Simultaneous study of individual and group correlations: an application example.

Zhang, James J. ; Hausenblas, Heather A. ; Barkouras, Alaxandros K. 等

Researchers in sport and exercise sciences often encounter hierarchical data structures (i.e., individual subjects are nested in groups, teams, classes, or schools). With hierarchically nested designs, researchers have traditionally analyzed the data by treating either the individual or the group as the unit of analysis. However, the individual analysis ignores the group aspect of the data and violates the assumption of independent measurement error; on the other hand, the group analysis uses the mean of individual scores within each group and ignores individual differences. It seems inevitable that non-independence among individuals exists in real groups because certain norms, climate, and social interactions cannot always be eliminated. Particularly in social and psychological studies, individual beliefs and behaviors are influenced by group members. Thus, it would be inappropriate to study individuals in group settings without considering the social context of the environment.

Unit of analysis is a complicated issue, and it has long been a concern in behavioral studies. When data are of a hierarchical structure, such as individual versus team, the unit of analysis should include both individual and group units at different levels (Zhu, 1997). However, a common practice is for researchers to focus on one level of analysis due to convenience; and thus cross inferences between data levels are often made about the research findings either by the researchers or the readers. "Cross-level inferences may be, and most often are, fallacies and grossly misleading" (Pedhazur, 1982, p. 528). Several researchers have attempted to draw attention to the fact that when correlations are calculated for within groups, between groups, and the total group, not only can they differ in magnitude, but also the direction can vary from being positive to negative, or vice versa (e.g., Lindquist, 1940; Robinson, 1950; Thorndike, 1939). The impact of inappropriate selection of the analysis unit could affect for mulating sound theories that would more accurately reflect reality and effectively direct practice. Hence, an appropriate method is necessary to deal with both individual and group effects simultaneously.

The general linear model is widely used to examine the interacting effect of the predicting variable(s) and the group variable(s) on the criterion, which generally follows the following regression model: Y' = a + b1X1 + b2X2 + b3X1 * X2, where X1 is the predicting variable and X2 is the group variable. The interaction component provides the information on whether the correlations across the groups are of similar magnitude by examining the homogeneity of regression lines. Following the general linear model approach, another way of examining correlation variability across groups is to establish confidence intervals of the mean correlation based on the correlations calculated within different groups. These procedures are useful to detect variations in the relationship between X and Y variables among groups (Jackson, 1989; Pedhazur, 1982; Pedhazur & Schmelkin, 1991). A number of published studies in exercise science have provided supporting evidence for the application of this general linear model approach. For examples, Cureton, Sloniger, O'Bannon, Black, and McCormack (1995), Jackson et al. (1990), and Ross and Jackson (1990) indicated that when developing formulas to predict cardiovascular endurance and body composition, the standard errors of estimate would be enlarged and the prediction validity would be reduced if the researchers did not consider the effects of gender group difference. Thus, the gender factor was incorporated into their formulas. Blair et al. (1989) found that after taking into consideration gender and age group factors, the relationship between aerobic fitness and mortality was more accurately evaluated. In these studies, applications of the general linear model enhanced prediction accuracy and overall variance explanation of the criterion variable.

Two recent studies have attempted to introduce the hierarchical linear modeling (HLM) to the field of physical education and exercise science (Zhu. 1997; Zhu & Erbaugh, 1997). HLM is a useful procedure to analyze multilevel data by identifying contributing variables at different levels and partitioning variance-covariance components within the selected model and variables. The following regression models are generally followed in two level hierarchical data: (a) Outcome Variable for Each Group = Intercept + [SIGMA]Slope * Individual Level Predictor + Error; and (b) Regression Coefficients for Each Group Intercept + [SIGMA]Slope * Group Level Predictor + Error. Correlations at both individual and group levels may be calculated based can the variance components of the variables in the model. Conducting a HLM analysis on the National Children and Youth Fitness Survey II (NCYFS II) data that had been previously examined by Pate and Ross (1987), Zhu (1997) re-examined school factors associated with health-related fitness and identified two significant school factors (percentage of classes taught by a physical education specialist and fitness tests administered); whereas, Pate and Ross (1987) originally identified a total of five significant factors (percentage of classes taught by a physical education specialist, fitness tests administered, minutes in recess per day, usually take physical education on school grounds, and warm climate) when the hierarchical structure of the data was ignored. Zhu (1997) speculated that greater probabilities of Type I errors might have occurred in the Pate and Ross's (1987) original study. In a study on psychological and social control causes of boredom among adolescents, Caldwell, Darling, Payne, and Dowdy (1999) indicated the necessity of applying HLM when assessing adolescents' level of boredom with respect to variables at the following two levels: (a) psychological reasons for participating in leisure activities and (b) social characteristics adolescents brought to the situation. Oth erwise, greater probabilities of inferential errors might have occurred, leading to less accurate findings in the prediction study.

Nonetheless, application limitations are associated with the general linear model and HLM procedures. The individual is usually the unit of analysis in the general linear model approach. This approach does not provide specific answer to the question if the group norm, climate, culture, and member interactions have a common effect in the correlation after individual differences are adjusted, nor does it provide information on the correlation at the individual level after adjusting for observation non-independence due to the group influence; thus, its usefulness may be limited in situations where both the individual influence and the group climates are present. Further, the magnitude and the nature of correlations derived from HLM are limited to the selected predicting variables at different levels. The model does not provide unique correlational information about the individual and the group effects when one is partialled out from the other. Rather, different procedures developed by Kenny and La Voie (1985) ma y fill this void, which provide adjusted bivariate correlations. When the interest is at the individual level, group norm effect can be partialled out of the correlation computation; on the other hand, when the research interest is at the group level, individual differences are partialled. Most often, unique correlations at both the individual and the group levels can be studied simultaneously.

Since their publication, the Kenny and La Voie's (1985) procedures have primarily been adopted within social psychology studies, and they have not received much attention in the field of sport and exercise sciences. This situation may be partially due to the fact that researchers in the field are unfamiliar with the technique. One exception is a study by Paskevich, Brawley, Dorsch, and Widmeyer (1995) who examined the relationship between collective-efficacy and sport team cohesion. They found that besides individual influences, multiple aspects of group influences and group cohesion were related to collective-efficacy and further indicated that the comparison of the relationships at the individual and the group levels considerably altered the theories that had primarily been established based on the traditionally single level examination. Overall, the Kenny and La Voie's (1985) procedures should be made known in the field of sport and exercise sciences.

Thus, the purposes of this study were to introduce the Kenny and La Voie's computational procedures for adjusted individual and group correlations and to demonstrate their application through a study examining the relationship between team-efficacy and sport competition success (Barkouras, 1999). Carron, Brawley, and Widmeyer (1998), Paskevich et al. (1995), and Paskevich, Estabrooks, Brawley, and Carron (2001) explained that the Kenny and La Voie's computational procedures are appropriate in situations where both individual and group influences are likely present and when there is a need to distinguish the correlations due to the effects of various levels. These experts further highlighted the potential of this technique in sport and exercise science research and encouraged its use in research issues related to group dynamics, such as collective-efficacy. The investigators of this current study believe that the following illustrations will help to provide additional support to these experts' recommendations. An application example on the relationship between team-efficacy and sport competition success was specifically chosen to demonstrate the application potential of the Kenny and La Voie's procedures in group dynamic studies.

Adjusted Correlations

According to Kenny and La Voie (1985), separating the individual and the group level correlations should follow five steps:

1. Test of non-independence of individual observations of both predicting and criterion variables through intraclass correlations (ICC), which is generally carried out through the following formulas:

ICC = MSb-MSw/MSb+MSw (n+1) (1)

F (k-1), k(n-1) = MSb/MSw (2)

where MSb and MSw are mean square between and within groups, respectively, and n is the number of individuals in each group when there are equal numbers of people among groups. When group sizes are unequal, n should be adjusted using the following formula:

n' = (N2 - [summation over]n2)/N(k-1) (3)

where N is the total number of subjects and k is the number of groups.

A positive ICC indicates that group members are more similar than nongroup members. A negative ICC indicates that group members are more dissimilar than non-group members. When a negative or nonsignificant positive ICC exists, the unit of analysis should be kept at the individual level because there is no evidence of group level effect. When a large positive ICC is statistically significant, the group should be used as the unit of analysis. Most commonly, both individual and group effects exist simultaneously. That is, there is small positive ICC and it is statistically significant. In such cases, the correlations at both the group and the individual levels may be computed and adjusted. Kenny and La Voie (1985) suggested that in order to minimize sampling errors and be sensitive to the commonly small positive ICC, the alpha level should be set at a very liberal level of .25 when conducting significance testing.

2. Calculating an unadjusted intercorrelation matrix separately using individual and group as the unit of analysis after it is decided that the effects of both levels are present.

3. Calculating the mean squares between groups for both predicting and criterion variables (MSbx and MSby), and calculating the mean squares within groups for both predicting and criterion variables (MSwx and MSwy) from one-way ANOVA, with group as the treatment variable.

4. Computing the mean cross-products between groups (MCPbxy) and within group (MCPwxy) may be obtained through the following formulas:

MCPwxy = [summation over(n/i=1)] [summation over(k/j=1)] (Xij-X.j)(Yij-Y.j)/k(n-1) (4)

MCPBxy = n[summation over(k/j=1)] (X.j-X..)(Y.j-Y..)/k-1 (5)

The numerators may be obtained from one-way MANOVA. MCPwxy and MCPBxy may also be obtained from the unadjusted individual and group correlations, and mean squares between groups, utilizing the following formulas:

MCPBxy=rx'y' [square root of((MSbx)(MSby))] (6)

MCPwxy = (nk-1)(rxy)(sx)(sy)-(k-1)(MCPbxy)/k(n-1) (7)

Where rx'y' is the unadjusted group correlation, rxy is the unadjusted individual correlations, sx and sy are the standard deviations for individuals ignoring groups. When group sizes are unequal, n' should be used.

5. Computing the adjusted intercorrelations at the individual and the group (r') levels through the following formulas:

r = MCPwxy/[square root of (MSwx) (Mswy)] (8)

r' = MCPBxy-MCPwxy/[square root of (MSbx-MSwx) (Msby-Mswy)] (9)

Application Example

Self-confidence affects every aspect of an individual's life, and it is the key to success or failure and happiness or sadness (Bandura, 1977). Bandura (1986) described that an individual's actions and responses are shaped by his/her self-confidence. Therefore, a person with high self-confidence will be more creative, better able to deal with his/her environment, and experience more joy in life. If people believe that they can accomplish something, they will become more inclined to do so, and they will feel more committed to their decision (Bandura, 1986). According to Bandura (1997), self-efficacy is a judgment regarding one's ability to perform a behavior required to achieve a certain outcome. In comparison, collective-efficacy is the extension of Bandura's self-efficacy concept toward groups, which is concerned with judgments that people make about a group's level of competency. Bandura (1982) introduced the concept of collective-efficacy to account for the fact that group-efficacy has important implicatio ns on group/team performance. Zaccaro, Blair, Peterson, and Zazanis (1995) defined collective-efficacy as "a sense of collective competence shared among individuals when allocating, coordinating and integrating their resources in a successful concerted response to specific situational demands" (p.309). Based on Mischel and Northcraft (1997) and Zaccaro et al. (1995), collective-efficacy is composed of two components: (a) group processes such as communication and coordination, and (b) member resources such as players' commitment and skills. Bandura (1990) speculated that there is an inherent relationship between collective-efficacy and group performance. That is, high efficacious teams would perform better than low efficacious teams. Logically, high efficacious teams should win the close games and finish higher in the final standings than low efficacious teams. However, these proposed collective-efficacy theories have not been studied in depth in the field of sport and exercise sciences. Therefore, limited lit erature is available to provide support of the anecdotal contemplation. Particularly, of the studies related to collective-efficacy of sport teams (Feltz & Lirgg, 1998; Moritz & Watson, 1998; Paskevich et al., 1995), the number of measurement items was usually small and the measurement characteristics of the items were usually not reported. The collective-efficacy frameworks developed by Mischel and Northcraft (1997) and Zaccaro et al. (1995) were not adopted in these studies. The following study was designed to develop a sound measure of team-efficacy by incorporating Bandura's (1977, 1982, 1986, 1990) theories and Mischel and Northcraft's (1997) and Zaccaro et al.'s (1995) theoretical frameworks, and to use the developed scale to examine the relationship between team-efficacy and competition success of high school male varsity basketball teams.

Method

Participants

Participants were 292 high school male varsity basketball players from 29 teams (M age = 16.3 years, SD = 1.0 year). The high schools were part of Division A (15 teams) and B (14 teams) public school athletic leagues in New York City, which are generally formed on the basis of competition success. Team size ranged from 10 to 15 players.

Measures

Basketball Collective-efficacy Questionnaire (BCEQ). The BCEQ was designed for this study to measure individual perceptions of group competence. Definition and theories of collective-efficacy developed by Bandura (1977, 1982, 1986, 1990), Mischel and Northcraft (1997), and Zaccaro et al. (1995) guided the scale's development. Accordingly, a scale of collective-efficacy should include the following two areas of variables that measure: (a) group processes and (b) member resources. The group process variables are related to team and task assignments, timing and activity pacing, problem identification and solution, motivational enhancement, communication, strategy monitoring and adjustment, and environmental characteristics. Member resource variables are related to the willingness, knowledge, abilities, skills, physical condition, and composition of the group members. Other relevant issues may be individual and group beliefs, social skills, coordination and integration capabilities, decision making abilities, com munication, and proper execution among players and coaches. A modified application of the Delphi technique (Thomas & Nelson, 1996) was followed to develop the items. Through individual interviews with the members of an expert panel of 4 members in sport socio-psychology and measurement, as well as a thorough review of literature, a total of 48 statements on a 7-point Likert scale ('strongly agree' to 'strongly disagree') were initially formulated for the scale. Tests of content validity by the panel members focusing on the relevance, representativeness, and clarity issues of items resulted in 40 items in the preliminary scale to measure individual perceptions of team-efficacy. These items were subject to a factor analysis and an evaluation of internal consistency.

Team Winning Index (TWI). The TWI was designed for this study to measure team winning capacity, which included the following seven win/loss related variables: (a) league affiliation, (b) total winning rate, (c) league winning rate, (d) league standings, (e) winning rate of close games within league, (1) winning rate of nonclose games within league, and (g) winning rate of away league games. High school basketball games are comprised of four quarters of eight minutes each. A preliminary survey was first conducted to define a "close game" for high school male varsity basketball competitions. The head coaches of the 29 teams were asked how they would define a close game for high school teams at the end of the third period of play. The responses ranged from 3 to 10 points, with an average of 7 points. Thus, for the purpose of this study a close game was operationally defined as one that was within 7 points at the end of the third period.

Procedures

The office of the school district superintendent was contacted and permission was granted to survey the men's varsity basketball players in all 29 high schools in the district. Athletic directors and coaches agreed to have their teams participate in this study. Informed consent was obtained prior to data collection. The questionnaire administration took place before or after a scheduled practice or game, between December 15, 1998 and January 15, 1999. The players responded to the BCEQ in approximately 15 minutes. Participants completed their responses individually, and they were assured of the confidentiality. The team head coach responded to the TWI questions. The team's season win/loss records were also obtained from a local newspaper to verify the coaches' responses.

Data Analyses

The data were first used to examine the construct validity of the BCEQ through a factor analysis. Principal component extraction and varimax rotation techniques were adopted to maximize variance explanation and to obtain unrelated factors with the variables (Tabachnick & Fidell, 1996). Decisions on the factors and the items were based on the following criteria as suggested by Disch (1989) and Nunnally (1978): (a) a factor had an eigenvalue equal to or greater than 1, (b) a factor is evidenced in the scree plot, (c) an item had a factor loading equal to or greater than .40 without double loading, (d) a factor was interpretable in terms of its items, (e a loaded item on a factor was interpretable in terms of other items within the factor, and (g) a factor had at least two items.

To some extent, the TWI variables were intercorrelated. Because of this situation, using all 7 variables in correlational analyses would be redundant and would also increase inferential testing errors. Multicollinearity could also occur in any further regression analysis. Therefore, a similar factor analysis was conducted, solely to reduce the number of win/loss variables to unrelated factors.

Results

For the BCEQ variables, Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy (Kaiser, 1974) was .88, indicating that the sample size was adequate for a factor analysis. Bartlett Test of Sphericity was 4107.23 (p < .001), indicating that the hypothesis of the variance and covariance matrix as an identity matrix was rejected. Hence, a factor analysis was appropriate. Although 10 factors were extracted, the rotated factor structure and the scree plot supported a 3-factor structure. Thus, 28 items under 3 factors were retained with 59.1% of the variance explained. These factors were labeled Execution/Implementation (E/I; 16 items), Cooperation/Coordination (C/C; 7 items), and Skills/Abilities (S/A; 5 items). The re-examined factor structure is presented in Table 1. Alpha reliability coefficients for the factors were .90, .75, and .73, respectively.

For the TWI variables, KMO was .84 indicating that the sample size was adequate for a factor analysis. Bartlett Test of Sphericity was 2974.34 (p < .00 1), indicating that a factor analysis was appropriate. Two factors were extracted from the principal component extraction. The factor structure, as well as the scree plot, supported the two-factor solution with 84.92% of the variance explained (see Table 2). The two factors were Winning Rate (WR; 5 items) and League Classification (LC; 2 items). Because the factor analysis for the TWI variables was for data deduction, instead of scale development, alpha reliability was not calculated for the factors.

Factor scores, a weighted linear combination of retained variables, were calculated for the BCEQ and the TWI factors. Using individual and team as the unit of analysis, descriptive statistics were calculated for the factors in the two scales (see Table 3). Intercorrelations between the two winning and three team-efficacy variables are presented in Table 4. These correlations are unadjusted correlations because the assumptions of independent observations were ignored at the individual level and the assumption of independent errors was ignored at the team level. At the individual level, the execution/implementation and the skills/abilities factors were positively (p < .05) related to the winning rate factor, while the skills/abilities factor was also positively (p < .05) related to the league classification factor. At the team level, similar findings existed except that no BCEQ Factor was found to be significantly (p > .05) related to the league classification. As expected, correlations between the two TWI fact ors and among the three BCEQ factors were non-significant (p > .05) because the factor scores were derived from orthogonal rotations.

To test nonindependence of individual observations of the BCEQ and the TWI factors, ICC were calculated and tested using Formulas 1 and 2. Because there was an unequal number of players on the teams, adjusted n' was used through Formula 3, which was equal to 10.054. Intraclass correlations for the winning and team-efficacy factors are presented in Table 5. All team-efficacy factors had significantly (p < .05) positive intraclass correlations, indicating that team members were more similar than nonteam members. However, considering that correlations were only between .09 and .34, it was apparent that individual differences also existed, suggesting that correlations at the individual and the team level should be adjusted. ICC for the two TWI factors was 1.00 because these two factors are the sole functions of teams.

Utilizing Formulas 4 to 9, the adjusted intercorrelations were computed and tested through z-tests (see Table 6). At the individual level, the skills/abilities team-efficacy factor positively (p < .05) predicted the league classification; at the team level, the skills/abilities and the execution/implementation factors positively (p < .05) predicted the winning rate.

Discussion

Computation of correlation coefficients in a hierarchical data setting is complicated by the presence of nonindependence. Unless a rigorous experimental design is used to eliminate the interactive effect of individuals and groups, the traditional method of using individual or group mean as the unit of analysis does not provide accurate information about the relationship between variables. Rather, the procedures developed by Kenny and La Voie (1985) allow for the computation of individual and team correlations uncontaminated by nonindependence. These procedures are different from the general linear model (Jackson, 1989; Pedhazur, 1982; Pedhazur & Schmelkin, 1991) and HLM (Zhu, 1997) because overall adjusted correlations are calculated, instead of examining the equivalence of regression coefficients over groups or identifying the variables contributing to correlations at the individual and the group levels. In fact, the Kenny and La Voie's (1985) procedures may be used together with the general linear model or HLM to obtain more thorough information.

As part of this study, two measurement instruments (i.e., BCEQ and TWI) were developed through theoretical frameworks and appropriate scale development procedures. Because factor scores from orthogonal rotations were used to examine the unadjusted and adjusted correlations at both the individual and the group levels, inter-factor correlations within a scale were minimized so as not to complicate the relationships between the scales. It appeared that both the individual and the team processes had occurred in the relationship between team-efficacy and winning. This can be seen from the significant intercorrelations at both the individual and the team levels and intraclass correlations. Therefore, there was a need to simultaneously study the individual and the group effects. Comparing the adjusted coefficients with those unadjusted correlations, it seems that overall the correlations at the team level increased, while at the individual level they decreased, suggesting that team-efficacy is more a function of tea m norm. Particularly, for unadjusted correlations, two BCEQ factors (execution/implementation and skills/abilities) were positively related to the winning rate factor at the individual level; however, these correlation coefficients were no longer statistically significant after the effect of nonindependence of observation was removed. The findings from the application example have highlighted the necessity of applying the Kenny and La Voie's (1985) procedures when dealing with group behaviors. Otherwise, the unadjusted results could be misleading. While publications are biased toward significant research findings, more accurate computations using the adjustment procedures are important. In the above application case, correlation coefficients were solely changed in magnitude after the adjustments. However, in other situations correlational direction may also change (i.e., from being positive to negative, or vice versa). Florin, Giamartino, Kenny, and Wandersman (1990) revealed this type of findings in their st udy on the relationship between organizational climate and job satisfaction, where organizational independence level changed from being negatively to being positively related to employee job satisfaction after partialling out the group effect.

From the application example, it can be seen that the Kenny and La Voie's (1985) procedures have applicability in sport and exercise psychology, socio-cultural studies, and pedagogical studies where group norms, mutual responsiveness, and common effects often occur. The procedure may also be useful in studies related to exercise science and fitness when data are hierarchically nested. For instance, adjusted correlations could be calculated for the situation in Zhu's (1997) study that was related to health-related fitness in school setting. Moreover, as Carron et al. (1998) suggested, the adjusted correlations may be further used in multiple regression, factor analysis, and other multivariate procedures.

When deciding whether to apply the Kenny and La Voie's (1985) procedures in sport and exercise science studies, the key issues here are related to research purpose (Carron et al., 1998; Paskevich et al., 1995, 2001) and measurement assumptions (Pedhazur, 1982; Pedhazur & Schmelkin, 1991). If the focus of the study is on the individual level and the assumption of independent measurement observation/error holds, or if the focus is on the group level and individual differences can be ignored, simultaneous study of individual and group correlations is not necessary. Only when both the individual and the group effects are present and both are of research interest, should the procedures be applied. A major difference between the Kenny and La Voie's (1985) procedures and the general linear regression approach is that the Kenny and La Voie's (1985) procedures examine the nature of the correlations at the individual and the group levels and provide unique individual and group correlation information after adjusting fo r each other's effect; whereas, the general linear regression approach only identifies group membership and examines the interactive effect between group membership and other predicting variable(s) on the criterion variable (Jackson, 1989; Pedhazur, 1982; Pedhazur & Schmelkin, 1991). HLM is also different from the Kenny and La Voie's (1985) procedures in that the Kenny and La Voie's (1985) procedures focus on the magnitude of unique correlations at individual and group levels, while HLM focuses on identify predicting variables tested at individual and group levels, where variance explanation is limited to the variables that are selected for the study (Caldwell et al., 1999; Zhu, 1997)

Finally, as Zhu (1997) stated, "no analytical model is perfect" (p. 134). When differences exist in variance and measurement error between data levels, one should be careful of comparing the magnitude of correlations between levels. According to Kenny and La Voie (1995), a restriction in score range may lower correlations. It often happens in social studies that the individual level has lower variance and consequently has lower correlations than the group level. On the other hand, because the mean scores are often used, group measures are usually more reliable and less opt to attenuating the magnitude of correlations. When unequal variance or measurement error exists, unstandardized regression coefficients should be computed instead of correlation coefficients. Additionally, Moritz and Watson (1998) recognized that until recently the Kenny and La Voie's (1985) procedures have only been used in bivariate relationships, and they suggested the need for the development of multivariate applications procedures.

Table 1

Factor Analysis for the BCEQ Variables

 Factor Loading
Factor/Items F1 F2 F3

Execution/Implementation (16
items):
 1. everybody is willing to practice
 hard for the good of the team. .75 .04 -.14
 2. everybody in this team gives
 100% at all times. .74 -.04 -.14
 3. we always make sure that we
 stick to the game plan. .71 .17 -.05
 4. most players know their role on
 this team. .70 .13 -.08
 5. in our games, we outwork and out
 hustle the other teams. .70 .18 .00
 6. everybody is willing to
 contribute maximal effort at all
 times. .68 .09 -.18
 7. during the game we can identify
 things that cause poor performance
 and correct them. .65 .12 -.16
 8. we execute with good timing the
 offensive and defensive systems. .60 .34 -.12
 9. our team is made up of players
 with good psychological skills
 (concentration, confidence). .59 .31 -.13
10. we know which style of a game
 (fast, slow) is most effective for
 our team. .58 .14 .-03
11. most of the players know and
 accept the team goals. .58 .16 .-11
12. in our games and practice,
 everyone comes motivated to play. .58 .08 -.13
13. we perform as well at home as
 at away games. .56 .17 .07
14. our coaches communicate
 effectively to us during time outs
 and during half time. .52 .26 -.02
15. we have a balanced team (as
 many good guards as forwards). .47 .34 -.13
16. we can identify any problem
 that might come up during the
 season and solve it (either on or
 off the court). .42 .29 -.20

Skills/Abilities (5 items):
17. our team has the ability to
 make the playoffs. .17 .77 -.01
18. our team has the ability to
 finish first in our league. .23 .69 -.13
19. our back court (guards,
 shooting guards) can compete
 against any back court in this
 league. .08 .67 -.06
20. our team have the ability to
 play good defense and offense. .32 .56 -.18
21. our front court (forwards,
 centers) is as good as any
 other front court in the
 league. .18 .54 -.16

Cooperation/Coordination (7 items):
22. we can communicate effectively
 to each other on the court. -.07 -.04 70
23. everybody is willing to play up
 to his potential. -.28 .07 .63
24. most of my teammates do have
 strategic knowledge (x's and
 o's) of the game of basketball. -.04 -.00 .63
25. during a game we can control
 the tempo. .00 -.16 .60
26. we can play together as a team. -.02 -.16 .58
27. during games everybody plays
 unselfishly. -.09 -.09 .53
28. when things are not going well
 we don't get disorganized. -.16 -.14 .52
Table 2

Factor Analysis for the TWI Variables

 Factor Loading
Factor/Items F1 F2

Winning Rate (5 items):
League winning rate .978 .135
League standings -.974 -.069
Non league winning rate .973 .022
Total winning rate .951 .174
Away game winning rate .934 .191

League Classification (2 items):
League category -.080 .871
Close game winning rate .297 .610
Table 3

Descriptive Statistics for the Winning and Team-efficacy Factor Scores
by Individual and Group as a Unit of Analysis

Variable N Min Max M SD

Individual as the Unit
WR 273 -1.862 1.791 1.54E-15 1.000
LC 273 -1.605 1.792 -7.98E-16 1.000
E/I 273 -3.234 1.977 1.28E-16 0.938
S/A 273 -2.618 1.959 1.49E-16 0.849
C/C 273 -2.322 2.020 1.04E-16 0.852

Group as the Unit
WR 29 -1.862 1.791 4.373E-02 1.042
LC 29 -1.605 1.792 -4.33E-02 1.032
E/I 29 -1.225 3.301 0.136 0.805
S/A 29 -1.340 0.757 2.202E-02 0.585
C/C 29 -0.704 0.933 3.299E-03 0.391
Table 4

Intercorrelations for the Group (below the diagonal N = 29) and for the
Individual (above the diagonal N = 292)

Measure: A B C D

Winning Rate (A) 1.00 .000 .197 .473
 (p=1.000) (p=.001) (p=.000)
League Classification (B) -.048 1.000 .089 .252
 (p=.805) (p=.151) (p=.000)
Execution/Implementation (C) .402 .039 1.000 .104
 (p=.030) (p=.841) (p=.085)
Skills/Abilities (D) .868 .292 .271 1.000
 (p=.000) (p=.125) (p=.147)
Cooperation/Coordination (E) -.120 -.142 .056 -.290
 (p=.536) (p=.463) (p=.769) (p=.120)

Measure: E

Winning Rate (A) -.077
 (p=.215)
League Classification (B) -.097
 (p=.117)
Execution/Implementation (C) -.056
 (p=.358)
Skills/Abilities (D) -.058
 (p=.338)
Cooperation/Coordination (E) 1.000
Table 5

Test of Significance for Intraclass Correlation Coefficients (ICC)

Variable [MS.sub.B] [MS.sub.W] ICC F P

Winning Rate 10.393 6.062E-11 1.000 ----- .000
League Classification 10.393 1.714E-07 1.000 ----- .000
Execution/Implementation 2.970 0.655 0.260 4.535 .000
Skills/Abilities 3.108 0.412 0.340 7.549 .000
Cooperation/Coordination 1.320 0.662 0.090 1.996 .003
Table 6

Correlations for the Team (below the diagonal) and for the Individual
(above diagonal) Controlling for Non Independence

Measure A B C D E

Winning Rate (A) 1.000 -- -.092 .016 -.047
League Classification (B) -- 1.000 .021 .225 * -.013
Execution/Implementation (C) .462 * .030 1.000 -- --
Skills/Abilities (D) .731 * .302 -- 1.000 --
Cooperation/Coordination (E) .180 -.188 -- -- 1.000

* (p < .05)

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Address Correspondence To: Dr. James J. Zhang, Dept. of Exercise & Sport Sciences, 100 Florida Gym, P.O. Box 118205, University of Florida. Phone:352-392-0584, Eemail:jamesz@hhp.ufl.edu