Achievement goals and self-efficacy: A meta-analysis

Educational Research Review 19 (2016) 119e137

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Achievement goals and self-efficacy: A meta-analysis Chiungjung Huang Graduate Institute of Education, National Changhua University of Education, 1 Jinde Road, Changhua, 50058, Taiwan

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 June 2015 Received in revised form 26 June 2016 Accepted 15 July 2016 Available online 18 July 2016

This meta-analysis examined the relations between achievement goals and self-efficacy. One hundred and twenty-five studies consisting of 148 samples (N ¼ 61,456) reporting the relations between academic achievement goals and academic self-efficacy were included. The correlations of mastery and mastery approach goals with self-efficacy were generally moderate to strong, while those of performance avoidance and mastery avoidance goals with self-efficacy were low. Goal valence was meaningfully related to selfefficacy, whereas the support for the goal definition was inconsistent. Publication status, proportion of males, mean age, and achievement goal measure did not exert significant moderating effects, whereas those for country where the research was conducted, the proportion of Caucasians, the self-efficacy measure, the domains of achievement goals and self-efficacy, and matching between achievement goal and self-efficacy domains varied with the achievement goal factor. The four-factor model was based on a relatively small number of samples, and so future research is needed to determine whether there are differences in correlations of mastery avoidance and performance avoidance goals with antecedents and consequences. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Achievement goals Goal orientation Self-efficacy Meta-analysis

1. Introduction Two major constructs in achievement motivation are (1) self-efficacy, referring to the perceived competence of an individual to succeed at or accomplish a certain task (Bandura, 1977, 1982, 1986), and (2) achievement goals, determined in terms of how competence is defined (Ames, 1992; Dweck & Leggett, 1988; Nicholls, 1984). Because competence forms the core of these two constructs, it is not surprising that achievement goal theorists have linked achievement goals and self-efficacy. For example, Dweck and Leggett (1988) suggested that individuals who believe that competence is malleable tend to adopt mastery goals, whereas individuals who believe that competence is fixed tend to adopt performance goals. Nicholls (1990) suggested that an individual who believes that competence is determined by effort is more likely to adopt mastery goals, while an individual who believes that competence is determined by normative comparison tends to adopt performance goals. Ames (1992) suggested that there are differences in how mastery and performance goals are linked to concepts of success. Because individuals adopting mastery goals focus on absolute or intrapersonal standards and believe that effort will lead to success and mastery, they tend to have a high perceived self-efficacy. In contrast, self-efficacy will be jeopardized when an individual who tries his or her best does not succeed. Elliot (1999) reported a link between achievement goals from a threefactor achievement goal model and self-efficacy, and suggested that students with high competence perceptions tend to adopt approach goals such as mastery and performance approach goals, while students with low competence perceptions tend to adopt avoidance goals such as performance avoidance goals.

E-mail address: [email protected]. http://dx.doi.org/10.1016/j.edurev.2016.07.002 1747-938X/© 2016 Elsevier Ltd. All rights reserved.

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Two lines of theories have been integrated in achievement goal theory that differentiates between (1) mastery from performance goals (Dweck & Leggett, 1988) and (2) approach and avoidance motivations (Elliot, 1999, 2006). Both of these perspectives are informative, and so they should be integrated to examine the correlation between achievement goals and self-efficacy. Hence, it is important to explain how the effects of goal definition and goal valence are related to self-efficacy. Research into achievement goals (Ames, 1992; Elliot & Dweck, 1988) suggests that mastery goals are related to adaptive learning behaviors, while performance goals are associated with maladaptive behaviors. Mastery goals would therefore be expected to be related to a relatively high self-efficacy, with performance goals related to a relatively low self-efficacy. In approach motivation, behaviors are directed toward desirable outcomes and are thus related to enjoyable learning experiences. On the other hand, behaviors are directed toward undesirable outcomes in avoidance motivation and have been associated with stressful learning experiences (Elliot, 1999, 2006). Approach motivation is therefore expected to be related to a relatively high self-efficacy, whereas avoidance motivation has been related to a relatively low self-efficacy. The achievement goal model has evolved from a two to a three to a four-factor model and conceptual distinctions among achievement goals have been established in the relevant literature. However, empirical differentiation remains unclear and agreement on how many factors should be included in the achievement goal model is lacking. To determine the utility of achievement goals, each achievement goal should be meaningfully correlated with antecedents and consequents. Accordingly, achievement goals should result in different nomological networks, so examining the correlation between achievement goals and self-efficacy is pivotal. If mastery and performance goals are differently correlated with maladaptive/adaptive behaviors, then differentiating mastery from performance goals has benefits. Differences should exist between the correlations of mastery and performance goals of the same goal valence with self-efficacy. The importance of approach versus avoidance motivations can also be argued, because it is well documented that the effects of these two motivations are related to desirable or undesirable affects or attitudes (Elliot, 2006). Therefore, different correlations should exist between approach and avoidance motivations of the same goal definition with self-efficacy. For example, if the correlations of the mastery approach and mastery avoidance goals with self-efficacy were similar, then bifurcating the mastery goal into mastery approach and avoidance components would be unnecessary. Further, the power of each achievement goal to predict selfefficacy should be established. If an achievement goal is highly correlated with self-efficacy, then the practical utility can be high. Some researchers (Barron & Harackiewicz, 2001; Harackiewicz, Barron, Pintrich, Elliot, & Thrash, 2002; Luo, Paris, Hogan, & Luo, 2011) have argued that mastery and performance goals are not mutually exclusive and have claimed that individuals can adopt multiple goals simultaneously (Pintrich, 2000). Recent research (e.g., Barron & Harackiewicz, 2001; Harackiewicz et al., 2002; Luo et al., 2011) has supported the multiple goal perspective and found that an individual with high mastery and performance approach goals tends to have high academic achievement. The multiple goal perspective was not adopted in this study owing to the insufficiency of the statistics in primary research (Harackiewicz et al., 2002). The following correlation pairs can be compared: 1. 2. 3. 4. 5.

Mastery goals and self-efficacy versus performance goals and self-efficacy. Mastery approach goals and self-efficacy versus performance approach goals and self-efficacy. Mastery avoidance goals and self-efficacy versus performance avoidance goals and self-efficacy. Mastery approach goals and self-efficacy versus mastery avoidance goals and self-efficacy. Performance approach goals and self-efficacy versus performance avoidance goals and self-efficacy.

Differentiating mastery goals from the performance goals was supported if the differences in pairs 1, 2, and 3 were sufficiently large, while the approach and avoidance motivations were warranted if the differences in pairs 4 and 5 were sufficiently large. 1.1. Empirical findings about achievement goals and self-efficacy The relations between achievement goals and self-efficacy have been studied extensively during the past decades, but the findings have varied. For example, Wey (1998) found that the correlation coefficients of mastery and performance goals with self-efficacy were 0.54 and 0.40, respectively; whereas Curda (1997) found them to be 0.26 and 0.13, respectively. The reported correlations between achievement goals and self-efficacy have also varied when using a three-factor model. For example, Bembenutty (2001) examined the relations between math achievement goals and math self-efficacy in a sample of 102 undergraduate students. The correlation coefficients of self-efficacy with the mastery, performance approach, and performance avoidance goals were 0.61, 0.01, and 0.39, respectively. Different strengths and directions of correlations were found by Valkyrie (2006), who sampled 500 college students with mean age of 24.54 years and found that the corresponding coefficients were 0.44, 0.12, and 0.02, respectively. The reported relations have also varied for a four-factor model. For example, Bong (2009) compared the following four groups of students using a four-factor achievement goal model: lower, middle, and upper elementary school students, and middle school students. The correlation coefficients of self-efficacy with the mastery approach, mastery avoidance, performance approach, and performance avoidance goals were from 0.46 to 0.67, 0.16 to 0.17, 0.40 to 0.54, and 0.08 to 0.25, respectively. Relatively low correlations were found by Cao (2012), who sampled 68 graduate students to examine these

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correlations for an educational psychology course: the correlation coefficients were 0.14, 0.03, 0.00, and 0.13, respectively. The marked variations in the correlations between achievement goals and self-efficacy prompted the present study to determine the relations between achievement goals and self-efficacy for two-, three-, and four-factor achievement goal models via meta-analysis in order to establish generality across studies. 1.2. Moderators The following ten moderators were examined based on the empirical findings and achievement goal and self-efficacy theories: publication status, country where the research was conducted, participant gender, participant age, participant ethnicity, achievement goal measure, self-efficacy measure, domain of achievement goals, domain of self-efficacy, and matching between the achievement goal and self-efficacy domains. These ten moderators are individually described in the following sections. 1.2.1. Publication status Studies producing significant results tend to get published more easily than those producing non-significant results (Duval & Tweedie, 2000). A meta-analysis that fails to include reports of non-significant results will lead to the inclusion of nonrepresentative studies in the data set, which can lead to overestimation of mean effect sizes and bias toward statistical significance. To determine whether the relations between achievement goals and self-efficacy were related to publication status, the mean relations among different publication outlets were compared. 1.2.2. Country where the research was conducted The effect of the country where the research is conducted on the correlations between achievement goals and self-efficacy has seldom been examined in primary research. Pintrich, Zusho, Schiefele, and Pekrun (2001) exceptionally compared these correlations between 69 U.S. and 256 German college students. The correlation coefficients of the mastery and performance goals with self-efficacy were 0.36 and 0.13, respectively, for the U.S. sample, and 0.44 and 0.24 for the German sample. Testing the potential effect of country can provide information about whether cross-cultural differences exist. For example, some countries might have moderate effect sizes, while others might have small effect sizes. This information not only provides empirical evidence of cultural influences but also facilitates theoretical development. 1.2.3. Participant gender It seems that gender exerts only a small effect on the correlations between achievement goals and self-efficacy. For example, Cavallo, Rozman, and Potter (2004) compared the correlations between achievement goals and self-efficacy for 103 male and 187 female students. The correlation coefficients of mastery and performance goals with self-efficacy were 0.30 and 0.02, respectively, for males, and 0.35 and 0.16 for females. Minor effects were also found by Meece, Herman, and McCombs (2003) for 2236 male and 2460 female adolescents. The correlation coefficients of mastery and performance goals with self-efficacy were 0.56 and 0.26, respectively, for males, and 0.59 and 0.15 for females. Bong (2005) used a longitudinal design to examine the correlations of achievement goals for three courses (Korean, math, and English) with selfefficacy particularly for female participants via structural equation modeling. The correlation coefficients between the latent constructs of self-efficacy with the mastery, performance approach, and performance avoidance goals were from 0.52 to 0.73, 0.29 to 0.48, and 0.08 to 0.02, respectively. As the correlations between two latent constructs were adjusted for attenuation, the magnitudes of correlations in Bong (2005) were expected to be higher than those based on observed variables. 1.2.4. Participant age Predictions of age effect can be obtained from knowledge of developmental patterns of achievement goals and selfefficacy. As mentioned previously, Nicholls (1990) suggested that people who believe ability to be determined by the effort made are likely to adopt mastery goals, while those who believe that ability is determined by normative comparison are likely to adopt performance goals. The shift from effort- to normative-based judgment of ability typically occurs during middle childhood and early adolescence. Further, self-belief theorists (e.g., Byrne, 1996) have argued that self-belief becomes more differentiated as individuals get older. It is therefore possible that the correlations between self-efficacy and achievement goals vary with the life stage. This issue was addressed by Midgley, Anderman, and Hicks (1995), who compared these correlations between elementary and middle school students. The correlation coefficients of mastery and performance goals with self-efficacy were 0.28 and 0.03, respectively, for elementary school students, and 0.37 and 0.18 for middle-school students. Based on the three-factor model, Bong (2009) compared the correlations among four groups of students, and found that the effect of participant age seemed to vary with the achievement goal factor. Specifically, the correlation coefficients of math mastery, performance approach, and performance avoidance goals with math self-efficacy were 0.46, 0.54, and 0.25, respectively, for lower elementary school students, 0.54, 0.43, and 0.03 for middle elementary school students, 0.67, 0.50, and 0.08 for upper elementary school students, and 0.67, 0.40, and 0.09 for middle school students. Similarly, Pajares and Cheong (2003) found that the correlation coefficients of writing mastery, performance approach, and performance avoidance goals with writing self-efficacy were 0.34, 0.03, and 0.23, respectively, for elementary school students, 0.37, 0.13, and 0.13 for middle school

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students, and 0.25, 0.15, and 0.13 for high school students. Mason, Boscolo, Tornatora, and Ronconi (2013) compared the correlations between science self-efficacy and science achievement goals for 213 fifth graders and 202 eighth graders. The correlations of science mastery, performance approach, and performance avoidance goals with science self-efficacy were 0.45, 0.38, and 0.57, respectively, for fifth graders, and 0.42, 0.53, and 0.40 for eighth graders. Using the four-factor model, Cao (2012) compared these correlations between 66 undergraduates with a mean age of 27.12 years and 68 graduate students with a mean age of 32.12 years, and found differences between these two groups for certain achievement goal factors. The correlation coefficients for an educational psychology were 0.14, 0.03, 0.00, and 0.13, respectively, for undergraduate students, and 0.31, 0.42, 0.20, and 0.27 for graduate students. 1.2.5. Participant ethnicity Few primary studies have examined the effect of participant ethnicity on the correlations between achievement goals and self-efficacy. One exception was the investigation of Usher (2007), who tested this effect among 541 Caucasians and 170 African Americans. The correlation coefficients of math mastery, performance approach, and performance avoidance goals with math self-efficacy were 0.44, 0.09, and 0.22, respectively, for Caucasians, and 0.39, 0.00, and 0.23 for African Americans. Hedgspeth (2007) surveyed 179 African American doctoral students with a mean age of 37.17 years. Self-efficacy was measured using the Motivated Strategies for Learning Questionnaire (MSLQ), and achievement goals from the threefactor model were measured using the Patterns of Adaptive Learning Scales (PALS). The correlation of mastery goals with self-efficacy was moderate to strong at r ¼ 0.39, while those of self-efficacy with the performance approach and performance avoidance goals were both weak (correlation coefficients of 0.07 and 0.06, respectively). Assessing the effect of ethnicity on the relations between achievement goals and self-efficacy is important because ethnic minorities can be subjected to lower achievement motivation, influencing their academic achievement. For example, Stevens, Olivarez, Lan, and Tallent-Runnels (2004) found that the mathematics self-efficacy of Caucasian students was higher than that of Hispanic students. Zusho, Pintrich, and Cortina (2005) compared the achievement goals of Asian and Anglo Americans and found a significant difference with respect to the approach avoidance goal. Owing to the possible existence of ethnic differences in self-efficacy and achievement goals, assessing the effect of ethnicity on the relation between achievement goals and self-efficacy is warranted. Information thus obtained may help practitioners to design intervention programs for students with particular ethnic backgrounds. 1.2.6. Achievement goal measure The Achievement Goals Questionnaire (AGQ, Elliot & Church, 1997; Elliot & Harackiewicz, 1996; Elliot & McGregor, 2001; Elliot & Murayama, 2008) and the PALS (Midgley et al., 1996, 2000, 1993) are commonly used to measure achievement goals. The original version of the AGQ (Elliot & Church, 1997) was based on a three-factor model. The three achievement goal scales each contained six items scored on a 7-point Likert scale. This original AGQ suffered from problems, such as the goals not being conceptualized as an aim (e.g., “It is important for me to understand the content of this course as thoroughly as possible”) and items being applicable both to mastery based and performance based goals (e.g., “My goal is to get a better grade than most of the other students”). These issues were addressed by revising the AGQ (Elliot & Murayama, 2008). For example, the item of “I am striving to understand the content of this course as thoroughly as possible” was changed to “My aim is to perform well relative to other students.” Because the mastery avoidance goal was neglected in the original version, the mastery goal was divided into mastery approach and mastery avoidance goals in the revised version (Elliot & McGregor, 2001) and a 2  2 achievement goal model was adopted. The original version of the PALS (Midgley, Maehr, & Urdan, 1993) was based on a two-factor model. This revised version adopted a three-factor model by developing separate subscales for performance approach and performance avoidance goals, deleting items that measured intrinsic value, and removing references to specific behaviors (Midgley et al., 1996, 2000). This revised version still has the problem of goals not being operationalized as an aim (Elliot & Murayama, 2008), such as the item “It's important to me that I learn a lot of new concepts this year” assessing a value rather than goals. The AGQ has been revised based on the critiques, while the PALS has not yet been modified to fully resolve these problems. Therefore, the AGQ and PALS may assess different underlying constructs. The presence of conceptual and measurement dissimilarity was supported by Hulleman, Schrager, Bodmann, and Harackiewicz (2010), and thus it is pertinent to examine whether correlations between achievement goals and self-efficacy depend on achievement goal measures. 1.2.7. Self-efficacy measure Self-efficacy is commonly measured using the MSLQ (Pintrich, Smith, Garcia, & McKeachie, 1993) and the PALS. The selfefficacy subscale of the MSLQ consists of eight items scored on a 7-point Likert scale (from 1 ¼ “Not at all true of me” to 7 ¼ “Very true of me”) measuring students' perceived competence and confidence in completing a task for a specific course (e.g., “I believe I will receive an excellent grade in this class”). All eight items were positively worded, meaning that higher scores indicated higher self-efficacy. The psychometric properties of the MSLQ have been widely scrutinized. For example,  and Phillips (2011) meta-analyzed 67 samples consisting of 19,900 college students and found that the mean correCrede lations of self-efficacy with intrinsic and extrinsic goal orientations were 0.51 and 0.28, respectively. The mean reliability for the self-efficacy subscale was 0.91. As for the evidence of validity, the mean relations of self-efficacy with the grade point average and grades were 0.18 and 0.30, respectively.

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The academic self-efficacy subscale of the PALS consists of five items scored on a 5-point scale (including 1 ¼ “Not at all true,” 3 ¼ “Somewhat true,” and 5 ¼ “Very true”) measuring the confidence of completing school work. For example, one of the items is “Even if the work is hard, I can learn it.” The reliability of the achievement goal subscales of the PALS were systematically examined in a meta-analysis by Ross, Blackburn, and Forbes (2005). The validity of the PALS has not been systematically examined in a meta-analysis. Because the MSLQ and PALS may measure somewhat different underlying constructs, they may produce different results for the correlations between self-efficacy and achievement goals. Hence, it was pertinent to examine the effect of self-efficacy measure. 1.2.8. Domain of the achievement goals The PALS is usually applied to elementary school and secondary school students (Anderman, Urdan, & Roeser, 2003), while the AGQ is mainly applied to college students (Harackiewicz et al., 2002). The PALS has normally been used to assess general academic achievement goals where it has been administered to elementary school students, because such students usually spend most of their time with the same teacher. Conversely, the PALS has normally been used to assess the achievement goals for a specific course when it has been administered to high school students (Anderman et al., 2003). Because the AGQ was originally developed for college students, it usually assesses the achievement goals for a specific course. Anderman and Midgley (1997) examined the relations of English and math achievement goals with English and math selfefficacy in a sample of 341 fifth graders, and found that the domain of the achievement goals had little effect. Specifically, the correlation coefficients of English self-efficacy with the English mastery and English performance goals were 0.41, and 0.07, respectively; the corresponding coefficients for math were 0.43 and 0.12. On the other hand, Bong (2001) found that the strength of the correlation between achievement goals and self-efficacy seemed to vary for certain achievement goal factors among 229 Korean middle school students and 195 Korean high school students. For the middle school sample, the correlation coefficients of Korean self-efficacy with the Korean mastery, performance approach, and performance avoidance goals were 0.57, 0.54, and 0.01, respectively; the corresponding coefficients were 0.70, 0.58, and 0.16 for English, 0.67, 0.68, and 0.26 for math, and 0.73, 0.65, and 0.21 for science. For the high school sample, the correlation coefficients of Korean self-efficacy with the Korean mastery, performance approach, and performance avoidance goals were 0.57, 0.44, and 0.02; the corresponding coefficients were 0.68, 0.51, and 0.00 for English, 0.69, 0.53, and 0.10 for math, and 0.72, 0.45, and 0.19 for science. Rinthapol (2013) examined the relation between achievement goals and self-efficacy using the four-factor achievement model for a sample of 55 high school students from low-income immigrant families, and found that the domain had only a minor effect. Specifically, the correlation coefficients of math mastery approach, mastery avoidance, performance approach, and performance avoidance goals with math self-efficacy were 0.48, 0.01, 0.06, and 0.29, respectively; the corresponding coefficients for English were 0.42, 0.08, 0.01, and 0.28. 1.2.9. Domain of the self-efficacy Self-efficacy can be assessed for different domains. As mentioned previously, general academic self-efficacy was usually assessed using the PALS and course-specific self-efficacy was measured using the MSLQ. To address the effect of the domain of self-efficacy, Anderman and Midgley (1997) compared these relations between English and math using the two-factor model for 341 fifth graders, and found a small effect. Specifically, the correlation coefficients of English mastery and performance goals with English self-efficacy were 0.41 and 0.07, respectively; the corresponding coefficients for math were 0.43 and 0.12. A small effect was also found by Wolters, Yu, and Pintrich (1996), who compared these relations among math, English, and social studies in 434 fifth graders with a mean age of 12.6 years. The correlation coefficients of math mastery and performance goals with math self-efficacy were 0.42 and 0.24, respectively; the corresponding coefficients were 0.49 and 0.32 for English, and 0.49 and 0.35 for social studies. The cross-culture evidence for a small effect of the domain of self-efficacy seemed inconsistent. For example, Bong (2005), who compared these relations among general academic subjects, Korean, English, and math in a sample of 389 Korean high school students using structural equation modeling. The correlation coefficients between latent constructs of academic mastery, performance approach, and performance avoidance goals with academic self-efficacy were 0.52, 0.32, and 0.04, respectively; the corresponding coefficients were 0.71, 0.29, and 0.01 for Korean, 0.70, 0.37, and 0.08 for English, and 0.73, 0.41, and 0.02 for math. Vrugt, Oort, and Waardenburg (2009) sampled 99 male and 107 female Dutch students to compare these relations between Dutch and math. The effect seemed small for males. For example, the correlation coefficients of math mastery and performance goals with math self-efficacy for males were 0.10 and 0.17, respectively; the corresponding coefficients were 0.07 and 0.12 for Dutch. The effect seemed noticeable for mastery goals for females. Specifically, the correlation coefficients of math mastery and performance goals with math self-efficacy were 0.08 and 0.31, respectively; the corresponding coefficients were 0.29 and 0.24 for Dutch. 1.2.10. Matching between achievement goal and self-efficacy domains The effect of matching the domains of achievement goals and self-efficacy appeared to be supported for certain achievement goal factors. For example, Bong (2001) assessed math, English, Korean, and science self-efficacy and achievement goals among 424 Korean middle and high school students. The correlations between mastery goals and self-efficacy ranged from 0.57 to 0.73 for domains that matched between achievement goals and self-efficacy, and from 0.03 to 0.49 for domains that did not match. The correlation coefficients between performance approach goals and self-efficacy ranged from 0.44 to 0.68 for matching domains, and from 0.09 to 0.47 for not-matching domains. On the other hand, the presence of

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matching domains did not strengthen the correlation for performance avoidance goals. Specifically, the correlation coefficients ranged from 0.02 to 0.21 for matching domains and from 0.08 to 0.20 for not-matching domains. Previous metaanalyses that have examined the effect of the matching of domains between predictor and criterion variables have produced inconsistent findings. A stronger correlation was observed for matching between the domains of self-belief and academic achievement (Valentine, DuBois, & Cooper, 2004), while this effect on the relation between achievement goals and achievement emotions and that between achievement goals and academic achievement were partially supported (Huang, 2011, 2012a). Due to the mixed findings, the present meta-analysis also explored these effects. 1.3. Previous meta-analyses Celler et al. (2011) identified 45 studies that determined the correlations between achievement goals and self-efficacy in academic, game, training, work, and simulation contexts. They found that the sample-size-weighted mean relations of mastery approach, performance, performance approach, and performance avoidance goals with self-efficacy for all contexts were 0.33, 0.02, 0.10, and 0.13, respectively; the corresponding coefficients in the academic context were 0.35, 0.03, 0.14, and 0.09. However, the number of data points for the academic context was small: 20, 11, 6, and 6 correlation coefficients were identified for the mastery approach, performance, performance approach, and performance avoidance goals, respectively. Further, moderator analyses were not conducted to examine the variability of the correlation coefficients. Carpenter (2007) analyzed 38 studies examining the relations between achievement goals and self-efficacy. For mastery goals, 48 effect sizes involving 12,466 participants were identified. The mean relation between mastery goals and self-efficacy was r ¼ 0.45. Forty-five effect sizes consisting of 11,894 participants were identified for the relation between performance goals and self-efficacy; the mean relation was r ¼ 0.15. The study by Carpenter suffered from at least three limitations: (1) a comprehensive search for potential studies was not conducted (only 38 articles were analyzed), (2) moderator analyses were not performed, and (3) only the correlations of mastery and performance goals with self-efficacy were examined, with other prevalent goals such as performance avoidance goals not being examined. 2. Method 2.1. Literature search To identify potential studies, computerized searches were undertaken that started with searches of the ERIC, PsycINFO, and ProQuest Dissertations and Theses databases use combinations of terms related to achievement goals (i.e., achievement goal, goal orientation, mastery goal, mastery approach goal, mastery avoidance goal, performance goal, performance approach goal, performance avoidance goal, and their variants) and self-efficacy up to September 2013. The reference lists for all relevant articles and previous review articles (Carpenter, 2007; Cellar et al., 2011; Day, Yeo, & Radosevich, 2003; Huang, 2011, 2012a; Hulleman et al., 2010; Linnenbrink-Garcia, Tyson, & Patall, 2008; Payne, Youngcourt, & Beaubien, 2007) were subsequently examined for additional studies not identified in computer-based searches. In addition, a manual search was conducted of the following journals: British Journal of Educational Psychology, Contemporary Educational Psychology, Educational Psychologist, Educational Psychology Review, and Journal of Educational Psychology. This study examined the correlations between academic achievement goals and academic self-efficacy. Academic achievement goals were defined as the purpose or aim of a person engaging in a behavior in an academic setting. Studies measuring general achievement goals were excluded, such as Chen, Gully, Whiteman, and Kilcullen (2000). Studies that included items measuring goals other than achievement goals were also excluded. For example, Herman (2000), Jackson (2000), and Meece et al. (2003) used the scale of Meece, Blumenfeld, and Hoyle (1988), which measured both performance and social goals (e.g., “I want do well in this class so my parents will think I am smart”), and therefore these studies was excluded. Academic self-efficacy was defined as how confident an individual was that he or she would be able to complete or perform a certain academic task. Self-efficacy for self-regulated learning refers to the efficacy of using self-regulated learning strategies (Zimmerman & Martinez-Pons, 1990) and does not involve the efficacy for executing an academic task. Studies assessing self-efficacy for self-regulated learning were thus excluded, such as Kennedy (2009). To ensure an emphasis on academic settings, studies measuring general self-efficacy were also excluded, such as Ford, Smith, Weissbein, Gully, and Salas (1998). The following inclusion criterion were applied. First, the literature was limited to studies assessing achievement goals in academic settings; studies examining achievement goals in other than academic settings were excluded, such as Alalyani (2008), which examined this relation for physical education. Second, studies involving measures of general academic and domain-specific self-efficacy were included, whereas studies examining general self-efficacy or self-efficacy unrelated to academic settings (e.g., social or health self-efficacy) were excluded. Third, to compute the mean effect size, studies were included if information about sample size and the correlation between achievement goals and self-efficacy was reported. Fourth, all correlation coefficients between achievement goals and self-efficacy needed to be reported. For example, Beghetto (2007) was excluded because the correlations of mastery and performance approach goals with self-efficacy were reported, whereas that between performance avoidance goals and self-efficacy was not. Finally, the studies had to be written in English.

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2.2. Coding Besides the information that was used to calculate effect sizes and weights of effect effects (correlations between achievement goals and self-efficacy and the sample size), various study characteristics were coded. All included studies were coded by the author on two occasions separated by a 3-month interval to ensure accuracy. For categorical variables, the percentages of agreement between the codes on two occasions were 100%, 100%, 93%, 89%, 90%, 89%, and 100% for publication status, country where the research was conducted, achievement goal measure, self-efficacy measure, domain of the achievement goals, domain of self-efficacy, and matching between the achievement goal and self-efficacy domains, respectively. For continuous variables, the correlations between the codes on the two occasions were 0.96, 0.98, 0.86, 0.90 and 0.85 for sample size, correlations between achievement goals and self-efficacy, participant gender, participant age, and participant ethnicity, respectively. 2.2.1. Publication status Publication status was coded as journal article, dissertation, thesis, conference paper, book chapter, or other. When other types of publication were chosen, the publication status was specified. 2.2.2. Country where the research was conducted The country where the participants were selected was specified. 2.2.3. Participant gender The proportion of males was coded. 2.2.4. Participant age The mean age of the participants was recorded. 2.2.5. Participant ethnicity The proportion of Caucasians was coded. 2.2.6. Achievement goal model The achievement goal model was coded as a two, three-, or four-factor model. 2.2.7. Achievement goal and self-efficacy measures The measures of achievement goals and self-efficacy were specified for each study. 2.2.8. Domains of achievement goals and self-efficacy The domains of achievement goals and self-efficacy were coded as general academic subjects, math, language arts, science, social sciences, or other. 2.3. Analysis As the correlation coefficient (r) grows increasingly larger than zero, its distribution becomes increasingly skewed (Rosenthal, 1994). The correlation coefficients between achievement goals and self-efficacy were converted to normalized correlations using the equation for Fisher's transformation of r into Zr. The fixed-effect model has been called a common-effect model (Borenstein, Hedges, Higgins, & Rothstein, 2000) because all studies are assumed to have one true effect size. The variation in the observed effect sizes is caused by sampling error, so only within-study variability is allowed. In randomeffects models, true effect sizes are allowed to differ. Hence, both the within-study (sampling error) and between-study (variation of true effect size across studies) variances were used to account for the variation of effect sizes. As the Type I error in significant tests of mean correlations and moderator variables is inflated for the fixed-effect models (Hunter & Schmidt, 2000), random-effects models were used in this study. The inverse of N-3 was used to estimate the within-study variance and the DerSimonian and Laird (1986) method was used to estimate the between-study variance. All analyses were conducted with MetaWin (Rosenberg, Adams, & Gurevitch, 1997). 2.4. Dependence When multiple domains of achievement goals and multiple domains of self-efficacy were assessed for a single sample, only the correlations between achievement goals and the corresponding self-efficacy were coded. For instance, if math and English achievement goals and math and English self-efficacy were examined, the correlations between math achievement goals and math self-efficacy as well as those between English achievement goals and English self-efficacy were coded. Multiple effect sizes were considered dependent when they were based on the same participants. To address the issue of dependence, each sample contributed one effect size to the computation of mean effect size for each achievement goal factor. However, for the analyses of the moderator effects of the domain of achievement goals, the domain of self-efficacy, and the

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matching between achievement goals and self-efficacy domains, multiple effect sizes associated with different achievement goal and self-efficacy domains were considered to be independent.

3. Results 3.1. Mean relations and outlier analyses The meta-analysis included 125 studiesdconsisting of 148 independent samples involving 61,456 participantsdthat reported correlations between academic achievement goals and academic self-efficacy. Because the inverse of N-3 was used to estimate the within-study variance, studies with large samples received large weights, meaning that they could have distorted the mean relations. Three studies had large samples: Chiang, Yeh, Lin, and Hwang (2011) sampled 3137 participants using the four-factor model, Lau and Lee (2008) sampled 9440 participants using the three-factor model, and McMillan et al. (2010) sampled 3242 participants using the two-factor model. When the study of Chiang et al. (2011) was excluded, the mean correlations of performance approach and performance avoidance goals with self-efficacy were 0.29 and 0.01, respectively. The remaining correlation coefficients were unchanged. That study was retained for further analysis. When the study of Lau and Lee (2008) was excluded, the correlation coefficients remained the same. That study was also retained for further analysis. When the study of McMillan et al. (2010) was excluded, the correlation coefficients of mastery and performance goals with self-efficacy were 0.39 and 0.13, respectively. Because that study did not unduly affect the relations, it was also retained. Table 1 presents the number of correlations, mean correlation, 95% confidence interval, and homogeneity tests. The mean correlations ranged from 0.08 to 0.45. The distributions of correlations between achievement goals and selfefficacy were homogeneous, because none of the Q statistics were significant. The mean correlation between the mastery goal in the two-factor model and self-efficacy was 0.40, representing a moderate-to-strong correlation based on the guidelines of Cohen (1992). The relation between performance goals and self-efficacy was positive but small, with a weighted mean correlation of 0.14. Because mastery and performance goals had different correlations with self-efficacy, the importance of goal definition was supported. The mean correlation between mastery approach goals and self-efficacy was about strong in the four-factor model, while that between performance approach goals and self-efficacy was moderate. These findings provide further support for the importance of the goal definition. On the other hand, the correlations of mastery avoidance and performance avoidance goals with self-efficacy were both low, with coefficients that did not differ significantly from 0. Thus, the importance of goal definition was partially supported in the four-factor model. For the three-factor model, the correlation between performance approach goals and self-efficacy was low to moderate, with r ¼ 0.19, while that between performance avoidance goals and self-efficacy was low, with r ¼ 0.08. The beneficial and detrimental effects of approach and avoidance motivations, respectively, were therefore supported. For the four-factor model, the mean relation between mastery approach goals and self-efficacy was r ¼ 0.45, while the coefficient for that between mastery avoidance goals and self-efficacy did not differ significantly from 0. The desirable effect of approach motivation was again supported. Similarly, a moderate and positive mean relation was observed between performance approach goals and self-efficacy, whereas there was no correlation between performance avoidance goals and self-efficacy. Because the approach and avoidance motivations had different correlations with self-efficacy, the importance of goal valence was supported.

Table 1 Summary of meta-analysis results for correlations between achievement goals and self-efficacy. k

Mean

95% CI

Q

Lower

Upper

2-factor achievement goal model M 52 P 52

0.40 0.14

0.35 0.08

0.44 0.20

60.31 39.97

3-factor achievement goal model M 72 Pap 72 Pav 72

0.43 0.19 0.08

0.40 0.15 0.13

0.46 0.23 0.03

74.47 80.56 71.32

4-factor achievement goal model Map 24 Mav 24 Pap 24 Pav 24

0.45 0.06 0.30 0.00

0.37 0.16 0.22 0.10

0.53 0.04 0.38 0.11

27.82 28.18 29.35 27.92

M ¼ mastery goal; P ¼ performance goal; Pap ¼ performance approach goal; Pav ¼ performance avoidance goal; Map ¼ mastery approach goal; Mav ¼ mastery avoidance goal.

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3.2. Testing publication bias The problem of publication bias may not have been an issue in the present study because both published and unpublished studies were included. Possible publication bias was tested for using Spearman rank correlation (rs), the Kendall's rank correlation (t), the test of Rosenthal (1991), and the fail-safe number of Orwin (1983). As indicated in Table 2, rs and t were not statistically significant except for the correlation between mastery goals in the two-factor model and self-efficacy. The test of Rosenthal (1991) was used to estimate the number of missing studies with a correlation of 0 required to increase the p-value to above the significance level of 0.05. To increase the significance level of the correlation between mastery goals in the two-factor model and self-efficacy to 0.05, 43,562 additional missing studies would be required. The fail-safe number of Orwin (1983) was used to estimate the number of missing studies required to reduce the correlation obtained in this study (r ¼ 0.40) to a near-zero correlation (r ¼ 0.01); it was found that 2259 missing studies would be required. These two numbers exceeded the threshold of 270 (5 k þ 10, where k ¼ 52 studies; Rosenthal, 1991), indicating that the impact of publication bias may be minor for mastery goals in the two-factor model. For mastery avoidance and performance avoidance goals, the fail-safe numbers of Orwin (1983) were all 0. This is because the mean correlations were low. In summary, publication bias was probably not a problem in the present study. 3.3. Description of included studies Of the 125 included studies, 16 studies had 2 samples, 2 studies had 3 samples, and 1 study had 4 samples, yielding 148 independent samples. Coding multiple correlation coefficients for various achievement goal and self-efficacy domains from the same participants yielded 162 correlation coefficients (i.e., four samples had three dependent effect sizes and six samples had two dependent effect sizes. The remaining samples each had one effect size). To test the possible problem of dependence, sensitivity analyses were conducted by comparing the mean effect sizes using multiple effect sizes per sample to those using one effect size per study. The means computed by these two analytic approaches were generally comparable and thus the problem of dependence was not severe. The two-, three-, and four-factor models included 58, 78, and 26 data points, respectively. The most frequently assessed domain of achievement goals was math (k ¼ 42), followed by general academic subjects (k ¼ 39); this was also the case for self-efficacy, with math (k ¼ 40) followed by general academic subjects (k ¼ 34). 3.4. Moderator analysis Fifty-two independent samples consisting of 15,969 participants were available in the two-factor model, 72 samples consisting of 35,477 participants for the three-factor model, and 24 samples consisting of 10,010 participants for the fourfactor model. Because the number of effect sizes in the four-factor model was not sufficiently large, the moderator analyses were conducted for the two- and three-factor models. 3.4.1. Publication status As indicated in Table 3, 32 correlations were reported in journals, 16 in dissertations, 2 in conferences, and 2 in book chapters for the two-factor model. The strength of the correlation between achievement goals and self-efficacy did not differ significantly with publication status. Publication status was not associated with the relation between achievement goals and self-efficacy in the three-factor model. These findings provide further evidence of no publication bias being present in this study.

Table 2 Tests of publication bias. Correlation

k

t

rs

Rosenthal

Orwin

5 k þ 10

r(2f-M, SE) r(2f-P, SE) r(3f-M, SE) r(3f-Pap, SE) r(3f-Pav, SE) r(4f-Map, SE) r(4f-Mav, SE) r(4f-Pap, SE) r(4f-Pav, SE)

52 52 72 72 72 24 24 24 24

0.20* 0.09 0.07 0.07 0.12 0.17 0.20 0.19 0.02

0.30* 0.14 0.09 0.10 0.16 0.17 0.29 0.27 0.06

43,562 4874 143,087 27,341 2779 17,606 53 7874 0

2259 821 3315 1689 0 1292 0 933 0

270 270 370 370 370 130 130 130 130

Note. All correlations were given a label that identifies the number of factors in the achievement goal model (2f, 3f, or 4f), the achievement goal factor (M ¼ mastery goal; P ¼ performance goal; Pap ¼ performance approach goal; Pav ¼ performance avoidance goal; Map ¼ mastery approach goal; Mav ¼ mastery avoidance goal), and self-efficacy (SE ¼ self-efficacy). t ¼ Kendall's rank correlations; rs ¼ Spearman's rank correlation; k ¼ number of correlation coefficients. *p < 0.05.

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Table 3 Effects of Categorical moderators on the relation between achievement goals and self-efficacy. Moderator

k

Mean r

95% CI

QB

Lower

Upper

The 2-factor model Mastery goal Publication status Journal Dissertation Conference Book chapter

32 16 2 2

0.39 0.41 0.41 0.41

0.32 0.31 0.89 0.92

0.45 0.50 0.98 0.98

Country US Israel Taiwan Netherlands

43 2 2 2

0.39 0.50 0.47 0.17

0.34 0.85 0.86 0.93

0.44 0.98 0.98 0.97

AG measure PALS Nicholls Miller GI MSLQ AMQ Ames

26 6 3 3 2 2 2

0.40 0.22 0.38 0.52 0.41 0.33 0.56

0.34 0.03 0.08 0.14 0.85 0.87 0.76

0.46 0.39 0.71 0.77 0.97 0.96 0.98

SE measure PALS MSLQ

19 12

0.41 0.46

0.33 0.36

0.49 0.55

AG domain Math Academics Science Language arts Social sciences

19 12 7 6 6

0.33 0.48 0.36 0.45 0.41

0.24 0.38 0.21 0.29 0.25

0.41 0.56 0.50 0.59 0.56

SE domain Math Academics Science Language arts Social sciences

18 11 7 7 6

0.33 0.43 0.36 0.43 0.41

0.23 0.32 0.18 0.27 0.22

0.42 0.54 0.51 0.57 0.57

Matching domains between AG and SE Match Not-match

47 5

0.39 0.41

0.34 0.18

0.44 0.60

Performance goal Publication status Journal Dissertation Conference Book chapter

32 16 2 2

0.12 0.16 0.26 0.19

0.05 0.07 0.87 0.92

0.18 0.26 0.95 0.96

Country US Israel Taiwan Netherlands

43 2 2 2

0.12 0.24 0.31 0.23

0.05 0.93 0.92 0.94

0.18 0.97 0.98 0.97

AG measure PALS Nicholls Miller GI MSLQ AMQ Ames

26 6 3 3 2 2 2

0.10 0.16 0.30 0.29 0.19 0.09 0.24

0.01 0.07 0.27 0.24 0.95 0.97 0.94

0.18 0.38 0.71 0.68 0.98 0.96 0.98

0.26

4.07

12.43

0.72

7.93

3.31

0.05

1.86

2.87

6.84

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Table 3 (continued ) Moderator

k

Mean r

95% CI

QB

Lower

Upper

0.06 0.24

0.06 0.09

0.17 0.37

19 12 7 6 6

0.10 0.16 0.06 0.15 0.23

0.01 0.04 0.11 0.04 0.04

0.20 0.28 0.24 0.34 0.41

SE domain Math Academics Science Language arts Social sciences

18 11 7 7 6

0.10 0.19 0.06 0.12 0.23

0.00 0.06 0.11 0.05 0.04

0.20 0.31 0.24 0.29 0.41

Matching domains between AG and SE Match Not-match

47 5

0.14 0.14

0.08 0.11

0.19 0.37

The 3-factor model Mastery goal Publication status Journal Dissertation Thesis Conference

39 27 4 2

0.43 0.42 0.35 0.61

0.39 0.36 0.09 0.60

0.47 0.47 0.57 0.97

Country US Korea Norway Italy Canada Singapore

49 4 3 3 3 2

0.42 0.63 0.37 0.45 0.30 0.62

0.39 0.49 0.03 0.15 0.05 0.34

0.45 0.74 0.63 0.67 0.59 0.95

59 8

0.44 0.42

0.40 0.31

0.47 0.52

22 20

0.47 0.43

0.41 0.36

0.52 0.49

AG domain Academics Math Science Language arts Social sciences

24 15 11 10 3

0.39 0.51 0.51 0.48 0.42

0.32 0.43 0.41 0.37 0.03

0.46 0.58 0.60 0.57 0.72

SE domain Academics Math Science Language arts Social sciences

18 15 11 11 6

0.42 0.51 0.51 0.47 0.39

0.34 0.43 0.41 0.37 0.20

0.50 0.58 0.60 0.56 0.56

Matching domains between AG and SE Match Not-match

63 6

0.47 0.31

0.43 0.13

0.50 0.47

4.43*

SE measure PALS MSLQ

19 12

AG domain Math Academics Science Language arts Social sciences

AG measure PALS AGQ SE measure PALS MSLQ

Performance approach goal Publication status Journal Dissertation

3.61

4.28

0.00

6.54

33.20***

0.08

0.87

7.77

5.04

5.79*

4.49 39 27

0.23 0.15

0.17 0.08

0.28 0.22 (continued on next page)

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Table 3 (continued ) Moderator

k

Mean r

95% CI

QB

Lower

Upper

Thesis Conference

4 2

0.09 0.10

0.22 0.91

0.38 0.94

Country US Korea Norway Italy Canada Singapore

49 4 3 3 3 2

0.13 0.49 0.39 0.47 0.11 0.27

0.08 0.30 0.03 0.16 0.27 0.71

0.17 0.64 0.65 0.70 0.46 0.89

AG measure PALS AGQ

59 8

0.17 0.29

0.12 0.15

0.22 0.42

SE measure PALS MSLQ

22 20

0.08 0.23

0.01 0.15

0.16 0.31

AG domain Academics Math Science Language arts Social sciences

24 15 11 10 3

0.13 0.23 0.35 0.23 0.19

0.04 0.12 0.23 0.10 0.31

0.21 0.33 0.47 0.36 0.60

SE domain Academics Math Science Language arts Social sciences

18 15 11 11 6

0.13 0.23 0.35 0.23 0.31

0.02 0.11 0.22 0.09 0.09

0.23 0.34 0.47 0.36 0.51

Matching domains between AG and SE Match Not-match

63 6

0.22 0.13

0.17 0.08

0.27 0.33

Performance avoidance goal Publication status Journal Dissertation Thesis Conference

39 27 4 2

0.13 0.04 0.12 0.13

0.19 0.12 0.23 0.96

0.06 0.05 0.44 0.94

Country US Korea Norway Italy Canada Singapore

49 4 3 3 3 2

0.09 0.15 0.12 0.42 0.04 0.07

0.13 0.10 0.49 0.69 0.37 0.89

0.04 0.38 0.29 0.04 0.44 0.85

AG measure PALS AGQ

59 8

0.07 0.19

0.12 0.35

0.01 0.01

SE measure PALS MSLQ

22 20

0.03 0.06

0.11 0.15

0.05 0.02

AG domain Academics Math Science Language arts Social sciences

24 15 11 10 3

0.03 0.06 0.11 0.06 0.24

0.12 0.17 0.24 0.20 0.64

0.05 0.05 0.03 0.09 0.26

57.26***

3.41

7.94**

10.96*

9.65*

1.13

6.59

25.47***

2.47

0.47

3.41

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Table 3 (continued ) Moderator

k

SE domain Academics Math Science Language arts Social sciences

18 15 11 11 6

Matching domains between AG and SE Match Not-match

63 6

Mean r

95% CI

QB

Lower

Upper

0.02 0.06 0.11 0.03 0.17

0.12 0.18 0.24 0.17 0.38

0.09 0.06 0.03 0.11 0.06

0.07 0.08

0.12 0.28

0.02 0.13

3.02

0.02

k ¼ total number of correlations included in the analysis; QB ¼ between-group homogeneity statistic; M ¼ mastery goals; Pap ¼ performance approach goals; Pav ¼ performance avoidance goals; AG measure ¼ the achievement goal measure, PALS ¼ the Patterns of Adaptive Learning Scales, MSLQ ¼ the Motivated Strategies for Learning Questionnaire, Nicholls ¼ Nicholls (1989), Nicholls et al. (1990), or Duda and Nicholls (1992). Miller ¼ Miller et al. (1993, 1996), GI ¼ the Goal Inventory, AMO ¼ the Achievement Motivation Questionnaire, Ames ¼ Ames & Archer (1988). *p < 0.05; **p < 0.01; ***p < 0.001.

3.4.2. Country where the research was conducted The moderating effect of country was significant in the three-factor model but not in the two-factor model. Based on 95% confidence intervals, the mean relations of mastery and performance approach goals with self-efficacy were stronger for Korean students than for the US students. 3.4.3. Participant gender As indicated in Table 4, the proportion of males was available for 43 and 63 independent samples in the two- and threefactor models, respectively. Participant gender had no significant moderating effect, indicating that the proportion of males included in the studies was not related to the strengths of the correlations between achievement goals and self-efficacy. 3.4.4. Participant age The mean age of sample was available for 51 and 69 independent samples in the two- and three-factor models, respectively. Participant age was not a significant moderator, which indicates that the correlations between achievement goals and self-efficacy were independent of age. 3.4.5. Participant ethnicity The proportion of Caucasians was reported for 30 and 38 samples in the two- and three-factor models, respectively, for studies conducted in North America. Participant ethnicity had no significant moderating effect on most of the achievement goals; this factor was associated with the relation between performance avoidance goals and self-efficacy, with b ¼ 0.31; specifically, Zr ¼ 0.08 þ (0.31) (ethnicity). Studies involving a greater proportion of Caucasians produced more negative correlation coefficients. The expected relation between performance avoidance goals and self-efficacy was Zr ¼ 0.08 (r ¼ 0.08) for non-Caucasian samples and Zr ¼ 0.23 (r ¼ 0.23) for Caucasian samples. Hence, the expected correlation between performance goals and self-efficacy was negative and low to moderate for Caucasian samples, and positive and low for nonCaucasian samples. 3.4.6. Achievement goal measure The original and revised versions of the AGQ were developed for three and four factors, respectively, and this questionnaire has not been used by studies that adopted the two-factor model. The PALS was administered to 26 of 52 samples in the

Table 4 Effects of continuous moderators on the relation between achievement goals and self-efficacy. % of male

age

% of white

b

p

Qreg

Qres

k

a

b

p

Qreg

Qres

k

a

b

p

Qreg

Qres

The 2-factor model M 43 0.41 P 43 0.10

0.02 0.04

0.88 0.79

0.02 0.07

44.95 40.12

51 51

0.45 0.12

0.00 0.00

0.79 0.84

0.07 0.04

58.38 38.23

30 30

0.46 0.24

0.02 0.25

0.92 0.09

0.01 2.82

36.81 24.40

The 3-factor model M 63 0.43 Pap 63 0.16 Pav 63 0.08

0.09 0.05 0.07

0.43 0.69 0.60

0.63 0.16 0.28

62.27 68.56 63.64

69 69 69

0.58 0.19 0.19

0.01 0.00 0.01

0.06 0.97 0.18

3.58 0.00 1.79

65.84 76.99 66.74

38 38 38

0.43 0.16 0.08

0.05 0.04 0.31

0.59 0.66 0.01

0.29 0.19 6.76

36.05 38.05 41.34

k

a

k ¼ total number of correlations included in the analysis; a ¼ intercept; b ¼ regression coefficient; p ¼ p value for regression coefficient; Qreg ¼ regression sum of squares; Qres ¼ residual sum of squares; M ¼ mastery goals; P ¼ performance goals; Pap ¼ performance approach goals; Pav ¼ performance avoidance goals.

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two-factor model. Most of the remaining measures were administered to only a few samples. For example, the scales of Nicholls and colleagues (Duda & Nicholls, 1992; Nicholls, 1989; Nicholls, Cobb, Wood, Yackel, & Patashnick, 1990) were administered to six samples, while that of Miller and colleagues (Miller, Behrens, Greene, & Newman, 1993, 1996) was administered to three samples. Averaged over three samples, the mean relation for the Goals Inventory (Roedel, Schraw, & Plake, 1994) was strong, with r ¼ 0.52. Similarly, averaged over two samples, the mean relation for Ames and Archer's scale (1988) was again strong, with r ¼ 0.56. In contrast, the mean relation for the scales of Nicholls and colleagues was low to moderate, with r ¼ 0.22. However, the achievement goal measure had no significant moderating effect on the relation between mastery goals in the two-factor model and self-efficacy. The PALS was administered to 59 of 72 samples in the three-factor model, while the AGQ was administered to 8 samples. Each of the remaining scales was administered to only one sample. Hence, only the mean relations between the PALS and AGQ were compared. The correlation coefficients between achievement goals and self-efficacy did not differ significantly for these two commonly used scales. 3.4.7. Self-efficacy measure Several self-efficacy scales have been used in primary research studies, most of which have included relatively small samples. Hence, the study compared the mean relations for two major measures: the PALS and MSLQ. This moderating effect was found to be significant for the relation between performance goals in the two-factor model and self-efficacy, with QB ¼ 4.43 (p < 0.05). The mean relation for the PALS was low, with r ¼ 0.06, while that for the MSLQ was about moderate, with r ¼ 0.24. Similarly, this moderating effect on the relation between performance approach goals and self-efficacy was significant, with QB ¼ 7.94 (p < 0.01). The effect size was about small for the PALS and about moderate for the MSLQ. The selfefficacy measure had no significant moderating effect on the remaining relations. 3.4.8. Domain of the achievement goals As mentioned above, multiple effect sizes were coded if studies reported correlations between various domains of achievement goals and various domains of self-efficacy. Coding multiple correlation coefficients yielded 19 data points for math, 12 for general academic subjects, 7 for science, 6 for language arts, and 6 for social sciences (e.g., a psychology course) in the two-factor model. The domain of achievement goals had no significant moderating effect in the two-factor model. For the three-factor model, the moderating effect on the relation between performance approach goals and self-efficacy was significant, with QB ¼ 10.96 (p < 0.05). The mean relation was approximately moderate (r ¼ 0.35) for science and low for general academic subjects (r ¼ 0.13). Based on 95% confidence intervals, the effect size was larger for science than for general academic subjects. The domain of achievement goals had no significant moderating effect of the remaining achievement goal factors. 3.4.9. Domain of self-efficacy The domain of self-efficacy had no significant moderating effect in the two-factor model. This moderating effect on the relation between performance approach goals in the three-factor model and self-efficacy was significant, with QB ¼ 9.65 (p < 0.05). The effect size for general academic subjects was small, close to moderate for math and language arts, and moderate for science and social sciences. 3.4.10. Matching between achievement goal and self-efficacy domains The effect of domains that matched between achievement goals and self-efficacy was significant on the relation between mastery goals in the three-factor model and self-efficacy, with QB ¼ 5.79 (p < 0.05). The mean relation for domains that matched between achievement goals and self-efficacy was strong, with r ¼ 0.47, while that for not-matching domains was moderate to strong, with r ¼ 0.31. 4. Discussion Recent work on achievement theory has focused both on mastery versus performance goals and approach versus avoidance motivations. Previous achievement goal theories did not predict all correlations between achievement goals in three achievement goal models and self-efficacy, which prompted the present meta-analysis to examine these relations. 4.1. Goal definition: mastery versus performance goals The results indicated that the mean relations between mastery goals and self-efficacy were moderate to strong. The correlation between performance goals in the two-factor model and self-efficacy was positive but low. Because the mastery and performance goals exhibited different correlations with self-efficacy, differentiating mastery from performance goals was warranted. The need to distinguish between mastery and performance goals was partially supported in the four-factor model, because self-efficacy was not correlated with either mastery avoidance or performance avoidance goals. Performance avoidance goals were driven by negative outcomes and were also affected by the possible detrimental effect of performance goals, while the beneficial effect of mastery goals was offset by the detrimental effect of an avoidance motivation in mastery avoidance goals. Surprisingly, the effect of performance avoidance goals on self-efficacy was not more harmful than that of

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mastery avoidance goals. The mastery avoidance goal was most recently introduced into the achievement goal model, and several researchers (Elliot & McGregor, 2001; Elliot & Murayama, 2008) have argued for its importance. The decision to refine or exclude the scale of mastery avoidance goals should be resolved based on consideration of its predictive usefulness. If there is convincing evidence that mastery avoidance and performance avoidance goals do not have different correlations with antecedents and consequences, mastery avoidance goals should not be retained. The four-factor model was based on a small number of samples, future research should address the issue of the discriminant validity of mastery avoidance and performance avoidance goals. On the other hand, self-efficacy was approximately strongly correlated with mastery approach goals but only moderately correlated with performance approach goals. Hence, the differentiation of mastery from performance goals was partially supported. Previous meta-analyses have identified the correlations between achievement goals and self-efficacy. Carpenter (2007) reported a similar correlation between mastery goals and self-efficacy, with a weighted mean correlation of 0.45. For the relation between performance goals and self-efficacy, a similar correlation (r ¼ 0.15) was reported in Carpenter (2007), while a near zero effect size (r ¼ 0.03) was observed in Cellar et al. (2011). The latter authors found that the mean relation between mastery approach goals and self-efficacy was 0.35, indicating a moderate correlation, and that the weighted mean relation between performance approach goals and self-efficacy was r ¼ 0.14, which is a somewhat smaller effect size than that found in the present meta-analysis. Further, the relation between performance avoidance goals and self-efficacy was r ¼ 0.09, similar to the low correlation observed in the present meta-analysis. 4.2. Goal valence: differentiating approach and avoidance motivations The correlation between performance approach goals and self-efficacy was low to moderate in the three-factor model and moderate in the four-factor model, while that between performance avoidance goals and self-efficacy was either low or nonexistent. There was a difference in the correlations of self-efficacy with mastery approach and mastery avoidance goals. These findings lend support to the need to differentiate approach from avoidance motivations. The correlations of self-efficacy with mastery and mastery approach goals were similar. This was possibly due to similarity in the items used to measure mastery and mastery approach goals, such as items in the mastery goal scales of the PALS (Midgley et al., 1996) and AGQ (Elliot & Church, 1997) both measuring the mastery approach goals. 4.3. Moderator effects 4.3.1. Demographic variables The relations between achievement goals and self-efficacy did not vary systematically with the proportion of males, suggesting that such links have remained constant despite variations in the gender compositions of the samples. Vrugt, Oort, and Waardenburg (2009) suggested that gender can moderate the relations between achievement goals and self-efficacy because gender differences in self-efficacy vary with the domain. A previous meta-analysis (Huang, 2013) found that although the gender differences in academic self-efficacy did vary across domains, these variations were generally small (based on the criterion of Cohen, 1992). It is therefore possible that gender differences in academic self-efficacy were also small in the present study, thus resulting in no significant moderator effect of gender. Byrne (1996) suggested that the belief system for younger children was less differentiated and thus that the relation between achievement goals and self-efficacy can vary with age. Such an age effect was not supported by the results obtained in the present study. Hedgspeth (2007) and Rinthapol (2013) found that minority students were vulnerable to academic failure, which suggests that the relations between achievement goals and self-efficacy vary with ethnicity. The proportion of Caucasians significantly affected the relation between performance avoidance goals and self-efficacy, but not any of the other relations. Thus, the moderating effects of demographic variables on the relations between achievement goals and self-efficacy were generally minimal. 4.3.2. Country where the research was conducted The moderating effects of country on the relations between achievement goals and self-efficacy were inconsistent across the achievement goal models. Specifically, this moderating effect was significant for the three-factor model but not the twofactor model. The mean relations were generally stronger for Korean students than for the US students. However, caution is necessary when interpreting country differences in the relation between achievement goals and self-efficacy. The number of Korean samples was quite small (k ¼ 4), and all of these studies were conducted by Bong (two samples in 2001, and one each in 2005 and 2008). Further, the correlations reported by Bong (2005) were based on latent constructs instead of observed variables. As mentioned previously, the correlation coefficients based on latent constructs were adjusted for attenuation, and would be larger than those based on observed correlation coefficients. Hence, findings related to the country effect in the present study should be considered to be suggestive only. Kim and Park (2006) found that the perceived academic competence differed between students from collective and individualist cultures. Students from individualist cultures generally perceive that they have a high academic competence, even when they perform poorly. In contrast, students from collective cultures have low academic confidence. Further research is needed to examine the possible effect of culture on the relations between achievement goals and self-efficacy. Such studies might verify the results for the country effect found in the present study.

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4.3.3. Measures of achievement goal and self-efficacy Because different measures may tap somewhat different underlying constructs (Hulleman et al., 2010), the moderating effects of measures of achievement goals was examined. The effect of achievement goal measures was mixed. For example, the mean correlation coefficients between mastery goals in the two-factor model and self-efficacy varied (from 0.22 to 0.56), but this effect was not statistically significant. The lack of significance could have been due to the low statistical power associated with most measures involving only a small number of samples. These results mean that future studies should compare the correlations for different measures; and such studies might allow firm conclusions to be drawn. The self-efficacy measure had a significant moderating effect on the relations of performance and performance approach goals with self-efficacy. The mean relation for the PALS was small, while that for the MSLQ was close to moderate. These findings seem to support that these two measures tap different underlying constructs. 4.3.4. Domains of achievement goal and self-efficacy measures The domains of achievement goals and self-efficacy significantly affected the relation between performance approach goals and self-efficacy. The mean relation was stronger when science achievement goals were assessed than for general academic achievement goals. In contrast, the domain of self-efficacy significantly affected the relation between performance approach goals and self-efficacy, but none of the pairwise comparisons were significant. Because the findings regarding the domain of self-efficacy were not conclusive, future research should further investigate this effect. It was expected that the correlations between achievement goals and self-efficacy would be stronger if there was matching between the domains of achievement goals and self-efficacy. However, this hypothesis was not generally supported. This effect was supported for mastery goals in the three-factor model, but for the remaining factors the effects were not significant. These findings were inconsistent with the self-belief literature (Huang, 2012b; Valentine et al., 2004). Because the notmatching domains were based on only a few data points, future research should focus on the effect of matching versus not-matching domains. This meta-analysis had some limitations. First, this study did not examine the moderating effects of observed variables versus latent constructs because of insufficient studies (k ¼ 5) were used to produce correlation coefficients based on latent constructs. Future research should determine the differences between adjusted and observed correlations. Second, some moderators may be correlated. As mentioned previously, the AGO was originally developed for college students whereas the PALS is usually used for elementary and secondary school students. The achievement goal measure and participant age may be correlated. However, such a confounding of moderators was difficult to disentangle owing to an insufficiency of data points. Third, the studies that were included in the present meta-analysis measured achievement goals and self-efficacy through self-reports and their research designs were mostly cross-sectional. The conclusions of the present meta-analysis may not be generalized to other informants and research designs. Fourth, despite the advantages of using multiple coders, the included studies were only coded by the author. Lastly, pairwise comparisons were made for categorical moderators to test the specific difference between two categories. Type I error may be inflated due to multiple comparisons. 5. Theoretical contributions and practical implications This work contributes to academic achievement goal theory in three ways. First, the present meta-analysis systematically examined the relation between academic achievement goals and academic self-efficacy by considering five paired comparisons. The findings revealed that (a) the correlations of mastery and performance goals with self-efficacy differed significantly; (b) the correlations of mastery approach and performance approach goals with self-efficacy were not similar; (c) the correlations of mastery avoidance and performance avoidance goals with self-efficacy were similar; (d) the correlations of mastery approach and mastery avoidance goals with self-efficacy differed significantly, and (e) the correlations of performance approach and performance avoidance goals with self-efficacy differed significantly. Second, this study clarified the relations of goal valence and goal definition with self-efficacy. Several researchers (e.g., Midgley, Kaplan, & Middleton, 2001) have stressed the importance of distinguishing between approach and avoidance motivations. The findings of this study support the fact that goal valence is meaningfully related to self-efficacy, and the approach component is positively associated with self-efficacy, while the correlation between the avoidance component and self-efficacy was low. In contrast, support for the goal definition was mixed, because the correlations of mastery avoidance and performance avoidance goals with selfefficacy were similar. Since the four-factor model was based on relatively few studies, future studies should investigate the discriminant validity of achievement goals for the four-factor model so that the optimal achievement goal model can be identified. Third, Midgley et al. (2001) have claimed that the performance approach goal is adaptive and have argued for revision of achievement goal theory. This study improves our understanding of the effect of the performance approach goal by examining its relation with self-efficacy. The findings of this study support the positive effect of the performance approach goal. The findings of the present meta-analysis have important practical implications. Ferguson (2009) provided reference points for assessing the practical importance for clinicians and researchers. Specifically, he considered the effect size r ¼ 0.2 to be the “recommended minimum effect size”, r ¼ 0.5 to be moderate, and r ¼ 0.8 to be strong. The overall predictive power of mastery and mastery approach goals to predict self-efficacy was close moderate. Encouraging students to adopt mastery or mastery approach goals is important. Further, correlations between the performance approach goal and self-efficacy were also meaningful. Parents and teachers must also foster a learning environment that can help students adopt a performance

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