Physical Self-Description Questionnaire: Psychometric Properties and a Multitrait-Multimethod Analysis of Relations to Existing Instruments

Transcription

1 JURNAL F SPRT & EXERCISE PSYCHLGY, 1994,16, Human Kinetics Publishers, Inc. Physical Self-Description Questionnaire: Psychometric Properties and a Multitrait-Multimethod Analysis of Relations to Existing Instruments Herbert W. Marsh Garry E. Richards U. Western Sydney, Macarthur Australian utward Bound School Steven Johnson, Lawrence Roche, and Patsy Tremayne U. Western Sydney, Macarthur Two samples of high school students (n = 315 and n = 395) completed the new Physical Self-Description Questionnaire (PSDQ). Confirmatory factor analysis (CFA) was used to demonstrate support for the 11 scales of physical self-concept (Strength, Body Fat, Activity, Endurance/Fitness, Sport Competence, Coordination, Health, Appearance, Flexibility, General Physical Self- Concept, and Self-Esteem) that the PSDQ is designed to measure, the replicability of its good psychometric properties in the two samples, and the replicability of the factor structure over gender. Subjects in Sample 1 also completed responses to the Physical Self-Perception Profile (Fox, 199) and the Physical Self-concept Scale (Richards, 1988). CFA models of this multitrait-multimethod data provided support for both the convergent and discriminant validity of responses to the three instruments. Comparisons of psychometric, theoretical, and pragmatic considerations of the three instruments led to the recommendation of the PSDQ in a wide variety of research and applied settings. Key words: physical self-concept, confirmatory factor analysis, factorial invariance, construct validity, Physical Self-Perception Profile, Physical Self- Concept scales There is general agreement among spordexercise psychologists and physical educators for the need to develop psychological instruments that focus on the physical domain and to evaluate such instruments within a construct validity framework (e.g., strow, 199; Nelson, 1989; Vealey, 1986). Gill, Dzewaltowski, Herbert W. Marsh, Steven Johnson, Lawrence Roche, and Patsy Tremayne are with the University of Western Sydney, Macarthur, P Box 555, Campbelltown, NSW 256, Australia. Gany Richards is with the Australian utward Bound School, Thanva, ACT 262, Australia.

2 Physical Self-Description Questionnaire / 271 and Deeter (1988) argued for multidimensional instruments based on theory, followed by item and reliability analysis, exploratory and confirmatory factor analysis, tests of convergent and divergent validity, and application in research and practice. Shavelson, Hubner, and Stanton (1976) and Wylie (1974, 1989) proposed similar criteria for the development and evaluation of self-concept instruments. In response to such needs, Fox and Corbin (1989), Richards (1987), and Marsh and Redmayne (1994) described preliminary development and validation of multidimensional physical self-concept instruments, based in part on the MarshIShavelson hierarchical, multidimensional self-concept model, that form the basis of the present investigation. In their reviews of self-concept instruments, both Shavelson et al. (1976) and Wylie (1974, 1989) emphasized the importance of multitrait-multimethod (MTMM) studies to test for convergent and discriminant validity, to assess patterns of relations between responses to different instruments, and to evaluate jingle fallacies (that scales with the same label measure the same construct) and jangle fallacies (that scales with different labels measure different constructs) (also see Marsh, 199a; Marsh & Gouvernet, 1989; Marsh & McDonald-Holmes, 199; Marsh & Richards, 1988). MTMM studies have not, however, received adequate emphasis in the evaluation of psychological instruments in sportlexercise research (strow, 199), and MTMM analyses have not been conducted with any of the three physical self-concept instruments considered here. Shavelson et al. (1976) reviewed existing research; developed a multifaceted, hierarchical model of self-concept; and described desirable measurement criteria in an evaluation of five multidimensional self-concept instruments. They proposed seven features of their construct definition of self-concept and presented a model in which general self appeared at the apex and was divided into increasingly more specific domains (e.g., physical, social, academic) at each level of the hierarchy. They emphasized that a theoretical model should provide a blueprint for constructing measurement instruments, for designing within-network studies of the proposed structure of self-concept, and for conducting between-network studies of relations with external constructs. Logically, the resolutions of some within-network issues using techniques such as factor analysis and MTMM analysis should precede between-network studies. Shavelson et al. (1976) found some support for the multidimensionality of self-concept in their review, but they reported no existing instrument that was able to differentiate between even the broad domains posited in their model. However, researchers subsequently developed self-concept instruments to measure specific domains based on explicit models, such as that proposed by Shavelson et al. (1976) and then used factor analysis to support these a priori domains. Wylie (1989) also noted that instruments designed to measure particular domains of self-concept that were confirmed by factor analysis were stronger than earlier instruments in which factor analysis was used to derive scales ex post facto from instruments not specifically designed to measure those factors. In reviews of this more recent literature, Marsh and Shavelson (1985; Marsh, 199a, 1993a) concluded that self-concept cannot be adequately understood if its multidimensionality is ignored. Particularly strong support for these contentions comes from a detailed evaluation of the theoretical rationale and empirical support (reliability, stability, factor structure, MTMM tests, construct validity) for Marsh's (199a,

3 272 / Marsh, Richards, Johnson, Roche, and Tremayne 1992) Self-Description Questionnaire (SDQ) instruments. The SDQ instruments have been evaluated to be among the best multidimensional instruments in terms of psychometric properties and construct validation research (Boyle, in press; Byme, 1984; Hattie, 1992; Wylie, 1989). Within this theoretical framework, it is also reasonable to posit more detailed hierarchies that are specific to particular domains of self-concept, such as the academic domain (Marsh, 199a, 199b, 1993a; Marsh, Byrne, & Shavelson, 1988), which led to the development of the Academic Self-Description Questionnaire (Marsh, 199b, 1993a) and, of particular relevance to the present investigation, the physical domain (Fox & Corbin, 1989; Marsh & Redmayne, 1994; Richards, 1987, 1988; Sonstroem, Harlow, & Josephs, 1994; Sonstroem, Speliotis, & Fava, 1992). Physical Self-concept In support of the construct validity of physical self-concept responses, factor analyses of SDQ responses (e.g., Marsh, 199a) have consistently differentiated responses to the SDQ Physical Ability and Physical Appearance scales from each other and from other SDQ scales. Jackson and Marsh (1986) demonstrated that athletic participation by high school and young adult women was substantially related to Physical Ability self-concept, but was substantially less correlated with nonphysical areas of self-concept. Marsh (1993d), using data from the Australian Health and Fitness Survey, showed that physical fitness self-concept was related to a wide variety of fitness indicators, whereas academic self-concept was not. Marsh and Peart (1988) demonstrated that physical fitness was substantially related to Physical Ability self-concept, modestly related to Physical Appearance self-concept, and unrelated to other areas of self-concept. They then found that an aerobics intervention had significant effects on Physical Ability self-concept but had no substantial effect on nonphysical SDQ scales. Marsh, Richards, and Barnes (1986) demonstrated that participation in utward Bound had significant effects on those SDQ factors most relevant to the program-particularly Physical Ability self-concept-and that the size and pattern of these effects were stable over an 18-month follow-up. Collectively, these studies support the construct validity of responses to broadly defined scales of physical self-concept. Researchers (Fox & Corbin, 1989; Marsh & Redmayne, 1994; Richards, 1987) subsequently developed multidimensional, hierarchical models of the physical domain of self-concept derived from the Marsh/Shavelson research and described physical self-concept instruments based on their models. Physical Self-concept Instruments For present purposes we focus on three multidimensional physical selfconcept instruments: the Physical Self-Perception Profile (PSPP; Fox, 199; Fox & Corbin, 1989), The Physical Self-concept (PSC) scale (Richards, 1988), and the Physical Self-Description Questionnaire (PSDQ; see Marsh & Redmayne, 1994). PSPP. The PSPP is the best known of these instruments. Fox and Corbin (1989; Fox, 199) summarized the development and preliminary validation of the instrument. Based on earlier empirical and theoretical research by Harter

4 Physical Self-Description Questionnaire / 273 (1982), Marsh (1987b; Marsh & Shavelson, 1985), and Shavelson et al. (1976), Fox and Corbin argued for the multidimensionality of self-concept. Noting that some self-concept instruments include separate physical scales, they were critical of single-score physical scales that combined and confounded a wide range of apparently differentiable physical components. Consistent with this multidimensional emphasis, the PSPP instrument measures four physical subdomains (bodily attractiveness, sports competence, physical strength, and physical conditioning/ exercise) as well as a global physical self-worth scale. Factor analyses identified the four subdomains (although the global physical scale was not included in these factor analyses) and exploratory factor analysis solutions were reasonably similar for responses by men and by women. PSPP responses were able to predict degree and type of physical activity involvement. Also, the pattern of relations among the self-concept scales supported their hierarchical model of physical self-concept that was based on the Shavelson et al. (1976) model. Self-concept researchers often evaluate gender differences in factor structures based on exploratory and, more recently, confirmatory factor analysis (see Byrne & Shavelson, 1987; Hattie, 1992; Marsh, 1987a, 1994). Fox (199), for example, argued that one of the strengths of the PSPP was that responses appear to be equally valid for both genders, stressing that genderspecific factor analyses should be conducted. Fox and Corbin (1989) modestly referred to their research as "development and preliminary validation" (p. 48). Particularly compared to most instruments in the sports and exercise field reviewed by strow (199), the development of PSPP is exemplary. Fox (199), however, emphasized that the construct validation of instruments is never completed and noted a number of directions for further research. From this perspective, it is disappointing that apparently so little construct validity research has been published since Fox (199; Fox & Corbin, 1989). In discussing potential limitations of the PSPP, Fox (199) emphasized that the psychometric support for the instrument was based exclusively on a population of young college students so that "use with other populations should be accompanied by a rigorous psychometric application in order to establish reliability and validity" (p. 17). Fox focused primarily on the internal structure of physical self-concept, giving limited emphasis to tests of the divergent validity of the different PSPP physical domains. Marsh and Redmayne (1994) specifically noted the need for divergent validity research showing that specific criteria form a logical pattern of relations with PSPP scales and the need for MTMM tests relating PSPP responses to those of other physical self-concept instruments like those considered here. PSC. Richards (1987, 1988) sought to develop a short, easily completed instrument to measure multiple dimensions of physical self-concept appropriate for males and females over the age of 12. Based on the Marsh/Shavelson model, the SDQ instruments, and a review of the physical self-concept literature, the PSC was initially developed to define eight a priori factors. Items were revised according to four criteria: internal consistency item analysis, stability over time, a well-defined factor structure, and a factor structure that was consistent over gender and age. As a consequence of this revision, seven factors were retained (Body Build, Appearance, Health, Physical Competence, Strength, Action rientation, and verall Physical Satisfaction). Each scale consisted of five items, and responses to each item were on an eight-category true-false scale.

5 274 / Marsh, Richards, Johnson, Roche, and Tremayne Richards (1987) summarized psychometric properties of PSC responses based on four groups (total N = 8): adolescent males and females (mean age = 13.9) and young adult males and females (mean age = 21). Coefficient alpha estimates of reliability were over.8 for all seven PSC scales in all four groups. Test-retest correlations over approximately 3 weeks were marginally lower than the internal consistency measures, but were also consistent over gender and age. Richards further demonstrated that the PSC factor structure (principal components followed by an oblique rotation) was very robust over gender and age. He presented the factor pattern matrix for one of the groups that was indicative of the four solutions in which every PSC item loaded at least.6 on the factor that it was intended to measure (target loadings) and no more than.3 on any other factor (nontarget loadings). Richards (1987) summarized age and gender trends for 3,5 respondents ages 1 to over 6. Male physical self-concepts were reasonably stable between the ages of 1 and the mid-2s. Although there was a slight decline in the 17-2 age range, this was followed by a strong surge in the late 2s, and a slight decline after 3. Males and females had similar scores between the ages of 1 and 12, but scores for women were systematically lower for all other ages (particularly in the age range). Richards (1987) also demonstrated the positive effects of participation in utward Bound programs on PSC responses. The PSC instrument appears to be very successful in relation to its intended goals, but thus far its development and evaluation has been described in only one unpublished conference paper (Richards, 1987). PSC research has focused primarily on factor structure and reliability, and there is limited support for its construct validity in relation to external constructs. Furthermore, although there is clear support for the a priori PSC scales, there are some idiosyncrasies in the scales which may influence their interpretation that are addressed in this investigation. PSDQ. Marsh and Redmayne (1994) described the development of a preliminary version of the PSDQ and examined relations between six components of physical self-concept and five components of physical fitness. Hierarchical confirmatory factor analyses supported the six components of physical selfconcept and a multidimensional, hierarchical model of physical self-concept. The pattern of correlations between specific components of physical self-concept and physical fitness generally supported the construct validity of the self-concept responses, and the correlation between second-order factors representing general physical self-concept and general physical fitness (r =.76) was substantial. The current version of the PSDQ instrument (see Appendix), first used in the present investigation, measures 11 scales: Strength, Body Fat, Activity, Endurance/Fimess, Sports Competence, Coordination, Health, Appearance, Flexibility, General Physical Self-concept, and Self-Esteem. The PSDQ scales reflect some scales from the SDQ instruments (Physical Ability, Physical Appearance, and Self-Esteem), scales from the earlier version of the PSDQ presented by Marsh and Redmayne (1994), and an attempt to parallel components of physical fitness identified in Marsh's (1993b) confirmatory factor analysis (CFA) of physical fitness indicators from the Australian Health and Fitness Survey. Because Marsh and Redmayne (1994) only considered girls, there is no evidence about gender differences in the factor structure for even the preliminary version of the PSDQ.

6 Physical Self-Description Questionnaire / 275 Comparison of the Item Contents There is a need to evaluate the construct validity of these three instruments. Hence, the main purpose of the present investigation is to compare responses to all three instruments using an adaptation of the CFA approach to MTMM analysis (Marsh, 1988, 1989, 1993~). In MTMM analysis, correlations between matching scales (convergent validities) should be systematically higher than correlations between nonmatching scales. n the basis of a preliminary content analysis of the items from the three instruments-which also provides information relevant to their content validity-we derived a priori predictions about which scales from the different instruments are "matching" (see subsequent discussion in Results section). PSDQIPSPP Relations. There appears to be a reasonable correspondence between the PSPP Strength, Sports, and Physical Self-Worth scales and the PSDQ Strength, Sports, and General Physical Self-concept scales. Each of the remaining two PSPP scales apparently combine distinguishable components of physical self-concept that are reflected by separate PSDQ scales. Items from the PSPP Condition scale (e.g., "take part in some form of regular vigorous physical exercise" and "ability to maintain regular exercise and physical condition") apparently reflect particularly the PSDQ Physical Activity scale, but they also reflect the PSDQ Endurance scale (e.g., the PSPP item "maintain a high level of stamina and fitness"). Items from the PSPP Body Attractiveness scale (e-g. "have an attractive body" and "admired because their physique or figure is considered attractive") are apparently most closely related to the PSDQ Physical Appearance scale, although this scale may also be related to the PSDQ Body Fat scale. PSDQIPSC Relations. There appears to be a reasonable correspondence between the PSC Strength, Appearance, Health, and Competence scales and the PSDQ Strength, Appearance, Health, and Coordination scales. Although the label of the PSC Competence scale does not directly match the PSDQ Coordination scale, the PSC items (e.g., "I am physically uncoordinated" and "My natural coordination and agility are good") apparently do. The PSC and PSDQ Activity scales and, to a lesser extent, the PSC Body and the PSDQ Body Fat scales also appear to be reasonably similar. The PSC Activity scale (e.g., "I dislike sports and physical activity" and "I like to keep out of games, sports, and other physical activities") actually reflects avoidance of activity, which appears to differ from the PSDQ Activity scale. The PSC Body scale reflects primarily body "shape and proportion" rather than body fat per se. Hence, the content of the PSC Body scale is more closely related to that of the PSPP Body scale than the PSDQ Body Fat scale. The PSC satisfaction scale (e.g., "I would like to be more physically able," "I would like to be more physically attractive," and "I would like to have better coordination and agility") reflects a desire to be different in each of the other components, differing from the PSDQ General Physical Self-concept scale, which measures generalized perceptions of physical competence. PSCIPSPP Relations. The PSC Strength and Body scales appear to reflect the same content as the PSPP Strength and Body scales. The PSPP Physical Self- Worth is more similar to the General Physical Self-concept scale from the PSDQ than to the PSC Satisfaction scale. Although no other PSC and PSPP scales are clearly matching, the PSPP Condition scale is expected to be related to the PSC

7 276 / Marsh, Richards, Johnson, Roche, and Tremayne Activity scale, and the PSPP Sports Competence scale is expected to be related to the PSC Competence (coordination) scale. Instruments Methods Responses to the PSPP, PSC, and PSDQ instruments are considered here. The final version of the PSDQ (Appendix) consists of 7 items designed to measure the 11 scales described earlier. Each item is a simple declarative statement, and subjects respond on a 6-point true-false response scale. The instructions, response format, and layout of the instrument are based on the widely used SDQII instrument (Marsh, 1992). The PSDQ is designed for adolescents 12 years of age or older like those considered here, but it should be appropriate for adults as well. Because this is the first application of the 11-factor, revised version of the PSDQ instrument, its psychometric properties are evaluated in detail. A considerably longer, pilot version of the PSDQ was used in Sample 1, and preliminary analyses (item analysis, reliability analysis, and factor analysis) not involving the PSPP and the PSC were used to reduce the initial item pool to the 7 items on the final instrument. These psychometric properties of the PSDQ responses were cross-validated in a second sample of adolescents as part of the present investigation. All analyses presented here are based on responses to only the 7 items on the final instrument. The PSC (Richards, 1987, 1988) is a 35-item instrument designed to measure seven scales described earlier. Each item is a simple declarative statement, and subjects respond on an 8-point true-false response scale. Research summarized earlier (Richards, 1987) indicated that PSC responses have good psychometric properties that generalize over age and gender. The PSPP is a 3-item instrument designed to measure five scales described earlier. Fox (199) reported factor analyses indicating that each item loads more highly on the factor that it is designed to measure and that individual scale reliabilities are in the 3s. Unlike the standard response formats used with the PSC and PSDQ instruments, the PSPP uses a nonstandard response format based on Harter (1982) in which each "item" consists of a matched pair of statements, one negative and one positive (e.g., "Some people feel that they are not very good when it comes to sports" vs. "thers feel that they are really good at just about every sport"). Subjects decide which of the two statements is most descriptive of them and then indicate whether the selected statement is really true for me or sort of true for me. Responses are scored on a 1-4 scale in which 1 represents a really true for me response to the negative statement and 4 represents a really true for me response to the positive statement. Although the response format is designed to reduce social desirability responding, Wylie's (1989) review of Harter's (1982) original instruments provided little or no support for this suggestion. A potential problem with this nonstandard response scale (Marsh & Gouvernet, 1989; Marsh & McDonald-Holmes, 199) is that subjects occasionally misunderstand the instructions, only responding to statements appearing on the left side or the right side of the page, or responding to both sets of statements. In the present investigation, for example, 23 of the 315 subjects incorrectly responded to

8 Physical Self-Description Questionnaire / 277 the PSPP so that their responses to the PSPP could not be used in the final analysis. As Fox (199) wams, the PSPP was originally designed for university students from the United States, and generalizations to our adolescent Australian population must be evaluated cautiously. Furthermore, Fox (personal communication, 1993) specifically noted an alternative, unpublished version of the instrument is available for junior high school students, but the factor structure was not so well defined in a study of British adolescents as in U.S. research. Procedures and Subjects Data considered here came from two samples. Sample 1 consisted of responses from 315 adolescents (28 boys, 17 girls) who completed the three physical self-concept instruments (PSDQ, PSPP, and PSC) as part of their normal participation in the Australian utward Bound school programs conducted in The students were ages 12 to 18 years (mean = 14.8). Subjects were students at one of eight coeducational or single-sex private schools and tended to come from middle-class and upper-middle-class backgrounds. Students from each school volunteered to participate in the program, but informal feedback from school administrators suggested that participants were generally representative of their school. The instruments were administered by the utward Bound instructors, who were experienced in administering questionnaires. The order of the instruments was systematically varied such that each of the instruments was equally likely to be completed first, second, or third. Sample 2 (the cross-validation sample) consisted of responses from 395 (217 males, 178 females) students in Bankstown Grammar School, a private, comprehensive high school in metropolitan Sydney, Australia. Students came from a wide range of family backgrounds, varying from lower middle class to upper middle class. All students in attendance on the day the questionnaire was administered completed the PSDQ (but not the PSPP or PSC) as part of the pretestbaseline data from a larger study. As is typical in Australian high schools, students were in Year 7 (mostly 12 or 13 years of age) to Year 12 (mostly 17 or 18 years of age). Teachers from the high school were asked to complete the questionnaire themselves and then met with project staff for training on how to administer the PSDQ. The instrument was then administered by teachers to intact classes of approximately 25-3 students. Statistical Analyses As recommended for analyses of SDQ responses (e.g., Marsh, 199a, 1992), all factor analyses were conducted on item-pair responses in which the first two items in each scale were averaged to form the first item pair, the second two items were averaged to form the second item pair, and so forth. This resulted in 3 or 4 item-pair indicators for each PSDQ scale (constructed from the six or eight items from each scale), 3 indicators for each PSPP scale (constructed from the six items from each scale), and 3 indicators for each PSC scale (constructed from the five items for each scale such that the final indicator was defined by a single item). Thus, analyses were conducted on responses to a total of 71 indicators used to represent 23 factors. The use of item pairs is recommended because itempair scores are more reliable and contain less idiosyncratic variance, because the

9 278 / Marsh, Richards, Johnson, Roche, and Tremayne distribution of responses to item pairs tend to be more normally distributed, and because the ratio of the number of measured variables to the number of subjects is halved. This is particularly important because in the present investigation, at least for some analyses, the number of subjects (N = 315) is small in relation to the number of items ( = 135 for the three physical self-concept instruments) and because self-concept responses tend to be negatively skewed. All correlational analyses were conducted using pair-wise deletion for missing data based on the item-pair responses. Because there were very few missing responses (less than.i%) and because an item-pair was defined as the response to the single nonrnissing response when one of the responses was missing, this was not a serious problem. Preliminary analysis indicated that responses to the PSC and PSDQ were similar for those students who did (292) and did not (23) respond correctly to the PSPP, and results presented here were similar for correlation matrices constructed with painvise and listwise deletion of missing data, so only the results based on the pair-wise deletion for missing values are discussed. Confirmatory Factor Analysis. CFAs performed with LISREL 7 (Jiireskog & Sorbom, 1988), were used to test the a priori factor structure underlying the self-concept responses. In CFA the researcher posits an a priori structure and tests the ability of a solution based on this structure to fit the data by demonstrating that (a) the solution is well defined, (b) parameter estimates are consistent with theory and a priori predictions, and (c) the xz and subjective indices of fit are reasonable (Marsh, Balla, & McDonald, 1988; McDonald & Marsh, 199). For present purposes the Relative Noncentrality Index (RNI) and the Tucker-Lewis Index (TLI) recommended by McDonald and Marsh (199) are considered, as well as the parsimony index based on the RNI (PRNI, see McDonald & Marsh, 199). The TLI and RNI vary along a -1 continuum in which values greater than.9 are typically taken to reflect an acceptable fit. The RNI contains no penalty for a lack of parsimony so that the addition of new parameters automatically leads to an improved fit that may reflect capitalization on chance, whereas the TLI contains a penalty for a lack of parsimony. The PRNI also imposes a penalty for a lack of parsimony that is typically considerably more severe than the penalty function in the TLI. Because CFA models considered here differ substantially in the number of parameters used to fit the data, the evaluation of model parsimony embodied in the TLI and PRNI is relevant. Tests of Factorial Invariance. As part of the present investigation, CFA solutions were compared in Samples 1 and 2. f greater substantive concern, the PSDQ factor solutions for males and females were compared for responses across the two samples. When parallel data exists for more than one group (i.e., Samples 1 and 2, or males and females), CFA provides a particularly powerful test of the equivalence of solutions across the multiple groups (see Marsh, 1993b, 1994). The researcher is able to fit the data, subject to the constraint that any one, any set, or all parameters are equal in the multiple groups. The minimal condition for "factorial invariance" is the equivalence of the factor loadings in multiple groups. It is also of interest to test for the invariance of factor correlations (see Marsh & Hocevar, 1985) that reflect relations among the different factors, factor variances, and measured variable uniquenesses that reflect measurement error. When comparing CFA solutions across multiple groups, analyses should be conducted with covariance matrices in which variables from the different

10 Physical Self-Description Questionnaire / 279 groups are scaled along a common metric and not correlation matrices in which each group is scaled in relation to its own mean and standard deviation (for further discussion see Joreskog & Sorbom, 1988). Although requiring parameter estimates to be equal across multiple groups necessarily results in poorer x2 and RNI values, the TLI incorporates a penalty based on the number of estimated parameters, so it is technically possible for such constraints to result in better TLIs (see McDonald & Marsh, 199, for further discussion). Preliminary Results In preliminary analyses, scale scores (the unweighted average of responses to items for each scale) and coefficient alpha estimates of reliability were computed for the two samples (Table 1). f particular interest is the comparison of coefficient alpha estimates of reliability in Sample 1 used to develop the PSDQ and the cross-validation Sample 2. Although the PSDQ reliabilities are good in Sample 1 (-82 to.92, median =.88), they are consistently somewhat higher in Sample 2 (.87 to.96, median =.91). Although PSC scales are defined with only five items, reliabilities (.77 to.88, median = 3.5) are good, except, perhaps, for the Satisfaction scale. Reliabilities for the PSPP scale (.77 to.79, median =.77) are somewhat lower than those for the other two instruments and somewhat lower than those reported in the test manual (Fox, 199) for U.S. university students. Reliability estimates for all three instruments are consistently somewhat higher for females than for males. Although not a substantively important aspect of this investigation, it is also relevant to determine the extent to which the factor structure in Sample 1 generalizes to Sample 2 using CFA tests of factorial invariance. Results in Table 2 indicate that when no invariance constraints are imposed (i.e., parameter estimates are not forced to be equal in the two samples), the fit of the a priori 1 1-factor solution is good for Sample 1 (TLI =.923), the cross-validation Sample 2 (TLI =.948), and their total (TLI =.939). Requiring all factor loadings to be equal across the two samples resulted in essentially no change in fit (TLI =.936 vs..939), providing strong support for this aspect of factorial invariance. The additional imposition of invariance constraints on factor variances and factor correlations also had little impact (TLI=.935). Although the restriction of the invariance of uniquenesses (measurement error) and factor loadings resulted in a small decrement in fit (TLI =.928) consistent with differences in reliability estimates in the two samples (Table I), even this effect was not large. Based on the PRNI that imposes a more severe penalty for lack of parsimony, the very parsimonious model imposing the complete invariance of all parameter estimates provided the best fit of all. Although the actual parameter estimates based on the PSDQ responses are examined in greater detail in subsequent analyses, these preliminary analyses provide good support for the replicability of the psychometric properties and factor structure of PSDQ responses. Results PSDQ Factor Structure and Gender In this first phase of the analysis, we consider the replicability of the PSDQ factor structure over gender based on the combined set of responses from Samples

11 Table 1 Descriptive Statistics and Gender Differences for the Physical Self-concept Instruments Sample 1 Sample 2 Total Males Females Total Males Females (n = 315) Coeff. (n = 28) Coeff. (n = 17) Coeff. (n = 385) Coeff. (n = 217) Coeff. (n = 178) Coeff. M SD alpha M SD alpha M SD alpha M SD alpha M SD alpha M SD alpha PSDQ Bfat Pact Endr S P ~ Cord Heal APP~ Flex Gpsc Estm (Marsh) * 4.43* 3.93* 4.29* 4.29* * 4.28* 4.37* 4.72*

12 PSPP (Fox) Strg Body 2.45* Cond 2.73* Sprt 2.69* Gpsw 2.65* PSC (Richards) Strg Body 5.38* Pact Comp 5.97* Heal % Appr 5.32* m Psat P- G Note. Strg = strength, Bfat = body fat; Pact = physical activity; Endr = endurance/fimess; Sprt = sports competence; Cord = coordination; Heal = 8 health; Appr = appearance; Flex = flexibility; Gpsc = general physical self-concept; Estm = esteem; Cond = condition; Gpsw = general physical self- 3. worth; Comp = competence; Psat = physical satisfaction. Respnses to the PSDQ, PSPP, and PSC instruments vary along a 1-6, a 1-4, and a 1-8 reg. S sponse scale, respectively. *Male/female means differ p <.5, two tailed. 9 2 g. EI E. 3 1 h) z

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14 Physical Self-Description Questionnaire / and 2 (N = 425 males, 285 females). Goodness-of-fit statistics for various models are presented in Table 2, and the factor solution imposing the invariance of factor loadings (but not factor variances, factor correlations, and uniquenesses) is presented in Table 3. When no invariance constraints are imposed, the fit of the model is somewhat better for females (TLI =.956) than for males (TLI = -929) or their total (TLI = -942). The imposition of the equality of factor loadings for the male and female solutions resulted in no change in goodness of fit, according to the TLI (both TLI =.942), and an improved fit according to the PRNI that more severely penalizes the lack of parsimony in the model with no invariance constraints. Inspection of the fit indices for other models imposing invariance constraints on other parameter estimates indicate only very slight decrements in the TLI and improvement in the PRNI. These results provide very good support for the invariance of the factor solutions across responses by males and by females. Inspection of the parameter estimates from the male and female solutions in which only the factor loadings are constrained to be equal also demonstrates a general pattern of similarity in the two solutions (Table 3). The most important aspect of this solution, perhaps, is the large factor loadings (.74 to.92, median =.87) that are invariant across solutions for males and females. These large factor loadings indicate that the factors are very well defined. Consistent with the moderately larger reliability estimates for females than for males (Table I), uniquenesses (measurement error) are slightly higher for males (median =.28) than for females (median =.25). Also consistent with the raw data, latent variable standard deviations are slightly larger for females (.97 to 1.11, median = 1.8) than for males (.92 to 1.2, median =.94). Gender differences in the pattern of correlations among the 11 PSDQ traits are typically small (Table 3), although the correlations are slightly larger for males (.1 to.84, median =.53) than for females (.2 to.82, median =.49). Although 11 of 55 correlations are significantly larger for males, two correlations are significantly larger for females (Strength is more highly correlated with Sports Competence and Flexibility for females than for males). In summary, the results of this analysis indicate that the a priori PSDQ model is able to fit the data well for both males and females and that the solutions for males and females are similar. There is particularly good support for the invariance of the factor loadings over gender, and reasonable support for the invariance of all parameter estimates. There are, however, some systematic differences between solutions for males and females. Responses by females, compared to males, are somewhat more reliable (less measurement error), somewhat more variable (latent variable standard deviations are higher), and somewhat more differentiated (factor correlations are smaller). ne possible explanation for these small differences is that females are better able to complete verbal questionnaires--or at least are more careful in doing so. It is, however, important to emphasize that the results suggest that the PSDQ is appropriate for adolescent males and females. Relations Between PSDQ, PSPP, and PSC Responses MTMM CFA Model With 23 Latent Constructs. A major purpose of the present investigation is to correlate responses to the PSDQ, PSPP, and PSC instruments based on responses by the 315 students in Sample 1. Although we

15 284 / Marsh, Richards, Johnson, Roche, and Tremayne Table 3 Confirmatory Factor Analysis of PSDQ Responses by Males and Females: Factor Loading Invariant Factor loadings (males and females invariant) Uniqueness Strg Bfat Pact Endr Sprt Cord Heal Appr Flex Gpsc Estrn Male Female Strgl Strg2 Strg3 Bfat 1 Bfat2 Bfat3 Pact 1 Pact2 Pact3 Endrl Endr2 Endr3 Sprtl spa;? spa3 Cord 1 Cord2 Cord3 Heal 1 Heal2 Heal3 Heal4 APP~~ APP~~ Appr3 Flex 1 Flex2 Flex3 Gpsc 1 Gpsc2 Gpsc3 Estml Estm2 Estm3 Estm4 Latent variable standard deviations Males * * Females (continued)

16 Physical Self-Description Questionnaire / 285 Table 3 (continued) Factor loadings (males and females invariant) Uniqueness Strg Bfat Pact Endr Sprt Cord Heal Appr Flex Gpsc Estm Male Female Factor correlations (males) Strg 1. Bfat Pact Endr Sprt.57* Cord Heal.25.3* * 1. Appr.47*.37.41*.46.61* Flex.39* * Gpsc *.68*.79*.84* * 1. Estm Factor correlations Cfemales) Strg 1. Bfat.5 1. Pact Endr Sprt Cord Heal Appr Flex Gpsc Estm Note. Strg = strength; Bfat = body fat; Pact = physical activity; Endr = endurance/fitness; Sprt = sports competence; Cord = coordination; Heal = health, Appr = appearance; Flex = flexibility; Gpsc = general physical self-concept; Estm = esteem. Each scale was represented by 3 or 4 indicators, the mean of a pair of items designed to measure that scale. Factor loadings were constrained to be invariant for males and females, but other parameters (uniqueness, latent variable standard deviations, and factor correlations) were not constrained to be invariant over gender. Parameter estimates of and 1. are fixed and not estimated. The model was fitted to separate covariance matrices for each group, and results are presented in a completely standardized metric that is common to both groups (Joreskog & Sorbom, 1989). *parameter estimates for males and female are significantly <.1). consider a variety of different CFA models derived from the MTMM literature (Marsh, 1988,1989,1993~), the initial model in Table 4 provides a good overview of the pattern of relations. In this a priori model, it is hypothesized that the 71 measured variables can be explained in terms of 23 latent constructs reflecting the scales that each instrument is designed to measure: 35 PSDQ variables define

17 Table 4 Confirmatory Factor Analysis of Three Physical Self-concept Instruments: 23 Trait Factors PSDQ PSPP PSC % a Uniqueness -$ a Factor loadings B PSDQ (Marsh) "$ 1 S t r g l S t r g a Strg B f a t l B f a t ~ Bfat n 3Pactl R P a c t & P a c t Y 4Endrl Endr $ E n d r Sprtl S p r t S p r t Cordl C o r d Cord H e a l l H e a l H H e e a a l l Apprl 9 19 A p p r w C m \ g

18 Appr3 9 Flex1 Flex2 Flex3 1Gpscl Gpsc2 Gpsc3 11 Estml Estm2 Estm3 Estm4 PSPP (Fox) 12 Strgl Strg2 Strg3 13Bodyl Body2 Body3 14Condl Cond2 Cond3 15 Sprtl Sprt2 Sprt3 16 Gpswl Gpsw2 Gpsw3 PSC (Richards) 17 Strgl Strg2 Strg3 (continued) 5

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20 5 Sprt Cord Heal Appr Flex Gpsc Estm PSPP (Fox) 12 Strg 86a Body 42 61b ab Cond b 7b Sprt Gpsw " PSC (Richards) 17 Strg 9a " Body Pact b Comp a ' 21 Heal " EL 22 Appr Psat U!43. Note. Strg = strength; Bfat = body fat; Pact = physical activity; Endr = endurancelfitness; Sprt = sports competence; Cord = coordination; Heal = health; Appr = appearance; Flex = flexibility; Gpsc = general physical self-concept; Estm = esteem; Cond = condition; Gpsw = general physical self Sj worth; Comp = competence; Psat = physical satisfaction. All coefficients vary between and 1 (decimal points are not presented to conserve space). Scales from different instruments that are predicted to be most highly correlated (i.e., the convergent validities in MTMM analysis) are in italics. Each variable was allowed to load on only the factor that it was designed to measure, and all other factor loadings were constrained to be zero. The com- g# pletely standard parameter from the LISREL analysis are presented. s 'Convergent validities between scales predicted a priori to be most closely matched. bconvergent validities between scales predicted a priori to be less &. closely matched. 8 '2, 1 h) \

21 29 / Marsh, Richards, Johnson, Roche, and Tremayne the 11 PSDQ factors, 15 PSPP variables define the 5 PSPP factors, and 21 PSC variables define the 7 PSC factors. Each measured variable is allowed to load on only the one factor that it is intended to measure. This very restrictive, a priori solution provided a reasonable fit to the data (TLI =.92), and it is therefore relevant to evaluate the parameter estimates in detail. Factor loadings reflect the relation between each measured variable and a latent construct-the "validity" of the measured variable. Because all 71 factor loadings are large (.67 to.9, median =.8), there is good support for this aspect of the factor solution for a11 23 factors. It is also useful to compare the sizes of factor loadings for the three instruments. Factor loadings for the PSDQ (.67 to.9, median = 33) tend to be higher than those for the PSC (.65 to 37, median =.8) and particularly the PSPP (.67 to.79, median =.74). Similarly, measurement error tends to be smaller for the PSDQ responses than for the PSC and particularly the PSPP responses. (For this model, the squared factor loading and the uniqueness sum to 1. for each measured variable.) These results are consistent with reliabilities of the 23 scales summarized in Table 1. In MTMM analyses (Campbell & Fiske, 1959; Marsh, 1988) it is typical to evaluate convergent and discriminant validity and method effects by comparing convergent validities (correlations between matching traits), heterotrait-heteromethod (correlations between different scales measured by different instruments), and heterotrait-homomethod correlations (correlations among nonmatching scales from the same instrument). Large convergent validities support the convergent validity of the responses, whereas discriminant validity is supported when convergent validities are larger than other correlations. Method effects are inferred when heterotrait-homomethod correlations involving a particular method approach 1. or are higher than heterotrait-heteromethod correlations. Correlations among the 23 latent constructs (Table 4) resemble a traditional MTMM matrix, with two important exceptions. First, the correlations represent relations among latent constructs that are appropriately correlated for measurement enor instead of correlations among simple scale scores that contain measurement error and that may not reflect the underlying factor structure. Hence many of the limitations in inspecting MTMM matrices based on scale scores are no longer relevant (see discussion by Marsh, 1993c; Marsh & Hocevar, 1988), greatly facilitating the interpretation of the MTMM data. Second, unlike the traditional MTMM design, the same set of traits is not measured by each of the three instruments (the multiple methods in this MTMM application). In fact, although there is an unambiguous matching of some of the scales in the three instruments (e.g., the three Strength scales), earlier discussion suggested that this is typically not the case. Hence, there is a certain degree of subjectivity in determining which correlations should be considered the "convergent validities." Although this feature complicates interpretations, it is, perhaps, a realistic problem in a relatively new area where the intended scales from independently designed instruments are not likely to be strictly parallel. Based on the earlier content analysis of items in the 23 scales, the 167 correlations between factors representing different instruments were classified into three a priori categories: 9 convergent validities in which the scales are most closely matched (those with a superscript a in Table 4), 6 convergent validities in which the scales are less closely matched (those with a superscript b in Table 4), and the remaining 152 (heterotrait-heteromethod) correlations. There is very