Kanupriya Rawat, Aleksandra Błachnio, Nibu Rkrishna Cross-cultural adaptation and psychometric properties of the achievement goal Questionnaire 3x2-Sport among Polish athletes

Artykuł jest dostępny na warunkach międzynarodowej licencji 4.0 (CC BY-NC-ND 4.0).

Introduction

Achievement motivation affects both the athlete, and the coach, as well as the results of their interaction. Much seems to depend on this (Smith et al., 2017). The athlete is pushed to pursue competitive goals due to an inherent force i.e., achievement motivation. It helps the athletes to develop motivational characteristics to reach the highest level in their respective sports (Vallerand, Miquelon, 2007; Baker, Young, 2014). On the contrary, highly motivated athlete who has dysfunctional beliefs (win-at-all-cost mentality, borderline perfectionism etc.) can encounter adverse effects like burnout, unethical behaviour, conflicts, health issues, and disengagement from the sport (Boiché, Sarrazin, 2009; Van de Pol, Kavussanu, 2012; Mudrak et al., 2018). Interest in achievement motivation emerged at the turn of the 1970s and 1980s (Elliot, 2005). Since then, it has evolved from a definition-based approach, i.e., a dichotomous model of achievement goals (Nicholls, 1984; Dweck, 1986; Ames, 1992) to a trichotomous goal framework (Elliot, Harackiewicz, 1996). Later, the 2x2 achievement goal framework was updated with a valence-based approach and avoidance dimensions (Elliot, 1999). A 3x2 achievement goal model is now trending, which is an expanded version of the 2x2 achievement framework (Elliot et al., 2011). Initial conceptual work recognized a definition-based approach with two factors, also known as the dichotomous model of achievement goals: mastery goals and performance goals(Dweck, Elliott, 1983; Nicholls, 1984; Ames, 1992). Mastery goals refer to situations in which athletes strive to develop and improve their skills, while in performance goals, athletes try to compare or compete with others in their abilities. This approach gained many supporters (Ntoumanis, Biddle, 1999; Biddle et al., 2003; Duda, 2005). There were also opponents who emphasized its limitations. According to Ames (1992) and Nicholls et al. (1989) both goals are approach in nature. Others argued the lack of valenced nature of the performance goal orientation (Skaalvik, 1997; Harackiewicz et al., 2002). Therefore, the theory shifted towards a trichotomous goal framework, given by Elliot and Harackiewicz (1996). Valenced-based approach and avoidance performance goals were added as a distinct type along with mastery goals (Elliot, Harackiewicz, 1996; Payne et al., 2007).

Incorporating the valence-based approach and avoidance dimensions into mastery and performance extended the trichotomous goal framework into a 2x2 achievement goal framework. Herein competence is evaluated in terms of definition and valence (Wang et al., 2017). The cross-tabulation of approach (positive achievement behavior) and avoidance (negative achievement behavior) with mastery goals, and performance goals results in the four achievement goals (mastery-approach, mastery-avoidance, performance-approach, performance-avoidance). The mastery-approach refers to the positive orientation toward attaining a skill or competence, and mastery-avoidance refers to avoiding the failure to attain
a skill. A performance approach promotes the presentation of skills, while performance-avoidance goals are negatively oriented so as not to appear inept compared to others. These frames have gained great popularity, but not in sports.

The 2x2 framework evolved into the 3x2 achievement goal framework, as Elliot et al. (2011) argued, “the separation of task-based and self-based goals from mastery goals. Task-based goals are solely based on the demands of the tasks while self-based goals are based on comparing oneself with one's own prior performances”. This distinction is supported on the basis of people’s engagement to complete the task only or to improve their skills. Few studies have examined the validity of the 3x2 model of AGQ in an academic or work context (Elliot et al., 2011; Diseth, 2015; León-del-Barco et al., 2019), fewer than that were examined in a sports context (Mascret et al., 2016; Lower, Turner, 2016; Wang et al., 2017).

The 3x2 achievement goal model was examined by Mascret et al. (2015) on the French population, where they reported two unique goals: task-based and self-based goals. They compared ten alternative models with the six-factor model, and found that the six-factor model was a good fit for the empirical data. Similar results were found in the study by Wang et al. (2017), where they altered some items because of the ambiguous nature of task-approach and task-avoidance dimensions. Instead of the phrases: "to perform well", "to obtain good results", and "to be effective” (Mascret et al., 2015), Wang et al. (2017) included the statements: "I aim to execute the skills correctly", "I strive to apply the right tactics and strategies", and "I want to execute every technique successfully". Instead of "to avoid performing badly", "to avoid bad results", and "to avoid being ineffective", they used items such as “I avoid making a lot of technical errors”, “I avoid applying the wrong tactics and strategies”, and “I avoid making a lot of mistakes” (Wang et al., 2017, p. 462–463). We agree with Wang et al.'s modifications, which is why we used them in the Polish adaptation of the 3x2 Achievement Goals Questionnaire - Sport. Other cultural adaptations are also available i.e. 3x2 AGQ-Sports (see Picoli et al., 2022; Nikitskaya, Uglanova, 2021), AGQ-Sports for physical education (Méndez-Giménez et al., 2014), and AGQ-Sports for recreational (Lower, Turner, 2016).

In Poland, two research teams – ours and Tomczak et al. (2024) – independently undertook the cross-cultural adaptation of the 3x2 Achievement Goal Questionnaire. Although both projects were conducted concurrently, Tomczak et al. (2024) completed theirs first and subsequently published their findings, which brought their work to our attention. Upon comparison, we identified differences between our version of the questionnaire, which was adapted from Wang et al. (2017) take on the 3x2 AGQ, and the version used by Tomczak et al. (2024), which was based on Mascret et al. (2015) study of the 3x2 AGQ. Acknowledging the value of replication, we decided to proceed with our project. Furthermore, our study offers additional contributions by comparing individual and team sports, and by assessing convergent validity to evaluate the relationships between the scale and other instruments measuring similar constructs – an area not addressed in the previous adaptation.

Therefore, this study assessed the psychometric properties of the 3x2 Achievement Goal Questionnaire-Sports in the Polish population, for example, construct validity and reliability. The criterion validity of the 3x2 Achievement Goal Questionnaire- Sports was examined, and research on its relationship with other scales, such as STAI and TEOSQ, was included. The research fill gaps in the literature on the subject and bring forth interesting findings as this is the first study to use modifications in the 3x2 AGQ-Sports suggested by Wang et al. (2017).

Method

Study group and procedure

This study includes 396 athletes as a sample, where female (N=191), and male (N=205) with the average age of (M=22.89, SD=3.82). Convenience sampling was used where the authors went to sports clubs and trainers to invite the players to participate in the data collection.

The study included participants from both individual and team sports, with individual sports (N= 215) and team sports (N= 181) participants. Team sports include football, volleyball, field hockey, and handball, while individual sports include sprinting, track (<400 m, 800-1500 m, >5000 m), marathon, field athletics, swimming (<400 m, 800 m+), kayaking, rowing and weightlifting. The research involved two groups of participants: 186 classified as recreational and 210 as high-performance athletes.The university's ethics committee approved this study. The subjects were given informed consent form to sign and they agreed to voluntarily participate in the study.

Measures

In addition to the Polish version of the 3x2 Achievement Goal Questionnaire-Sports, participants filled out two additional questionnaires (Task and Ego Orientation in Sport Questionnaire (PL) and State and Trait Anxiety Inventory (PL)). These two questionnaires were used to assess the validity of the 3x2 AGQ–Sports. In addition, participants responded to the demographic questions, e.g., gender, age, sports played, frequency of training per week, career duration, quality of career etc.

Achievement Goal Questionnaire-Sports(3×2AGQ-S), Mascret et al. 2015, modifications made by Wang et al., 2017: This questionnaire measures the task-based, self-based, and other-based goals in terms of approach and avoidance dimensions. Elliot et al. (2011) measured the 3x2 achievement goals in a general undergraduate classroom context. The 3×2 AGQ was revised by Mascret et al. (2015) in a sports setting. Some terms like “questions” and “answers” were replaced with “skills”, “techniques”, “tactics”, and “strategies”. Similarly, “other students” was replaced with “others” or “players”, and “in this class” with “in my sport”. However, the questionnaire was further modified by Wang et al. (2017) due to the ambiguous nature of items in task-approach and task-avoidance. Some examples of modifications made in the questionnaire are following: "I aim to execute the skills correctly", "I strive to apply the right tactics and strategies” items were changed in task-approach, and in task-avoidance goals: “I avoid making a lot of technical errors”, and “I avoid applying the wrong tactics and strategies” items were changed. A 7-point scale of “strongly disagree” (1) to “strongly agree” (7) were used for taking response from athletes. Each achievement goal consists of three items.

Adaptation Procedure

Three experts were involved in translating the 3x2 Achievement Goal Questionnaire-Sports from English to Polish. A linguist and psychologist, an English and Polish expert, translated the questionnaire from English to Polish. Then, it was given to a sports psychologist to review its accuracy. The Polish version of the 3×2 AGQ-S instrument was also tested for readability, carried out by Polish language experts and a few students of Physical education and sports players to check the instructions and readability of the items. After back-translation, we started a pilot study on high-performance and recreational sports players. The good fit model for the Polish version of the 3x2 Achievement goal questionnaire-sports was analyses using CFA. Then, the study was conducted on main sample.

Task and Ego Orientation in Sport Questionnaire (TEOSQ),(Tomczak et al., 2020); Tomczak et al. (2020) modified this scale specifically for the Polish population. Seven items pertain to task orientation and six to ego orientation, for a total of thirteen statements. An individual uses a scale from 1 to 5 to indicate how much a statement relates to them. The Cronbach’s alpha for task subscale, and ego subscale were .81, and .84 respectively.

State-Trait Anxiety Inventory (STAI); Polish adaptation-Wrzésniewski et al. (2012): State anxiety and trait anxiety are the two categories that STAI measures. State anxiety and trait anxiety are two subscales of this scale. Each subscale consists of 20 items each. All items are rated on a 4-point scale in both subscales. The scores can range from 20-80, where higher scores indicate high anxiety. One can tell the difference between trait anxiety and situational anxiety by comparing the results of the subscales.

Data analysis

In this segment, we outline the outcomes of the initial examinations pertaining to the following: the evaluation of item reliability, confirmatory factor analysis (CFA) for 12 models, the methodologies employed for conducting the invariance assessment across gender, athlete type, and sport type, as well as the Spearman correlation and Mann-Whitney U test. First, The item reliability assessment included an analysis of factor loadings and their squared values, which reveal how much of each item's variance is attributed to a specific concept. This approach was instrumental in assessing the convergent validity indices for the 3x2 AGQ-S scale. The minimum standardised loading value of .40 indicates a high degree of flexibility, whereas a value of .70 indicates that the factor accounts for around 50% of the item's variance. Following the methods proposed by Fornell and Larcker (1981), the study then calculated the composite reliability (CR) and average extracted variance (AVE) for each sub-scale.

Scholarly consensus supports the notion that a CR score exceeding .6 (or .7) and an AVE value surpassing .5 are generally regarded as indicative of sound convergent validity. On the other hand, the assessment of discriminant validity involved a comparison between the maximum shared variance (MSV), and the average variance extracted (AVE) of the same latent variable. Discriminant validity for the construct is deemed to be established when the AVE value exceeds the MSV, in accordance with the criteria outlined by Fornell and Larcker (1981).

The intraclass correlation coefficient (ICC) and Cronbach's alpha were utilised to determine the reliability of the scale. The ICC was calculated using repeated assessments of the same athlete at two-week intervals (N=100, with all athletes completing the scale twice). The differentiation capability of a particular test item was determined through an analysis of its correlation with the total score of the subscales.

To evaluate construct validity, 12 alternative models were evaluated for confirmatory factor analysis. The analysis was done according to the Mascret et. al. (2015) study, where, firstly a 3x2 achievement goal model with six factors—task-approach, task-avoidance, self-approach, self-avoidance, others-approach, and others-avoidance—was estimated for Polish population based on 3x2 achievement goal theory. Next, 11 other models (see Table 2) were estimated to assess the validity by extracting the subscales of the questionnaire in different ways and then comparing them with other models. CFI and TLI values over .90, and RMSEA and SRMR values below .08 were used to indicate that the proposed models fit the data well (Whittaker, 2016). The Satorra-Bentler correction was applied due to the deviation of the multivariate data from the normality assumptions (Satorra, Bentler, 2001).

Furthermore, we explored the concept of scale invariance in the context of gender, level of sports participation and type of sports. Initially, a configural invariance model was estimated, followed by the estimation of a metric invariance model in which factor loadings were constrained within the respective groups. The regression intercepts were then fixed, and subsequently, a model ensuring scalar invariance was fitted. Finally, the residuals within the comparison groups were fixed, and a model for strict invariance was estimated. Significant group differences were revealed by a decrease in CFI greater than .01 and an increase in RMSEA exceeding .015. Furthermore, statistically significant group differences become evident when SRMR increases by .01 in cases of strict and scalar invariance and by .03 in instances of metric invariance(Chen, 2007).

The association between the 3x2 AGQ-Sports, TEOSQ, and STAI questionnaires was explored through the utilisation of the Spearman correlation approach. Mann-Whitney U test was used to find significant differences between achievement goal orientation and variables like level of sports participation. The analysis in this study was conducted using SPSS version 29.1.0 and R version 4.2.2.

Results

Sample

The findings from the analysis of descriptive statistics, as presented in Table 1, indicate that the self-approach goal had the greatest average value (M=17.55, SD=3.56), followed by the task-approach goal (M=16.98, SD=3.81).

In reliability analysis, the Cronbach’s coefficient for the TAp, TAv, SAp, SAv, OAp, and OAv subscales were .853, .894, .873, .889, .906, and .827 respectively. While the discriminant power coefficients for the subscale’s items were: TAp (1- .83, 2- .87, 3- .86), TAv (4- .91, 5- .90, 6-.88), SAp ( 7- .87, 8- .87, 9- .85), SAv (10- .88, 11- .90, 12- .90), OAp (13- .92, 14- .88, 15- .93), OAv (16- .85, 17- .91, and 18- .78) respectively. Cronbach's alpha for the scale as a whole was .93. McDonald’s Omega for the whole scale was .91.

The factor loadings and squared multiple correlations of items 1 to 18 were .823 (.677), .813 (.66), .80 (.64), .841 (.707), .874 (.763), .866 (.749), .827 (.683), .816 (.665), .861 (.741), .839 (.703), .901 (.811), .822 (.675), .87 (.756), .836 (.698), .92 (.846), .755 (.57), .939 (.881), .68 (.462), respectively. The values for composite reliability, average extracted variance, and maximum shared variance were presented in Table 1. The assumption of discriminant validity was made based on the observation that the average variance extracted (AVE) values for each subscale were higher than the maximum shared variance (MSV) values. Intraclass correlations (ICC) of the scale were: Total achievement motivation=.966, TAp=.896, TAv=.943, SAp=.971, SAv=.972, OAp=.925 and OAv=.891.

Table 1. Descriptive statistics and reliability analysis for the Polish version of the 3x2 achievement goal questionnaire-sports

		TAp M (SD)	TAv M (SD)	SAp M (SD)	SAv M (SD)	OAp M (SD)	OAv M (SD)
	Total (N = 396)	16 .98 (3.81)	16.28 (3.93)	17 .55 (3.56)	16.46 (4.02)	13.76 (4.9)	12.97 (4.67)
Gender	Female (N = 191)	17.13 (3.8)	16.35 (3.92)	17 .59 (3.63)	16 .59 (4.08)	13.8 (4.88)	13.56 (4.63)
	Male (N = 205)	16.83 (3.82)	16.2 (3.95)	17 .51 (3.5)	16.34 (3.97)	13.73 (4.92)	12.41 (4.65)
Level of sports participation	Recreational (R) (N = 186)	16 .78 (3.79)	16.32 (3.68)	17.45 (3.56)	16.32 (3.89)	12.58 (5.13)	12.5 (4.83)
	High Performance (HP) (N = 210)	17 .15 (3.83)	16.24 (4.16)	17.64 (3.57)	16 .59 (4.14)	14.8 (4.44)	13.38 (4.49)
Type of sports	Individual sport (N = 215)	17.14 (3.34)	16.35 (3.56)	17 .57 (3.28)	16.31 (3.74)	13.43 (4.81)	12.65 (4.71)
	Team sport (N = 181)	16 .77 (4.29)	16 .18 (4.33)	17 .51 (3.87)	16.63 (4.33)	14.14 (4.97)	13.33 (4.60)
Reliability analysis	CR	.853	.895	.873	.89	.908	.838
	AVE	.659	.74	.695	.732	.769	.646
	MSV	.51	.51	.614	.614	.27	.27
	α	.853	.894	.873	.889	.906	.827

Note. TAp = task-approach; TAv = task-avoidance; SAp = self-approach; SAv = self-avoidance; OAp = other-approach; OAv = other- -avoidance, CR = Construct Reliability; AVE = Average Variance Extracted; MSV = Maximum Shared Variance; α = Cronbach’s Alpha

Figure 1. Factor loadings for the 3x2 AGQ

Note. TAp= task-approach; TAv= task-avoidance; SAp= self-approach; SAv= self-avoidance; OAp= other-approach; OAv= other-avoidance

Construct validity: Factor structure

Parameters (CFI, TLI, RMSEA, and SRMR) suggested an adequate fit to the data, as shown in the test results (Table 2). Table 2 illustrates that the 6-factor model most effectively accounted for the empirical data. The data analysis reveals that the 6-factor model has a good level of fit among individuals of each gender, and across both level of sports participation and type of sports, as seen in Table 2. The factor loadings, which were determined to be statistically significant based on a 6-factor model with a p-value of less than .001, exhibited a range from .68 to .939.

Table 2. CFA models for Polish version of the 3x2 achievement goal questionnaire-sports

Models	N	Chi-square (df )	p	CFI	TLI	RMSEA 90%CI	SRMR
6-factor	396	221.34 (120)	<.001	.98	.97	.046 [.037, .056]	.045
1 factor	396	1818.41 (135)	<.001	.67	.63	.177 [.17, .185]	.122
2 × 2 Achievement Goal Model	396	102.13 (134)	<.001	.82	.8	.129 [.122, .137]	.075
Trichotomous goal model (OAp, OAv, all other goals)	396	709.97 (132)	<.001	.88	.87	.105 [.098, .113]	.063
Dichotomous goal model (Other-based goals, all other goals)	396	102.13 (134)	<.001	.82	.80	.129 [.122, .137]	.075
TAp/TAv, 5-Latent Factors Model	396	351.83 (125)	<.001	.95	.94	.068 [.059, .076]	.050
SAp/SAv 5-Latent Factors Model	396	308.1 (125)	<.001	.96	.95	.061 [.052, .069]	.049
OAp/OAv 5-Latent Factors Model	396	534.6 (125)	<.001	.92	.9	.091 [.083, .099]	.061
Approach goal model	396	1041.7 (129)	<.001	.82	.79	.134 [.126, .141]	.103
Avoidance goal model	396	1095.72 (129)	<.001	.81	.77	.138 [.13, .145]	.103
Definition model	396	102.13 (134)	<.001	.82	.8	.129 [.122, .137]	.075
Valence model	396	1781.19 (134)	<.001	.68	.63	.176 [.169, .184]	.122
Male	205	161.24 (120)	.007	.98	.98	.041 [.022, .056]	.05
Female	191	246.73 (120)	<.001	.95	.94	.074 [.061, .088]	.051
High-performance athletes (HP)	210	189.84 (120)	<.001	.97	.96	.053 [.038, .066]	.053
Recreational athletes (R)	186	213.93 (120)	<.001	.96	.95	.065 [.051, .079]	.05
Individual game	215	173.75 (120)	<.001	.97	.97	.046 [.030, .060]	.044
Team game	181	198.01 (120)	<.001	.97	.96	.060 [.045, .075]	.063

Note. TAp = task-approach; TAv = task-avoidance; SAp = self-approach; SAv = self-avoidance;
OAp = other-approach; OAv = other-avoidance; CFI = Comparative Fit Index; TLI = Tucker– Lewis Fit Index; RMSEA = Root Mean Square Error of Approximation; SRMR = Standardized Root Mean Square Residual

Analysis of invariance in measurement

The findings of an invariance analysis conducted on the Polish adaptation of the AGQ-Sports questionnaire are presented in Table 3. The hypothesised models performed well in analyses grouped by gender, level of sport participation, and types of sport. Given that no instances of the aforementioned scenario (i.e., a decrease in CFI exceeding .01 and an increase in RMSEA exceeding .015) were observed in any instance, it can be concluded that the Polish version of the AGQ-Sports can be considered a universally valid and reliable instrument, irrespective of the participant's sports level, type of sport or gender.

Table 3. Measurement invariance of the AGQ-Sports by gender and level of participation

	CFI	RMSEA	SRMR	ΔCFI	ΔRMSEA	ΔSRMR
Gender (males vs females)
Configural	.993	.030	.042	-	-	-
Metric	.993	.030	.046	0	0	.004
Scalar	.993	.029	.046	0	–.001	0
Strict	.993	.028	.048	0	–.001	.002
Level of sports participation (High Performance vs Recreational)
Configural	.993	.031	.042	-	-	-
Metric	.993	.029	.044	.001	–.002	.002
Scalar	.992	.030	.046	–.001	.001	.001
Strict	.991	.031	.050	–.001	.001	.004
Types of sports (Individual and Team Sports)
Configural	.992	.032	.043	-	-	-
Metric	.991	.034	.049	–.002	.002	.006
Scalar	.991	.034	.050	0	0	.001
Strict	.990	.033	.053	0	–.001	.003

Note. CFI = Comparative Fit Index; TLI = Tucker–Lewis Fit Index; RMSEA = Root Mean Square Error of Approximation; SRMR = Standardized Root Mean Square Residual

Relationship between 3x2 achievement goals, goal orientation, and state and trait anxiety among athletes

The analysis in Table 4 reveals significant associations among the 3x2 achievement goal, goal orientation, and anxiety levels. Notably, moderate positive correlations were observed between other-approach goals (3x2 AGQ-Sports) and ego orientation (TEOSQ). There is a moderate positive correlation between task-approach, task-avoidance, self-approach, and self-avoidance goals (3x2 AGQ-Sports) and task orientation (TEOSQ), with task-approach and self-approach goals showing stronger correlations. Regarding anxiety and athletes’ 3x2 achievement goals, state anxiety (STAI) exhibits a weak positive correlation with other-approach goals (3x2 AGQ-Sports), while trait anxiety (STAI) demonstrates a weak negative correlation with task-approach goals (3x2 AGQ-Sports).

Table 4. Correlations between 3x2 achievement goals, athletes’ goal orientation, and state and trait anxiety

3x2 AGQ-S (N = 246)	TEOSQ-Ego orientation	TEOSQ-Task orientation	STAI-S (Form X-1)	STAI-T (Form X-2)
TAp.2***.56***–.028–.15*
TAv	.24***	.52***	–.021	–.078
SAp	.27***	.57***	–.010	–.058
SAv	.25***	.48***	–.046	–.046
OAp	.55***	.29***	.17**	–.112
OAv	.33***	.07	.14*	.061

Note. TAp = task-approach; TAv = task-avoidance; SAp = self-approach; SAv = self-avoidance; OAp = other-approach; OAv = other-avoidance; * p < .05, ** p < .01, *** p < .001

Mann-Whitney U test between achievement goals and other variables

Level of sports participation (High-Performance vs Recreational athletes) did not have any significant effect on any achievement goal orientations, except other approach goal orientation (see Table 5). By comparing the means of other approach goals of high-performance and recreational athletes, it shows that high-performance athletes (M=14.8) have higher value of mean than recreational athletes (M=12.58).

Table 5. Mann-Whitney test between achievement goals and level of sports participation

	LOP
3x2 AGQ-S (N = 396)	Z	p	Effect size
TAp	–1.247	.212	–.063
TAv	–.45	.653	–.023
SAp	–.696	.486	–.035
SAv	–.965	.335	–.048
OAp	–4.213	<.001	–.212
OAv	–1.76	.095	–.084

Note. TAp = task-approach; TAv = task-avoidance; SAp = self-approach; SAv = self-avoidance; OAp = other-approach; OAv = other-avoidance; * p < .05, ** p < .01, *** p < .001

Discussion

Achievement Goal Questionnaire-Sports (AGQ-S) is a reliable and valid scale for Polish athletes. Additionally, we investigate the associations between the 3x2 achievement goals, anxiety and goal orientation. The hypothesised six-factor model was the best fit among all measurement models (see Table 2), exhibiting strong fit indices with CFI exceeding .95, TLI exceeding .95, and RMSEA below .08. These results align with previous literature findings (Elliot et al., 2011; Diseth, 2015; Mascret et al., 2015; Lower, Turner, 2016; Wang et al., 2017; Picoli et al., 2022). The 6-factor model of the Polish calculated on the whole scale, showed a better fit to the data compared to the Chinese (Wang et al., 2017) and Brazilian results (Picoli et al., 2022). Similar to the French analysis (Mascret et al., 2015), the six-factor model exhibits a strong fit with the Polish data, both in the overall sample and in distinct subgroups: gender and sports activity level. All items exhibit factor loading values greater than or equal to .50 (see results 3.1), i.e., their values are acceptable (Ghozali, 2017; Hair et al., 2019). The AVE values are also satisfactory (see Table 1). The convergent validity is proved with high composite reliability values for TAp, TAv, SAp, SAv, OAp, and OAv (see Table 1). Discriminant validity of all subscales is met since AVE is greater than its MSV. Hence, the internal consistency reliability of the six Polish AGQ-Sports subscales is satisfactory.

Result show the overall value of Cronbach’s alpha for the instrument is .93, and for the subscales .83-.91. The values are better than the Chinese version (Wang et. al., 2017) and comparable to the results of French analysis (Mascret et. al., 2015). The test-retest reliability (ICC= .80-.97) was satisfactory.

Furthermore, the study revealed that the measurement was unaffected by varying degrees of sports engagement (i.e., high performance athletes, recreational athletes), gender (i.e., male and female), and by types of sport (i.e., individual and team sports). Four basic types of measurement invariance were incorporated: configural, metric, scalar, and strict (see Table 3). The analysis proved measurement invariance among high-performance and recreational male and female athletes involved in any type of sport in the Polish version of AGQ-Sports. These results are consistent with earlier studies demonstrating measurement invariance across gender (Wang et al., 2017; Picoli et al., 2022), type of sport (Wang et al., 2017) and level of sports engagement (Tomczak et al., 2024).

Following the approach of Elliot et al. (2011), a series of ten alternative models were tested to compare their fit with the hypothesized model. The alternative models included a 2×2 model, where other-based goals loaded on their specific latent factors, while same-valenced task-based and self-based goals loaded together on combined latent factors. The Trichotomous model allowed other-approach and other-avoidance goals to load on their respective latent factors, with task-based and self-based goals combined on a single latent factor. In the Dichotomous model, all other-based goals loaded together on one latent factor, while task-based and self-based goals loaded on another.

Additional models included the Tap/Tav (task-approach/task-avoidance) model, where all items loaded on their hypothesized factors except task-approach and task-avoidance items, which loaded on a combined factor, and the Sap/Sav (self-approach/self-avoidance) model, where self-approach and self-avoidance items loaded together on a single latent factor. Similarly, the Oap/Oav (other-approach/other-avoidance) model combined other-approach and other-avoidance items on one factor. The Approach model grouped all approach-based items together on a combined latent factor, while avoidance items retained their hypothesized loadings; conversely, the Avoidance model grouped all avoidance-based items on one factor while retaining hypothesized loadings for approach items. The Definition model grouped items based on shared competence definitions, and the Valence model combined items with shared valence on joint latent factors. As shown in Table 2, the comparisons revealed that the hypothesized model offered a better fit to the data than any of the alternative models, supporting its robustness and validity in capturing the intended constructs.

The correlation between the 3x2 achievement goals, task and ego orientations, and state and trait anxiety were explored (See Table 4). The results show task-based and self -based goals have moderately positive correlations with task orientation while other-based goals have moderately positive correlation with ego orientation which is theoretically accurate and inline with the literature. However, no relevant conclusions can be made by correlating the 3x2 achievement goals and state or trait anxiety, suggesting that heightened physical activity may mitigate anxiety symptoms, as supported by previous research (Biddle, Asare, 2011; Rebar et al., 2015). Notably, only other-approach achievement goal displayed a weak positive correlation with state anxiety, indicating anxiety related to the desire to outperform others (Ntoumanis, Biddle, 1998). Additionally, there was no significant correlation between achievement goals and trait anxiety, except for task-approach achievement goal, which displayed a weak negative correlation. This aligns with existing literature where the task-approach goal serves as a negative predictor of trait anxiety (Thomas, 2021).

The analysis on the differences between achievement goals and other variables such as level of sports participation. Level of sports participation (high performance athletes, recreational athletes) reveals a significant difference solely in other approach orientation (OAp). High performance athletes demonstrate higher levels of other approach orientation (OAp) compared to recreational athletes. Despite inconsistent findings in previous studies, our results align with research by Yperen, Renekema (2008) and Lachman (2014), which reported higher performance-approach goals among high-performing athletes.

This study has several limitations; first, it evaluates the relationship between 3x2 achievement goals and only two other relevant variables. In future studies, the number of variables should be increased in order to better understand and influence the achievement motivation of athletes. Second limitation is the small sample size which restricts robust analysis when breaking down into smaller samples. Lastly, it is worth continuing the research on different age groups and career levels of the sports players (regional to international and world class groups) which can yield better results.

Conclusion

Intercultural validation studies, although they do not introduce new categories, are important. In international cooperation, they shall ensure the sameness of measured indicators, and implemented solutions. In practice, with multicultural teams, they give practitioners good tools for their daily work with athletes. Our work facilitates a better understanding of achievement motivation in the sports domain. This study successfully established the high factorial validity and reliability of the Polish version of the 3x2 achievement goal questionnaire in the sports domain. The 3x2 achievement goals correlated with state or trait anxiety and goal orientation, which are essential variables in achievement motivation literature. Goal orientation’s relationship with the 3x2 achievement goals shows a clear distinction where task orientation is correlated with task-based and self-based goals, and the ego orientation is correlated with other-based goals. In anxiety, weak correlations between the 3x2 achievement goals and state or trait anxiety, suggest that heightened physical activity may mitigate anxiety symptoms. High-performance athletes had higher other approach goal orientation (OAp) than recreational athletes which is inline with the previous researches. Although these issues are significant, they require additional investigation and research. Nevertheless scale is suitable for planning and controlling interventions in the field of changes related to the achievement of goals in Polish athletes.

Translated by Authors

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