left with the notion that previous performance is the only, or even the most important, predictor of subsequent performance. If these notions were true, the best way to increase subsequent performance would be to have performed better in the previous performance. Our finding suggests that, on average, a coach can expect that his or her team’s collective efficacy prior to performance, a variable that is amenable to change, is likely to impact subsequent team performance along with previous performance. Second, in contrast to recent studies (Vancouver et al., 2001, 2002) that have suggested that efficacy beliefs can exhibit a weak and negative effect on subsequent performance within subjects when the task is constant across time, in our study, the effect is moderate and positive. We suspect that this effect in our study is positive because the task is meaningful to the participants and permits progressive changes in collective efficacy and team performance across time. Practically, our findings are important in that coaches are not left with the notion that, on average, collective efficacy exhibits a debilitating effect on team performance. If this notion

were true, to increase subsequent performance, coaches would need to decrease their team’s collective efficacy prior to performance. Our findings suggest that a coach can expect that, on average, increasing his or her team’s collective efficacy prior to performance will enhance team performance. Although we concede that there are instances when overconfidence can lead to decreased performance, in most scenarios increased confidence leads to increased performance. Additionally, the finding that the average influence of Friday performance on Saturday collective efficacy is small and positive after removing the influence of Friday collective efficacy from Friday performance extends the literature in at least two ways. First, previous studies have reported a positive influence of previous performance on subsequent collective efficacy across teams (Feltz & Lirgg, 1998; Myers et al., 2004) and a negative influence of previous performance on subsequent collective efficacy within teams (Myers et al., 2004). The small and positive effect in our study extends Feltz and Lirgg’s findings by reporting a similar effect while addressing the dependency in the data, and supports the contention that Myers et al.’s findings may be attributable to design limitations. Second, previous studies did not remove the effect of previous collective efficacy on previous team performance before modeling the influence of previous performance on subsequent collective efficacy. Our findings suggest that a coach can expect, on average, that previous performance will exert a positive influence on subsequent collective efficacy even after negating the influence of previous collective efficacy. Methodologically, this study extends the relevant literature in at least two ways. First, in this study HLM was used, and game-level variables were specified as random or fixed as appropriate. Previous studies (Feltz & Lirgg, 1998; Myers et al., 2004) used meta-analytic frameworks in which the game-level variables were estimated only within teams (i.e., “random” in HLM terminology) regardless of the level of within-team variance around the average effect. In HLM, treating an effect as fixed (i.e., ignoring the nesting of observations) is advantageous empirically because of the increased degrees of freedom, and important conceptually because it suggests that the said effect is similar within


COLLECTIVE EFFICACY

teams. Second, in this study, growth rates across the season were handled in the most comprehensive way to date. In previous research, either growth rates were not addressed (Feltz & Lirgg, 1998) or nonsignificance of the average growth rate across teams was used as a justification to ignore the variability of the growth rates within teams (Myers et al., 2004). In this study, although the average growth rates were nonsignificant, team variation around the average was significant and was modeled. Conceptually, it makes sense that the average growth rate in team performance across the season would not be significantly different from zero because team performance is likely to be heavily influenced by quality of the opponent, and team schedules generally do not follow a linear pattern. But, it also makes sense that growth rate in team performance may be significantly variant within teams as teams’ schedules follow different patterns across the season. These results also have implications for other intact groups that are characterized by meaningful tasks with similar levels of task interdependence. Collective efficacy and performance show a reciprocal relationship, and because collective efficacy is amenable to change, managers and team leaders can use techniques to improve it among their members. Feltz (1994) and others (e.g., Lindsley et al., 1995) have outlined some strategies for enhancing collective efficacy and stopping downward efficacy–performance spirals that include setting short-term goals that focus on process versus outcome variables, redefining success and failure, and using simulation training to build coping efficacy. These techniques have yet to be investigated empirically with teams. The primary limitations of this study are the number of games and teams for which data were collected and the lack of Level 2 predictors. Game-level sample size is modest within teams (range ⫽ 7 to 12 weekends) and particularly noteworthy for the model in which there are two predictors (i.e., where Saturday performance was the dependent variable). Team-level sample size was also small (N ⫽ 12). Small sample sizes at both levels limit confidence in the stability of all of the coefficients. The lack of team-level predictors is problematic in that the influence of Saturday collective efficacy on Saturday performance appears to be somewhat different within teams. That team-level predictors

193

were not collected in this study is probably justifiable given the status of this line of inquiry. That is, we are unaware of any theory that posits why the relationship between collective efficacy and team performance would be variant within teams. Future studies with a larger number of both game-level and team-level observations could provide greater certainty in the proposed relationships, and future studies that model variability in the relationship between collective efficacy and team performance could extend this study and advance this line of inquiry.

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