The utility of general self-esteem and domain-specific self-concepts: their influence on indigenous and non-indigenous students' educational outcomes.

Bodkin-Andrews, Gawaian ; O'Rourke, Virginia ; Craven, Rhonda G. 等

Introduction

Indigenous Australians have become recognised as one of the most disadvantaged of Indigenous nations across all developed Western countries (Cooke, Mitrou, Lawrence, Guimond & Beavon, 2007). The inequities suffered by Indigenous Australians, when compared to their non-Indigenous counterparts, extend across a wide range of quality-of-life indicators including higher levels of unemployment, lowered levels of physical health and economic well-being, and an increased prevalence of negative mental health outcomes and psychosocial stressors (De Maio et al., 2005; Human Rights & Equal Opportunity Commission, 1997; Zubrick et al., 2005). In addition, Indigenous Australians are the most educationally disadvantaged Australians. This is of dire concern, given that education predicates life opportunities (Mellor & Corrigan, 2004; New South Wales Aboriginal Education Consultative Group & New South Wales Department of Education & Training, 2004; Shkolnikov et al., 2006). It is indisputable that education should be recognised as a pivotal point of intervention for righting the inequities suffered by people from disadvantaged backgrounds. Furthermore, identifying culturally appropriate methods of redressing the inequities between Indigenous and non-Indigenous students is also of paramount importance (Craven & Marsh, 2004).

Erasing the educational inequities: The search for answers

Researchers have noted that traditional methodologies have focused too strongly on ethnicity and socio-economic welfare as an assumed sole cause for pre-existing educational inequities (Jonas, 2003; Rowe, 2003). The implications of this conceptually limited research agenda has arguably produced a considerable amount of doubt as to whether effective schooling interventions could be produced. Indeed, Rowe cited a number of prominent studies that advocated this very attitude: for example, Coleman and colleagues (1966, p. 3) argued that 'schools bring little influence to bear on a child's achievement that is independent of his background and general social context'. Rowe (2003) argued that such research lacked generalis-ability due to an over-reliance on small case studies, a lack of longitudinal data and, most importantly, overly simplistic statistical methodologies that failed to fully grasp the complexity of factors influencing any child's receptiveness and performance within the schooling context. This emphasis on ethnicity and socio-economic status may also be seen as a direct reflection of what is known as the deficit approach to education (a blaming-the-victim approach with an overemphasis on explaining academic performance through genetic or cultural practices, or both), which was rampant throughout early research into Indigenous education (Partington, 1998). Although most educational researchers now contest such a perspective, the deficit model is still evident in some Indigenous Australian educational research almost to the extent that the 'disparity in educational outcomes of Indigenous and non-Indigenous students has come to be viewed as 'normal' and incremental change seen as acceptable' (Ministerial Council on Education, Employment, Training, and Youth Affairs, 2006, p. 16).

Hattie (2009) also has highlighted how such deficit approaches may be disingenuous to understanding the multitude of factors that may influence any students' educational outcomes. In analysing more than 800 meta-analyses, which incorporated 52,637 studies targeting many millions of students, Hattie identified six overall factors that have been found to influence the achievement patterns of students: the child; home; school; curricula; teacher; and teaching approaches. Although varying conceptualisations of a student's background were found to be weakly related to achievement (for example, gender, birth weight, ethnicity), Hattie identified numerous other student factors that were more strongly linked to achievement (for example, self-perceptions, recognition of cognitive and emotional stages of development, engagement) rather than factors associated with deficit approaches. Indeed, Hattie noted that ethnicity had minimal to no effects, which led him to conclude: What seems more important is that students have a positive view of their own racial group, and that educators do not engage in the language of deficit theorizing. Accepting that students come to school and have difference in cultural heritages and that they can be allowed and encouraged to have a positive image of their own racial group or heritage is an acknowledgement of the importance of culture, and can show the students that they are accepted and welcomed within the learning environment. (2009, p. 57)

These findings also reflect more recent directions in Indigenous educational psychology research whereby researchers have argued that salient psychological constructs underpin schooling success (Craven & Bodkin-Andrews, 2006; McInerney, 2003; Purdie et al., 2000).As such, researchers have considered the potential impact of varying dimensions of self-concept as important determinants of both Indigenous and non-Indigenous students' schooling outcomes (Craven & Marsh, 2004; McInerney, 2003; Pedersen & Walker, 2000; Purdie & McCrmdle, 2004).

Understanding self-concept

Considering that a positive self-concept has long been understood to be a desirable outcome in and of itself, posited to causally affect achievement and facilitate multiple educational outcomes (Marsh & Craven, 2006), it is surprising that one of the most pertinent issues still plaguing much of self-concept research and intervention strategies is the ambiguity of the exact nature and definition of the self-construct used (Marsh & Craven, 1997,2006). For the purposes of this investigation, and consistent with the labels utilised within the Self-description questionnaire II (short version--Marsh et al., 2005), 'general self-esteem' will refer to one's overall perceptions of oneself, where as 'self-concepts' will refer to more domain-specific constructs (for example, verbal self-concept). There are distinctions between domain-specific self-concept and self-esteem constructs but the current labels are used to remain consistent with the literature reviewed within this article.

This problem of ambiguous definition lingers, despite a seminal early review of self-concept and self-esteem literature that provided a strong foundation for understanding the nature of self-concept (Shavelson, Hubner & Stanton 1976). Starting from a definition that self-concept must be understood as one's perceptions of oneself largely drawn from individual interactions with the surrounding environment and other people, Shavelson, Hubner and Stanton (1976) argued that self-concept should be seen as an important construct that is useful for predicting and explaining how an individual may act, in that the positive or negative self-evaluations act as a critical motivating source behind the behaviour of an individual in any given situation. In addition, Shavelson, Hubner and Stanton (1976) highlighted the need to consider the multidimensional nature of self-concept, whereby each dimension, or sub-facet of the self, plays varying roles in not only the categorisation of oneself but also as varying dimensions of the self may influence a wide variety of behaviour. They proposed that self-concept was multidimensional and hierarchical in nature, comprising a general academic self-concept component--which was theorised as English, history, mathematics and science self-conceptsand non-academic components of the self--which were broadly split into social, emotional, and physical self-concepts (which were further split into more precise domains).

Multiple dimensional self-concepts: Academic self-concepts

Based on the theoretical foundation provided by Shavelson, Hubner and Stanton (1976), an expanding body of international research has found considerable support for the multidimensionality of the self-concept construct and the usefulness of targeting specific self-concept domains (see Marsh & Craven, 2006). For example, Marsh and O'Mara (2008) tested the extent to which academic self-concept and general self-esteem predict academic achievement and educational attainment over five time-waves of data (spread over eight years, beginning in Year 10). Across all waves of data, and after socio-economic status and prior ability had been controlled for, significant and positive relations were found between academic self-concept and subsequent achievement or attainment (and vice versa). In contrast, significant paths for global self-esteem were fewer; when such paths were significant, they were consistently and substantially weaker in comparison. In consideration of these results they argued that:

practitioners need to target specific components of self-concept logically related to their performance goals and intended outcomes. Whereas targeting global components such as self-esteem may result in increased happiness ... These results do not generalise to desired outcomes. This has particular implications for intervention research. (Marsh & O'Mara, 2008, p. 549)

There is also an expanding body of research suggesting that more domain-specific academic self-concepts (for example, mathematics self-concept) hold a strong causal influence over matching schooling outcomes (for example, mathematics achievement) (Marsh, 1992; Marsh et al., 2005; Marsh & Koller, 2003; Marsh & Yeung, 1997). But there is a paucity of research examining the explanatory power of both domain-specific self-concepts and general self-esteem with regard to schooling outcomes.

Self-concept research and Indigenous Australians

In Indigenous Australian educational research, general self-esteem has been considered as an important construct for Indigenous Australian students. For example, within the Ways forward report on Indigenous mental health, Swan and Raphael (1995) argued that a key factor in aiding self-determination for Indigenous peoples would be the promotion of a stronger sense of self amongst the younger generations. They were careful to stress, though, that any process seeking to enhance the

self-esteem of Indigenous Australians must also consider strategies to develop a stronger sense of cultural identity, self-reliance, adaptive coping strategies to aid in stress management, and the ability to achieve their aspirations and full potential. More recently, The report of the review of Aboriginal education (NSWAECG & NSWDET, 2004) has emphasised the need to bolster the self-esteem of Indigenous students by stating that: A recurring theme from the field trips indicated that the success of Aboriginal students in junior secondary school, as in other phases of schooling, will only improve if schools can support and strengthen the self-esteem of their students. (p. 110)

Craven and Tucker (2003), who undertook semi-structured focus group discussions with representatives from a number of regional New South Wales Aboriginal education consultative groups, also identified as an overwhelming theme the need to enhance Indigenous students' self-concepts as a method of obtaining stronger schooling and post-schooling outcomes for Indigenous students. Craven and Tucker moved beyond investigating generalised notions of the self and found that participants stressed the importance of specific domains of self-concept pertaining to identity, reading, leadership, peer relations, sport and physical health domains. Despite this finding, and advances in self-concept theory demonstrating that 'self-concept cannot be adequately understood if its multidimensionality is ignored' (Marsh & Craven, 1997, p. 137), a number of studies and investigative reports involving Indigenous participants have continued to emphasise solely general self-esteem and as such focus on a unidimensional conceptualisation of the self-concept construct (for example, Swan & Raphael, 1995; Zubrick et al., 2006). Interestingly, studies that have used objective educational outcomes (for example, standardised achievement, student grades and teachers' ratings of students) have found no significant relations between global self-esteem and academic achievement (Pedersen & Walker, 2000; Purdie & McCrmdle, 2004; Zubrick et al., 2006).

Only a small number of studies targeting relations between academic self-concept and educational outcomes for Indigenous Australian students exist (Craven & Marsh, 2005; Craven et al., 2005; McInerney, 2003; Pedersen & Walker, 2000; Purdie, 2005; Purdie & McCrindle, 2004) and the results of such studies are relatively consistent and meaningful. The earliest of these studies targeted Indigenous and non-Indigenous primary school children aged between 6 and 12 years (Pedersen & Walker, 2000). Although Pedersen and Walker used a scale designed to capture differing facets that may affect schooling outcomes (for example, in-group preference, general self-esteem, general academic self-concept), only academic self-concept was found to be significantly correlated with teachers' ratings of student ability for the Indigenous students (as well as for non-Indigenous students). Similar results were also reflected in another study across Indigenous and non-Indigenous students ranging from primary to late secondary school (Purdie, 2005), whereby academic self-concept held the strongest relations to students' self-perceptions of their achievement when compared to other self-concept facets relating to self-perceptions of peer relations, career aspirations, family relations and overall self-acceptance measures.

The strength of academic self-concept is not limited to achievement constructs, as is demonstrated in research by Craven and Marsh (2005). Using data from a large-scale study involving Indigenous and non-Indigenous secondary students (Craven et al., 2005), Craven and Marsh identified significant paths emanating from academic self-concept to varying schooling outcomes, over and above predictive paths emanating from socio-economic status. These paths suggested that academic self-concept predicted more positive levels of school aspirations to finish Year 12, future goals for post-secondary schooling, school enjoyment and academic ability, in addition to lower levels of absenteeism for both Indigenous and non-Indigenous students. In further analyses of the data, Bodkin-Andrews, Craven and Marsh (2005) found that, across 12 different dimensions of self-concept, academic self-concept was the most consistent variable in holding strong relations with the more generalised schooling outcomes of school enjoyment, school aspirations and lowered levels of absenteeism.

Although these findings are promising, some concerns have been raised as to the nature of more Westernised notions of self-concept. Traditionally, Westernised self-concept measures have more often than not failed to acknowledge the sensitive link between self-perceptions and varying notions of cultural identity for Indigenous Australians. Indeed, cultural identity, and confidence to freely express one's identity, has been repeatedly argued to be a critical construct for Indigenous children (for example, Kickett-Tucker, 2009; NSWAECG & NSWDET, 2004; Purdie, 2003). The argument that a sense of cultural value can bolster students' educational attainment is not newthe practice of endorsing students to experience academic success while also maintaining their cultural competence forms the basis of culturally inclusive curriculum and pedagogy (Ladson-Billings, 1994, 1995). Indigenous communities and academics have also long advocated culturally inclusive practices in the classroom as a catalyst to improve educational outcomes with the emphasis on using students' personal cultures to establish robust and enduring school achievement. For example, Ladson-Billings (1995) emphasised the fundamental role culturally inclusive curriculum and pedagogy perform in determining students' successful educational outcomes, especially for those students who are not part of the schools' cultural majority student body. A decade later, Mellor and Corrigan (2004) emphasised that a failure to acknowledge Indigenous history and culture as part of the formal curriculum further reinforced Indigenous people's invisibility; they endorsed more culturally inclusive practice to help achieve equitable educational participation and achievement rates of Indigenous and non-Indigenous students.

New solutions are needed to ensure that students from culturally diverse backgrounds have equal access and participation within a high-quality education that endorses high expectations and outcomes for each student's educational achievement (Phuntsog, 1999). As a result, schools are attempting to recognise, respect and respond meaningfully to students' cultures within the school context, as this is considered a potential pathway to successful student educational outcomes. In this manner, the importance of cultural competence within education settings is understood and adopted by teachers who use students' cultures as conduits for learning and are aware that meaningful learning is relevant to the lives of students and aligns to students' cultural values and knowledge (Ladson-Billings, 1995). Gay (2002) noted that such teachers go beyond perfunctory acts, such as simply identifying students' cultural backgrounds within the classroom, and move to recognising and interacting respectfully to the different cultural values present in the classroom as tools to enhance enduring opportunities for equitable student success.

Although international research has examined aspects of the relations between identity, self-esteem, some domains of self-concept, academic achievement, and engagement for various minority groups (for example, Awad, 2007; Cokley, 2002), studies incorporating both cultural identity and self-concept constructs for Indigenous students are limited at best. Of the small amount of empirical evidence that does exist, some findings suggest that there may be little or no link between notions of identity and achievement for Indigenous students (Pedersen & Walker, 2000). However, other studies have linked notions of identity with higher levels of general self-esteem (Kickett-Tucker, 2009; Purdie, 2003). Although the link between identity and school achievement may be weak, it could be argued that specific domains of self-concept may facilitate the development of achievement for Indigenous students and may also act as a 'missing link' between Indigenous students' sense of identity and educational success. Academic self-concept may indeed be a pivotal and powerful construct for schooling interventions. Unlike advances in the international literature though, little research has been carried out into the relations between Indigenous Australian students' domain-specific self-concepts and important schooling outcomes (for example, grades, academic aspirations and attendance), and compared and contrasted these relations for both Indigenous and non-Indigenous students.

Research aims

Given that research has identified self-concept as a key psychological construct with positive impact on students' schooling outcomes, it is critical that recent advances in self-concept research be capitalised and extended upon to include the perspectives of Indigenous Australian students and to examine how their perceptions may differ from non-Indigenous students. In undertaking such a cross-cultural research direction, it is essential that a number of standards be met to ensure that the measurement instruments are psychometrically sound across the two broad cultural groups considered. Although much traditional research has sought to compare various groups with regard to the mean scores across a number of measures, too little thought has been given to whether the measures themselves are equivalent in meaning and structure across the differing groups (Byrne, 2003; Byrne & Campbell, 1999).

* The first research aim of this investigation thus seeks to deal with this issue by using recent advances in statistical techniques in order to compare and contrast the equivalence of the reliability and structural validity of the measures of self-esteem, self-concept (mathematics and verbal), schooling outcomes (teacher grades, aspirations, absenteeism) and home resources used within this investigation for Indigenous and non-Indigenous students to ascertain whether they are psychometrically sound for both Indigenous and non-Indigenous samples.

If the measurement instruments are found to be structurally equivalent across Indigenous and non-Indigenous students, meaningful group comparisons may then be made with a greater level of confidence (Marsh, 1993).

* A second research aim is to test whether significant differences are present for Indigenous and non-Indigenous students for general self-esteem, mathematic-sand verbal self-concepts, teacher grades, aspirations and absenteeism.

Finally, with the structural equivalence of the measurement instruments examined, and the mean group differences determined, the primary purpose of this investigation will be considered.

* The third research aim is to identify the extent to which general self-esteem, mathematics, and verbal self-concepts will predict the schooling outcomes of teacher grades, aspirations, and absenteeism for Indigenous and non-Indigenous students.

Methodology

Participants

Four secondary public schools across rural and urban localities within the state of New South Wales participated in the present investigation. School selection was based upon the schools having a minimum enrolment of 10% Indigenous students. From these schools, all students from Years 7 to 10 were invited to participate in the study (pending parental permission). This yielded a sample of 1369 school students from Years 7 to 10, with a mean age of 13.75 years. Of these students, 694 (50.16%) were male and 675 (49.84%) were female, with 217 (14.45%) being Indigenous Australian and 1152 (85.55%) being non-Indigenous Australian. Of the non-Indigenous students, in an open-ended question asking them to list their cultural background, 154 (13.37% of the non-Indigenous sample) acknowledged having another cultural background (with only 15 students not acknowledging some form of 'Australian' cultural background). Considering the small sample of non-Indigenous students recognising non-Australian cultural backgrounds, and that government policy documents (for example, Department of Education, Science and Training, 2006) and educational research within Australia often uses 'all other Australians' as a comparative point for the progress of Indigenous students, no omissions or adjustments were made with regard to all further analyses within this paper. These students were drawn from four, predominantly rural, secondary schools within the Australian state of New South Wales.

Materials

General self-esteem A six-item overall general self-esteem measure (for example, 'Overall, I have a lot to be proud of') obtained from the Self-description questionnaire II--short version (Marsh et al., 2005).All items were scored on a 6-point Likert scale, ranging from 1 (false) to 6 (true).

Mathematics self-concept A four-item measure of confidence in mathematics (for example, 'MATHEMATICS is one of my best subjects') obtained from the Self-description questionnaire II--short version (Marsh et al., 2005). All items were scored on a 6-point Likert scale, ranging from 1 (false) to 6 (true).

Verbal self-concept A five-item measure of confidence in English measure (for example, 'I learn things quickly in ENGLISH classes') obtained from the Self-description questionnaire II--short version (Marsh et al., 2005). All items were scored on a 6-point Likert scale, ranging from 1 (false) to 6 (true).

School aspirations A single-item three-point self-report scale assessing when students may aspire to leave secondary school (Craven et al., 2005). The highest rating simply indicates a wish to complete Year 12 of high school, whereas the lowest rating indicates that the student wishes to leave school as soon as possible.

Absenteeism An open-ended, single-item self-report measure whereby students listed how many days they were absent in their previous year of schooling.

Student grades Ratings of student grades to reflect the school grades offered in the end-of-year student report cards were obtained from teachers of mathematics and English. Due to some schools offering differing reporting methods (for example, one school offered a percentage value whereas others ranked from 1 to 7), scores were standardised within each year level to control for potential year level and school effects.

Home educational resources A self-report measure used by Craven et al. (2005), which listed a total of 10 resources that can be found within the home environment (for example, a room of one's own, a desk to study on). Students answered 'yes' or 'no' as to whether they had access to such resources at home and affirmative responses were totalled.

Procedure

A survey containing the self-report items was administered in school halls under examination conditions. Across all schools, students were split into year groups for each survey. To control for varying literacy levels, the survey was read aloud by the researchers using a microphone.

Data screening

A slightly disproportionate number of missing responses were identified with regard to the student grades, as a total of 88 students were missing either mathematics or English grades, or both (approximately 6% of the total sample). The nature of these missing responses was difficult to determine, although, during data collection, a number of teachers noted that a number of children had recently moved from or into the school, and hence grade scores were unavailable for them. These participants were removed from the analysis. Careful attention was then placed on list-wise deletion for participants who did not complete either 75% of the multiple indicator variables (for example, mathematics self-concept), which resulted in another 5 participants being deleted. The remaining overall response data showed that there was less than 5% of data missing, and based on Tabachnick and Fidell's (2007) recommendations, the EM substitution method was used for the remaining randomly missing data. Univariate and multivariate outliers were also identified and either modified (for univariate outliers) or deleted (for multivariate outliers) from the sample. As a result, another 58 participant response sets were deleted from analysis, and the final overall sample size was reduced to 1218 participants (with a mean age of 13.76 years, 50.16% male and 49.84% female, 14.45% Indigenous Australians and 85.55% non-Indigenous Australians).

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Statistical analysis techniques

Statistical software

All data obtained for this investigation was entered and screened in SPSS v.17.0 and all statistical analysis techniques were undertaken in SPSS 17.0 and LISREL 8.72 (Joreskog & Sorbom, 2004).

Statistical analyses

Confirmatory factor analyses (CFA) After identifying the basic descriptive statistics (for example, means and alphas), two CFA analyses (see Figure 1) were conducted to test the extent to which indicator items reflect the underlying theoretical factor structure (Byrne, 1998) for Indigenous and non-Indigenous students. For this investigation, the iterative method known as maximum likelihood estimation was used to estimate the parameters in the specified models (Kaplan, 2000), as this procedure is robust with respect to violations of normality that can potentially affect parameter estimates and goodness-of-fit indices (Hu, Bentler & Kano, 1992). With regard to model fit, the root mean-square error of approximation (RMSEA), the non-normed fit index (NNFI; also known as the Tucker Lewis Index), and the comparative fit index (CFI) were used (see Marsh, Balla & Hau, 1996).

Factorial invariance testing This extension of CFA testing was conducted to determine if the measurement instruments were equivalent in meaning and structure across the differing groups (Byrne & Campbell, 1999).

Using recommended techniques (Byrne, 1998; Marsh, 1994; Parker, Dowson & McInerney, 2007), testing of factorial invariance consisted of five increasingly restrictive models. The first model is the least restrictive model (completely free), with no between-group invariance constraints placed on the estimated parameters. In the second model, the factor loadings were held invariant across the specified groups; which is typically considered the minimum condition of factorial invariance (Byrne, 1998; Cheung & Rensvold, 2002). The third model held the factor loadings, factor variances and the covariances constant, and is often recommended as the minimal requirement of equivalence test, especially when dealing with more sensitive cultural groups (Bodkin-Andrews et al., 2010). The fourth model is stipulated as holding the factor loadings and the uniquenesses invariant. Finally, the fifth model assessed was the most restrictive in that it held all parameters invariant across the groups (totally invariant model). Generally speaking, the final two models are considered to be overly restrictive in the judgements of invariance, yet should be tested as part of good practice (Byrne, 1998). Cheung and Rensvold (2002) also emphasised that, with models two to five, a change of no more than +/- .01 in the CFI (when compared to the baseline model) is needed to assume invariance.

Multiple-indicator-multiple-cause (MIMIC) models Differences in levels of designated factors between groups (for example, how Indigenous and non-Indigenous students may hold differing levels of mathematics self-concept) were assessed by utilising the MIMIC technique. This technique simultaneously estimates the underlying factor structure of the instrument (whether it be discrete and/or continuous variables) in addition to determining the extent to which the specified observed or grouping variables (for example, Aboriginality) may 'cause' the latent factor (for example, school self-concept--see Kline, 2005; Marsh et al., 2005; Marsh, Tracey & Craven, 2006 for more detailed overviews of this procedure).

Structural equation modelling (SEM) path analyses An SEM path analysis was employed to determine the extent to which independent latent or directly observed variables relate to, or more accurately predict, any number of latent or directly observed outcome variables (Schumacker & Lomax, 1996). As a result, a SEM path analysis was conducted to determine the extent to which the indicator variables (that is, general self-esteem, mathematics self-concept, verbal self-concept and home educational resources) may predict the schooling outcomes (for example, English and mathematics grades, aspirations, and absenteeism). Figure 2 offers a pictorial representation of the structural component path analyses conducted across the Indigenous and non-Indigenous samples.

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Moderating path analyses A moderating path analysis within SEM is essentially a combination of traditional invariance testing and path analysis techniques, whereby the predictive paths between at least two constructs (whether they be latent or directly observed) are simultaneously tested to determine whether they differ across two separate groups (compare Frazier, Tix & Barron, 2004; Little et al., 2007). As such, a moderating path analysis answers the simple question of which variable most strongly predicts another variable across differing groups, and tests the extent to which these differences in prediction significantly differ across groups. A chi-square differences test is conducted to identify if the predictive paths are significantly different across the groups identified (Little et al., 2007).

Results

Descriptive statistics and mean differences for Indigenous and non-Indigenous students

As can be seen in Table 1, overall, for both the Indigenous and non-Indigenous Australian samples, on average, more positive notions of self-concept were reported as the students agreed to possessing higher levels of general self-esteem, mathematics and verbal self-concepts. The reliability estimates for self-concept measures were strong across the two samples. Indigenous students in comparison to non-Indigenous students displayed statistically significant lower scores for general self-esteem, mathematics self-concept, verbal self-concept, home educational resources, English grades and mathematics grades. They also displayed statistically significant higher mean scores for absenteeism although the magnitude of these differences was small with variance explained estimates not exceeding 3.13%. There were no significant differences for aspirations.

Confirmatory factor analysis for psychometric properties and factor relations

Two CFA models (see Table 2) were applied to further test the psychometric properties of the measures employed for Indigenous and non-Indigenous students. Goodness of fit indices were excellent for both Indigenous (RMSEA = .047, NNFI = .97, CFI = .98) and non-Indigenous students (RMSEA = .038, NNFI = .99, CFI = .99). Based on the completely standardised solution, where relevant, all item-to-factor loadings were significant and acceptable according to minimum loading criteria of .30 (Hills, 2008) for both Indigenous and non-Indigenous students. For Indigenous students, significant positive standardised latent factor correlations (see Table 2) were present for general self-esteem with all domains of self-concept, mathematics grade and aspirations, yet no significant standardised latent factor correlations were present for home educational resources and absenteeism. Mathematics self-concept was significantly positively correlated with verbal self-concept and mathematics grades, yet was uncorrelated with home educational resources, English grades, aspirations and absenteeism. Verbal self-concept was positively and significantly correlated with all constructs with the exception of home educational resources and absenteeism, which was not significantly correlated. A similar pattern of correlations was present for non-Indigenous students, yet it should be noted that significance was reached more often, possibly due to the large sample size.

Factorial invariance testing across the Indigenous and non-Indigenous student samples

Although the psychometric properties of the instruments produced sound results across the Indigenous and non-Indigenous Australian samples and a number of significant mean differences were observed across the latent and directly observed constructs, the essential question of the instrument's measurement equivalence for cross-cultural research (Byrne, 1998; Parker, Dowson & McInerney, 2007) has yet to be considered. table 3 provides the results for tests of invariance. The first model produced an excellent fit (CFI = .984, NNFI = .988, RMSEA = .039) and provided the frame of reference for judgements on invariance for the remaining models. The second model (factor loadings invariant) displayed no observable variation in the goodness of fit criteria (CFI = .984). The third invariance model (factor loading and the variance/covariance parameters) produced a slight change with the CFI (.986). Hence, the minimum requirements (+/- .01 change in the CFI--Cheung & Rensvold, 2002) for the assumption of invariance of measurement across the Indigenous and non-Indigenous students were met for this investigation (Bodkin-Andrews et al.,2010; Marsh,Tracey & Craven, 2006). The strength of the model though is further emphasised in Models 4 and 5 (CFI = .982 and .983 respectively), as it can be seen that complete measurement invariance was achieved.

SEM path analyses for Indigenous and non-Indigenous students

Two SEM path analyses were conducted to examine the extent to which the indicator variables (general self-esteem, mathematics self-concept, verbal self-concept, home educational resources) were able to predict the schooling outcomes (school aspirations, absenteeism, and English and mathematics grades). For Indigenous students, 8.92% of the variance was explained for English grades with verbal self-concept being the only significant (and positive) predictor of this outcome (explaining 7.72% of the variance) (see Table 4). For mathematics grades, 18.57% of the variance was explained, with home educational resources explaining positively 9.10% of the variance and mathematics self-concept explaining positively 7.53% of the variance. For school aspirations, 13.23% of the variance was explained, with general self-esteem explaining positively 5.95% of the variance and verbal self-concept explaining positively 5.96% of the variance. For absenteeism, although 2.71% of the overall variance was explained for Indigenous students, none of the predictors significantly contributed.

For non-Indigenous students, English grades were significantly and positively predicted by verbal self-concept (8.26% of variance explained), mathematics self-concept (2.23%) and significantly negatively predicted by general self-esteem (1.16%). Mathematics grades were significantly and positively predicted by mathematics self-concept (18.84%) and home educational resources (1.07%), and significantly negatively predicted by general self-esteem (2.40%). School aspirations were positively predicted by verbal self-concept (3.91%), home educational resources (2.71%), and mathematics self-concept (2.57%). Finally, levels of self-reported absenteeism were significantly and negatively predicted by general self-esteem (3.00%).

Moderating path analyses

From the SEM path analyses, a number of notable differences in the predictive power of the constructs could be observed between Indigenous and non-Indigenous students (see Table 4). Considering that little research has sought to statistically compare differences in the predictive strength of the constructs used in the investigation in relation to schooling outcomes, it was necessary to take a more exploratory approach (as opposed to directed testing of individual a priori paths) by firstly testing if there is an overall model difference between the predictive paths (see Table 5). As can be seen from Table 5, a significant difference between the two models was identified through the chi-square difference test, suggesting that the model is better understood by acknowledging the differences between the predictive paths across the Indigenous and non-Indigenous students.

Since the overall predictive model differed significantly between the Indigenous and non-Indigenous students, it became necessary to identify the individual paths that may have contributed to this finding. As a result, a post hoc set of moderating analyses was run across the 16 predictive paths to determine if they differed significantly for Indigenous and non-Indigenous samples. Due to the post hoc and repeated nature of the testing, the significance level was adjusted to p<.003 to determine significance, yet limited attention was also placed on paths that reached the traditional .05 alpha level of significance. In Table 6 only the significantly differing paths are reported.

Across the 16 post hoc moderating analyses, only one pair of paths differed significantly at the adjusted alpha level of .003, that being the path from home educational resources to mathematics grades, whereby the positive predictive power of home educational resources to mathematics grades was stronger for Indigenous students. Although this path was the only one to be significant at the adjusted significance level, a number of paths did reach the customary .05 significance level, and thus may be tentatively considered to be of some importance. Briefly, general self esteem was a significantly more positive predictor of school aspirations for Indigenous students, whereas mathematics self-concept was a significantly more positive predictor of school aspirations for non-Indigenous students. Finally, mathematics self-concept was a significantly stronger positive predictor of mathematics grades for non-Indigenous students.

Discussion

Within this investigation three primary aims were considered. Firstly, and most importantly with regard to the cross-cultural nature of this research, the general within-construct validity of the quantitative research measures were considered. Secondly, a number of significant differences were identified across the latent (for example, general self-esteem) and directly observed (for example, English grades) measurement constructs. Finally the predictive power of self-esteem, self-concept constructs and home educational resources in relation to the schooling outcomes were determined for Indigenous and non-Indigenous students, with some substantive differences in the predictive strength of these constructs being identified across the two cultural groups. These results are now discussed in more detail.

Research aim 1: Psychometric properties of the instrumentation

Through a battery of reliability, CFA and invariance tests, questions pertaining to the appropriateness of the measures used in this investigation for both Indigenous and non-Indigenous students were considered. Reliability estimates were all strong for the multi-item measures, the separate group CFAs showed excellent goodness of fit indices and adequate to strong item-to-factor loadings. A closer examination of the correlations across both the Indigenous and non-Indigenous student samples adds support to the structural validity of the domain-specific self-concept measures, as each self-concept domain was more highly correlated to its matching domain outcome (for example, mathematics self-concept correlated most strongly with mathematics grades) than with non-matching outcomes (for example, mathematics self-concept and English grades). More importantly, CFA invariance testing demonstrated that the combination of instruments used in this investigation not only met the minimal requirements of invariance but also achieved full invariance across all models. The strength of these findings is extremely promising and brings into question criticisms about quantitative research being used to advance Indigenous education (Fraillon, 2004; Tchacos & Vallance, 2005). With an emphasis on strict requirements for determining the equivalence of measures across varying groups (Byrne, 2003; Parker, Dowson & McInerney, 2007), more confidence may be drawn from quantitative research seeking to tap sensitive cultural groups (Walter, 2005).

Research aim 2: Using Aboriginality as a predictor of self-concept and academic outcomes

With the CFA invariance testing resulting in a finding that supported the completely invariant measurement model, increased confidence could be drawn from conclusions resulting from analyses seeking to make between-group comparisons for the Indigenous and non-Indigenous student samples (Byrne, 1998; Marsh, 1994). In examining differences in the mean findings, the results seemed to suggest that Indigenous and non-Indigenous students held positive (above mid-score) self-concepts. But, consistent with the limited educational research targeting both Indigenous and non-Indigenous students (for example, Bortoli & Cresswell, 2004; DEST, 2006; Craven & Marsh, 2005), Indigenous students consistently reported lower self-concepts and schooling outcomes. MIMIC testing demonstrated that, across all measures (with the exception of self-reported absenteeism), Indigenous students' scores were significantly lower compared to non-Indigenous students' scores, although only a small amount of variance was explained. Given self-concept has been demonstrated to be a predictor of life opportunities and to share a reciprocal causal relation with achievement (Marsh & Craven, 2006) this may be of some concern.

It should be noted though that when Indigenous or non-Indigenous status was used as a predictor of levels of self-confidence and student outcomes, the size of these differential effects were minimal, suggesting that using ethnicity as an explanatory variable for student outcomes is questionable. This finding is consistent with previous research, which has suggested that any attempt to understand and redress educational inequities between specific cultural groups must look more carefully at the dynamic interplay of a number of psychological and social variables rather than just dismissing these factors in favour of an overly simplistic and inaccurate deficit type of reasoning (Bodkin-Andrews et al., 2009; Hattie, 1992; Jonas, 2003; Rowe, 2003).

Research aim 3: Self-esteem and self-concept predicting student outcomes

In considering the final aim of this investigation, two separate SEM path analyses were conducted for Indigenous and non-Indigenous samples, whereby general selfesteem, verbal and mathematics self-concepts, and home educational resources predicted the schooling outcomes of teacher grades, aspirations to complete Year 12 and self-reported absenteeism. Arguably the most notable result to emerge from these findings is that, across each outcome (with the exception of absenteeism), a substantial amount of variance was explained by this combination of predictors for both Indigenous and non-Indigenous students.

For English grades, totals of 8.92% and 12.12% respectively constituted explained variance for Indigenous and non-Indigenous students. The strongest predictive power of verbal self-concept was similar across the two groups. Mathematics self-concept and general self-esteem were also significant predictors for non-Indigenous students. Although it is possible that the path from general self-esteem could be identified as a negative suppression effect for non-Indigenous students (see later discussion). The significant path from mathematics self-concept to English grades should be interpreted with caution, although diffusion effects of self-concept are a possible explanation (see Craven et al., 2001) and the results are consistent with a construct validity approach whereby domains of self-concept less relevant to the target subject area have lesser effects compared to the target self-concept domain (see Craven, Marsh & Burnett, 2003).

For mathematics grades, totals of 18.57% and 18.61% respectively comprised explained variance for Indigenous and non-Indigenous students. Mathematics self-concept was the strongest predictor of mathematics grades. Another point of interest is that home educational resources were a stronger predictor of mathematics grades for Indigenous students (.29) when compared to non-Indigenous students (.07), and this difference was significant in the post hoc moderating analysis. This suggests that home educational resources have a positive relation with mathematics achievement. As with English achievement, general self-esteem negatively predicted mathematics achievement, but this may possibly be interpreted as a statistical suppression effect (see later discussion).

For aspirations, totals of 8.69% and 13.23% respectively constituted explained variance for Indigenous and non-Indigenous students. Mathematics self-concept and home educational resources were stronger significant predictors of aspirations for non-Indigenous students but, based on the post hoc moderating analyses, only mathematics self-concept was statistically significant. General self-esteem significantly and positively predicted aspirations for Indigenous students only, but this difference was not significant.

Finally, with regard to self-reported levels of absenteeism, totals of 2.71% and 4.12% respectively comprised explained variance for Indigenous and non-Indigenous students. General self-esteem significantly and negatively predicted this variable (suggesting that the higher the level of general self-esteem, the lower the levels of absenteeism) for the non-Indigenous students only. This was the only significant predictive path across the two student groups.

General self-esteem and suppression effects

Two significant suppression effects may have been identified. That is, although general self-esteem significantly and negatively predicted both mathematics and English grades for the non-Indigenous students, the original correlations between these variables were positive and significant, thus suggesting evidence for a statistical suppression effect (Maassen & Bakker, 2001). Initially, within regression analyses, a suppressor variable was identified when this variable originally had little or no relation with an outcome, yet its inclusion as a predictor may 'purify' and increase the predictive power of another variable over the outcome variable (Horst, 1941). Maassen and Bakker (2001) have identified a number of extensions of the suppression effect phenomena and highlighted the case of a 'negative suppression effect'. Within this form of suppression effect, the suppressed variable and another predictor variable are correlated not only with each other but also with the designated outcome variable and, as a result, the predictive power of the suppressed variable becomes negative (thus it is probable that the domain-specific self-concept s may have absorbed and negatively suppressed the predictive power of general self-esteem). That is, once the explanatory variance of general self-esteem over the grades was better accounted for by the domain-specific self-concept s, what explanatory variance that remained was, in all actuality, negative in orientation. If this negative suppression effect is a reflection of reality, then perhaps, for non-Indigenous students, an intervention seeking to increase students' grades through a heightened self-concept must target matching domain self-concept s only.

Conclusion

In this investigation, the strongest predictors of the outcomes were mostly found emanating from the self-concept variables for both Indigenous and non-Indigenous students. Although the strength of these predictions in some cases suggested significant and possibly substantive differences across Indigenous and non-Indigenous students, clearly domain-specific facets of self-concept had the strongest predictive power on the outcome variables (especially grades and aspirations) for both Indigenous and non-Indigenous students. These results imply that no teacher is wasting his or her time in enhancing specific domains of self-concept in order to influence schooling outcomes.

Within school settings, effective classroom teachers account for the greatest predictor of student academic success (Hattie, 2009). What is more, quality teaching is fundamental to enhancing specific domains of self-concept and employing culturally inclusive pedagogy (for example, Ladson-Billings, 1994). These practices include, for example, enabling students to experience academic success, which is postulated to enhance self-concept, to maintain cultural competence and enhance identity and to develop a broader socio-political consciousness. Quality teachers and quality teaching, clearly have a pivotal role in enhancing self-concepts and related important culturally inclusive practices for enhanced student success (Stoicovy, 2002).

In considering that culturally inclusive pedagogy is more responsive to student culture, it can then be argued that learning may become more personally meaningful and that the subsequent learning processes will take place more fluidly and with a greater depth of understanding (Gay, 2002). This should ultimately result in engagement, and attainment, as students are able to access instruction that taps their personal cultures and experiences, thus directly linking culture to education, and providing the foundation for an increased self-concept within education (Gay, 2002; Ladson-Billings, 1995) In the words of Purdie (2003, p. 32): The challenge for educators is to ensure that schools are places where Indigenous students want to be, where their presence and participation is valued, where they feel successful, and where they see value in completing their schooling ... What stood out most was the individual influence of teachings in developing learner identity amongst Indigenous students.

This study also has a number of limitations that need to be considered when interpreting the findings. Indigenous Australians are not a homogeneous culture (Craven & Rigney, 1999; Mellor & Corrigan, 2004) but, as with the general non-Indigenous grouping, are characterised by immense diversity (for example, Parbury, 2005). Measures that meet psychometric and invariance testing criteria for one Indigenous sample may not give equivalent results for other samples of Indigenous Australian participants. We have also used a well-established and internationally validated self-concept instrument but Indigenous Australians may also emphasise other additional areas of self-concept (for example, identity, cultural values, community cohesion, attachment to traditional country). Given the more recent emphasis on culturally inclusive pedagogical practices within Australian schools, such facets of Indigenous students' self-concept may become increasingly more important for seeding educational success. Finally, the cross-sectional nature of this data prevents causal inferences. There is a plethora of international research suggesting the need to consider what is known as the reciprocal effects model (REM) between self-concept and achievement, whereby, over time, self-concept positively and causally influences achievement and achievement positively and causally influences self-concept (Marsh & Craven, 2006). As per one of the major criticisms listed in their review of Indigenous educational research, Mellor and Corrigan (2004) highlight that too frequently the relation between cause and effect has been asserted rather than the inferences tested through research. Hence longitudinal causal modelling research is needed to elucidate the key factors that seed successful educational outcomes for both Indigenous and non-Indigenous students.

In summary, this research adds evidence to the potentially potent worth of targeting domain-specific self-concepts to influence both Indigenous and non-Indigenous students' educational outcomes. Given that tackling Indigenous education is a social justice issue of our time, the results of this study and the words of Craven and Marsh (2008, p. 113) are especially pertinent: the enhancement of the self-concept construct for Indigenous students may provide a potential turning point for intervention ... Hence, in Australia, enhancing self-esteem has been acknowledged as a vital key to improving educational outcomes for Aboriginal Australians.

Keywords self-concept self-esteem Indigenous Australians achievement structural equation modelling suppression effects

Acknowledgements

This investigation was funded by the Australian Research Council under a Strategic Partners Industry Linkage Grant scheme, with contributions of funding, resources and valued advice from the D'harawal Traditional Descendants' and Knowledge Holders' Council, the Aboriginal Education Council (NSW) Inc., and the Self-concept Enhancement and Learning Facilitation (SELF) Research Centre (now the Centre for Educational Research), University of Western Sydney.

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Gawaian Bodkin-Andrews

Virginia O'Rourke

Rhonda G. Craven

University of Western Sydney

Gawaian Bodkin-Andrews is Post-doctoral Fellow in the Centre for Educational Research, University of Western Sydney. Email: g.bodkinandrews@uws.edu.au

Virginia O'Rourke is a tutor and doctoral candidate in the Centre for Educational Research, University of Western Sydney.

Rhonda Craven is a Professor in the Centre for Educational Research, University of Western Sydney. Table 1 Mean scores, standard deviations, and reliability estimates for the Indigenous (n = 176) and non-Indigenous (n = 1042) samples, and MIMIC results for differences between the latent mean scores Factors Mean Standard Deviation Non- Non- Indige- Indige- Indige- Indige- nous nous nous Indige General self-esteem 4.62 4.86 .84 .82 Maths self-concept 3.42 3.80 1.47 1.45 Verbal self-concept 3.80 4.20 1.37 1.26 Home educational resources 6.63 7.64 1.87 2.01 English grades -.17 .06 .93 .99 Maths grades -.18 .06 .99 .99 Absenteeism 13.05 12.41 11.59 10.90 School aspirations 2.51 2.66 .76 .66 Factors Cronbach's [beta] %V [alpha] Non- Indige- Indige- nous nous General self-esteem .80 .84 .11 * 1.14 Maths self-concept .91 .92 .10 * .94 Verbal self-concept .91 .91 .11 * 1.23 Home educational resources -- -- .18 * 3.13 English grades -- -- .08 * .65 Maths grades -- -- .08 * .71 Absenteeism -- -- .08 * .62 School aspirations -- -- -.02 -- Note: [beta] = predictive beta path (where a positive path indicates that non-Indigenous students possess higher latent mean scores); %V = significant variance explained. Fit indices for the MIMIC model are as follows: chi square = 425.18, degrees of freedom = 159; non-normed fit index = .98; comparative fit index = .99; and RMSEA--root mean square error of approximation = .04. * significant at p < .05. Table 2 CFA results for all measures including goodness of fit criteria, factor loadings and factor correlations for the Indigenous (n = 176) and non-Indigenous (n = 1042) samples Goodness of fit criteria Chi square Degrees of Non-normed freedom fit index NON IND NON IND NON IND 363.236 203.29 147 147 .99 .97 ([dagger]) ([dagger]) ([dagger]) Root mean square Comparative square error of fit index approximation NON IND NON IND .99 .98 .038 .047 ([dagger]) ([dagger]) Item General Maths self-esteem self-concept NON IND NON IND 1 .70 .57 ([dagger]) .83 .85 ([dagger]) 2 .78 .76 ([dagger]) .93 .93 ([dagger]) 3 .79 .76 ([dagger]) .87 .84 ([dagger]) 4 .70 .75 ([dagger]) .81 .75 ([dagger]) 5 .59 .58 ([dagger]) 6 .58 .40 ([dagger]) Factor loadings Item Verbal Home English self-concept educational grade resources NON IND NON IND NON IND 1 .73 .65 ([dagger]) 1.00 1.00 1.00 1.00 ([dagger]) ([dagger]) 2 .78 .85 ([dagger]) 3 .86 .68 ([dagger]) 4 .91 .92 ([dagger]) 5 .86 .85 ([dagger]) 6 Item Maths Aspire Absent grade NON IND NON IND NON IND 1 1.00 1.00 1.00 1.00 1.00 1.00 ([dagger]) ([dagger]) ([dagger]) 2 3 4 5 6 Factor correlations (non-Indigenous/Indigenous) ** General Maths self-esteem self-concept General self-esteem -- .42 * ([dagger]) Maths self-concept .52 * -- Verbal self-concept .43 * .18 * Home educational resources .30 * .22 * English grade .10 .15 * Maths grade .15 * .41 * Aspire .16 * .19 * Absent -.20 * -0.13 Verbal Home self-concept educational resources General self-esteem .42 * ([dagger]) .08 ([dagger]) Maths self-concept .31 ([dagger]) .06 ([dagger]) Verbal self-concept -- .05 ([dagger]) Home educational resources .23 * -- English grade .28 * .11 Maths grade .11 .15 * Aspire .22 * .20 * Absent -.11 -.10 English grade Maths grade General self-esteem .08 ([dagger]) .18 * ([dagger]) Maths self-concept .08 ([dagger]) .30 * ([dagger]) Verbal self-concept .27 * ([dagger]) .l9 * ([dagger]) Home educational resources .13 ([dagger]) .31 ([dagger]) English grade -- .41 ([dagger]) Maths grade .48 * -- Aspire .16 * .21 * Absent -.06 -.l0 Aspire Absent General self-esteem .28 * ([dagger]) -.10 ([dagger]) Maths self-concept .09 ([dagger]) -.14 ([dagger]) Verbal self-concept .28 * ([dagger]) -.09 ([dagger]) Home educational resources .15 * ([dagger]) .06 ([dagger]) English grade .17 * ([dagger]) -.02 ([dagger]) Maths grade .24 * ([dagger]) -.20 ([dagger]) Aspire -- .00 ([dagger]) Absent -.09 -- * Significant at p < .05. ** Correlations presented above the diagonal are for the Indigenous students (([dagger])) and those presented below the diagonal are for the non-Indigenous students. Table 3 Invariance tests across Indigenous and Non-Indigenous students for the measurement instruments Model Chi Degrees of Non- square freedom normed fit index Completely free 571.83 294 .988 Factor loadings = invariant 588.36 306 .987 Factor loadings = invariant; factor variance and covariance = invariant 675.56 342 .984 Factor loadings= invariant; uniqueness = invariant 729.46 321 .984 Completely invariant 828.70 357 .982 Model Comparative Root mean fit index square error of approximation Completely free .984 .039 Factor loadings = invariant .984 .039 Factor loadings = invariant; factor variance and covariance = invariant .986 .040 Factor loadings= invariant; uniqueness = invariant .982 .046 Completely invariant .983 .047 Table 4 Latent path analysis for predictor and outcomes for the Indigenous (n = 176) and non-Indigenous (n = 1042) samples General self-esteem [beta] %V NON IND NON IND English grade -.12 ([dagger]) -.06 1.16 -- Maths grade -.13 ([dagger]) .01 2.40 -- Aspire -.03 .21 -- 5.95 Absent -.15 ([dagger]) -.04 3.00 -- Maths self-concept [beta] %V NON IND NON IND English grade .15 ([dagger]) .01 2.23 -- Maths grade .46 ([dagger]) .25 18.84 7.53 Aspire .14 ([dagger]) -.07 2.57 -- Absent -.03 -.11 -- -- Verbal self-concept [beta] %V NON IND NON IND English grade .30 ([dagger]) .29 ([dagger]) 8.26 7.72 Maths grade .07 .09 -- -- Aspire .18 ([dagger]) .21 ([dagger]) 3.91 5.96 Absent -.02 -.04 -- -- Home educational resources [beta] %V NON IND NON IND English grade .04 .12 -- -- Maths grade .07 ([dagger]) .29 ([dagger]) 1.07 9.10 Aspire .14 ([dagger]) .13 2.71 -- Absent -.04 .07 -- -- Home educational resources SSMC NON IND English grade 9.80 * 8.92 * Maths grade 18.61 * 18.57 Aspire 8.69 * 13.23 * Absent 4.12 2.71 Goodness of fit criteria Degrees of Non-normed Comparative Root mean Chi square freedom fit index fit index square of approxi- mation NON IND NON IND NON IND NON IND NON IND 203.392 369.09 147 147 .97 .99 .98 .99 .047 .038 Note: [beta] = Standardised predictive path, %V = significant variance explained by the predictor variable, SSMC = Sum of squared multiple correlation (a.k.a. total variance explained across selected outcome), NON = non-Indigenous, IND = Indigenous. ([dagger]) Significant at p <.05. * Due to the negative explained variance over English grades for general self-esteem and aspirations for mathematics self-concept, the SMC is underestimated within the LISREL output, as it subtracts the negative explained variance from the positively explained variance. By treating the negatively explained variance as an absolute value, one can grasp a more accurate SMC which simply adds all the independent explanatory variance. As a result, the SMC should be considered as 9.78% for English Grades and 14.49% for Aspirations for the Indigenous students and 12.12% for English grades, 23.41% for mathematics grades and 9.69% for aspirations for the non-Indigenous students. Table 5 Results of the chi-square difference test Chi Degrees of Root mean square freedom square error < of approximation Model 1 (free) 781.7 341 .046 Model 2 (invariant) 828.70 357 .047 Difference 47 * 16 Comparative Non- fit index normed fit index Model 1 (free) .984 .982 Model 2 (invariant) .983 .982 Difference * p = .0001 (significant) Table 6 Chi-square difference testing across predictive paths for the Indigenous (n = 176) and non-Indigenous (n = 1042) samples Chi Indigenous Non-Indigenous square P Path [beta] [beta] dif value General self-esteem .21 -.03 7.73 .013 [right arrow] Aspirations Maths slef-concept .25 .46 6.51 .021 [right arrow] Maths grade Maths self-concept -.07 .14 6.50 .022 [right arrow] Aspirations Home educational .07 11.3 .002 * resources [right .29 arrow] Maths grade Note. [beta] = predictive value, p = significance (two-tailed). * p < adjusted .003 significance level. All differences in degrees of freedom values = 1.