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Propósitos y Representaciones

versión impresa ISSN 2307-7999versión On-line ISSN 2310-4635

Propós. represent. vol.10 no.2 Lima may./ago. 2022  Epub 31-Ago-2022 

Research articles

Academic Self-Efficacy : Analysis of Internal Structure and Invariance in High School Students from Lima Metropolitana

Erick Chávez Flores1  *

1Universidad Privada del Norte, Lima, Perú


The objective of the research study was to evaluate the confirmatory factorial structure and the invariance of the measurement according to gender of the scale of perceived self-efficacy specific to academic situations (EAPESA) in high school students of a private educational institution in Metropolitan Lima. A total of 291 high school students participated in the study, made up of 127 women and 164 men with an age range from 12 to 16 years (M=14.010, SD= 1.317). The research developed an instrumental design. A confirmatory factorial structure composed of a single factor (discarding item nine) with adequate adjustment indices (CFI= 0.99, TLI= 0.99, RMSEA= 0.07 IC 90% [0.05-0.09], SMR= 0.03) was evidenced. Likewise, the invariance of the measurement according to sex in high school students was demonstrated (ΔCFI < 0.01 and ΔRMSEA < 0.015). In addition, the values ​​of the internal consistency coefficients were acceptable (α= 0.907 and ω= 0.908). Consequently, the EAPESA presented adequate psychometric properties for use in the field of educational psychology and in the field of research.

Keywords: Self-efficacy; Reliability; Invariance; Educational psychology


Cognitive social theory addresses perceived self-efficacy as a belief that a person adopts to achieve an objective based on their perseverance or motivation (Bandura, 2005). Likewise, people value their abilities in order to be able to carry out their activities (Schunk, 2012). Self-confidence is considered relevant (Rodríguez-Rey and Cantero-García, 2020) and the person's behavior and performance are emphasized (Gunawan et al., 2019). Consequently, the study of self-efficacy in the field of education is important for the development of learning and school performance. Therefore, academic self-efficacy refers to the student's self-assessment with the aim of attaining academic achievement (Robles, 2020) with an outstanding motivation for learning (Yokoyama, 2019). Self-efficacy is important, psychologically, to cope with academic environments.

In Latin America and the Caribbean, various countries as a result of COVID-19 ceased face-to-face classes in schools, colleges and universities, but in turn adopted some measures to not interrupt the educational service by offering distance education to a greater extent (Economic Commission for Latin America and the Caribbean , 2020). Meanwhile, regular basic education in Peru has undergone great changes towards the adoption of virtual education. In this regard, there is a digital gap between urban and rural areas, as well as a limitation in Internet coverage and its infrastructure (Mateus & Suárez-Guerrero, 2017). Likewise, according to Garcia (2020), the pandemic has generated detrimental impacts, one of them being the worsening of mental health of children and adolescents, causing stress or anxiety in some cases. The change from face-to-face education to virtual education in such a short period of time generated several difficulties of adaptation and an overload of tasks (López-Aguilar & Álvarez-Pérez, 2021). For this reason, expectations of self-efficacy are considered as an effective component in stressful situations and other factors that affect the person (Cabanach et al., 2010; Freire & Ferradás, 2020).

The impact of virtual education has caused the use of multiple digital platforms that provide interaction with students to enhance their learning objectives (Crisol-Moya et al., 2020). In the virtual educational context, the participation of the student in learning acquisition is very important. Therefore, trust in their abilities is vital in order to have a high level of motivation in learning that leads them to have success in the field of education (Galleguillos-Herrera & Olmedo-Moreno, 2019), aligned with the learning objectives (Ramudo et al., 2017), and to develop high values of academic performance (Yokoyama, 2019). Therefore, academic self-efficacy is fundamental to achieve a significant evolution from school to university, being able to adapt to new learning contexts (Van Rooij et al., 2017). It also provides relevant knowledge regarding motivation, attitude and subsequent preferences (Pajares & Schunk, 2001).

Palenzuela (1983) studied academic self-efficacy from the construction of the Perceived Self-efficacy Scale Specific to Academic Situations (EAPESA by its Spanish initials) for high school and university students. The scale was composed of 10 items with a single factor exploratory factor structure and with adequate reliability (α = 0.91). In this context, several international studies aimed at adolescents are presented, such as the research conducted by García-Fernández et al. (2010) that validated EAPESA in adolescents aged 12 to 16, through the analysis of main components, evidencing a one-dimensional factor structure. Likewise, García et al. (2016) performed a psychometric analysis in schoolchildren in Chile, and adequate values were obtained. Similarly, Navarro-Loli and Dominguez-Lara (2019) showed acceptable rates in a sample of high school students.

Likewise, studies aimed at university students are presented, as in the Del Valle et al. (2018) research, which showed acceptable indices, resulting in a one-dimensional model with re-specified indices. Dominguez et al. (2012) considered a psychometric analysis in Peruvian university students, establishing an exploratory structure. Likewise, Dominguez (2014) analyzed the factor structure with adequate indicators, validating a one-dimensional model. Finally, Moreta-Herrera et al. (2021) carried out their research with a sample of Ecuadorian university students, and proved a single structure and an acceptable omega coefficient.

Research turns out to be important in knowing the importance of academic self-efficacy in high school students to address their tasks and/or activities at school, thereby helping them cope with stressful situations derived from the burden of academic activities. Teachers, pedagogical specialists or psychologists are the most competent professionals to identify those students who present a problem with their academic or motivational achievement. Therefore, they can exercise programs or accompanying sessions that facilitate their permanence in the educational system, avoiding suspension in their studies. Return to face-to-face education seeks to reduce the digital divide and encourages interaction and visualizes some factors that could influence students' school performance. For this reason, teachers must strengthen and optimize students' skills to guarantee their educational achievement. The objective of the research was to evaluate the confirmatory factor structure (CFA) and the invariance of the measurement of the perceived self-efficacy scale specific to academic situations (EAPESA) in high school students from a particular educational institution in Metropolitan Lima.



The study employed an instrumental design because the psychometric properties of a scale will be considered (Ato et al., 2013; Montero & León, 2007). A non-probability convenience sampling was applied (Otzen and Manterola, 2017) and their inclusion criteria were to be currently enrolled high school students (from first to fifth grade).


The participation of 291 students from the first to the fifth grade of high school from a private educational institution in Metropolitan Lima, aged from 12 to (M= 14.01, SD= 1,317), was considered. This sample consisted of 127 women (43.64%) and 164 men (56.36%).


Palenzuela (1983) created the EAPESA to measure expectations of self-efficacy in a sample of adolescents and university students. This scale is made up of 10 items and describes four response options using the Likert type measurement scale (never= 0, sometimes= 1, quite a few times= 2 and always= 3), being the structure of this instrument one-dimensional. For this research study, the scale validated by Dominguez et al. (2012) was used for the Peruvian context, taking into consideration only nine items of the original version (deleting item 9), resulting in a single-factor structure with an explained variance of 56.261%. In addition, it reported indicators with a good fit χ2 = 64.687 (p<0.01), CFI= 0.978, GFI= 0.969, RMSEA= 0.056 and RMR= 0.029. In the case of reliability, the instrument was considered acceptable (α = 0.881).


We proceeded to collect the data online using Google Forms with an approximate response time of students ranging from 10 to 15 minutes. Parents' consent was obtained and the research is based on the ethical principles of the university researcher. Likewise, the students were told that their participation is anonymous, maintaining the confidentiality of their data, and voluntary, informing them about the objective of the research and the explanation of the scale to respond. Subsequently, the data were processed in the JASP program version to carry out the procedures of the descriptive statistics and internal consistency coefficients. Finally, evidence of the internal structure such as confirmatory factor analysis (CFA) and also the invariance of the EAPESA measurement was carried out using the R program version 4.1.0.

Data Analysis

First of all, a descriptive process of EAPESA items that comprises the values of the mean, standard deviation, asymmetry and kurtosis was conducted. And with respect to the last two descriptive measures, the range of ± 1.5 will be considered to verify the univariate normality using JASP program version Secondly, the multivariate normality analysis was evaluated by means of the Mardia test; and then the CFA was performed using the R program version 4.1.0, using the estimation of robust weighted least squares (WLMSV). Likewise, the Chi-square statistic (χ2) and the normalized chi-square ratio (χ2/gl) were estimated with a value less than three (Hair et al., 1999; Kline, 2016) and in addition to the global goodness of fit indices: comparative fit index (CFI) ≥ 0.95, mean quadratic standardized residual root (SRMR) ≤ 0.05, mean quadratic error of approximation (RMSEA) ≤ 0.05 to 0.08, Tucker-Lewis index (TLI) ≥ 0.95, for the overall evaluation of the theoretical model (Kline, 2016; Schumacker & Lomax, 2016).In addition, measurement invariance for multiple groups was calculated using the procedures of configural, metric (or weak), scalar (or strong), and strict (or residual) invariance to verify invariance on the validated model (Brown, 2015) with values of ΔCFI ≤0.01 and ΔRSEAM ≤0.015 (Chen, 2007; Cheung & Rensvold, 2002). Finally, internal consistency was determined by means of the JASP program version, estimating the McDonald's (ω) and Cronbach's (α) omega coefficients with acceptable values from the value of 0.70 for both coefficients (Campo-Arias & Oviedo, 2008; Ventura-León & Caycho-Rodríguez, 2017).


Descriptive Analysis of Items

Table 1 shows the descriptive measures for each of the EAPESA items. Item seven presented a higher average (M= 2,162) and item nine presented a lower average (M= 1,031). Regarding variability, item five presented greater variability (SD= 0.871) and item one presented less variability (SD= 0.728). Regarding the values of asymmetry and kurtosis, both univariate statistics are within the range ± 1.5 (Ferrando & Anguiniano-Carrasco, 2010; George & Mallery, 2003).

Table 1 Descriptive statistics of EAPESA items (n=291) 

Note. M= mean; SD= standard deviation.

Internal Structure Evidence

The ACFA of EAPESA was performed, initially the Mardia test was performed with the MVN package (Multivariate Normality Tests) of the R program (Korkmaz et al., 2014), demonstrating a multivariate non-normality (p< 0.05) with respect to asymmetry and multivariate kurtosis. Therefore, the robust weighted least squares estimation method (WLSMV) was used. In addition, the response options are measured on a Likert scale (Lloret-Segura et al., 2014; Li, 2016). For the CFA, a first model was evaluated with the 10 original items of the EAPESA instrument, and it was observed that item nine showed a low factor load (< 0.50) and a single factor structure. Then, a second model was evaluated with nine items, excluding item nine, and acceptable factor loads (0.50) were obtained in its one-dimensional structure. Table 2 shows the values of the goodness of fit of the CFA. In this regard, the second model yielded a statistic valueχ2(gl)= 66.53(27) and adequate goodness of fit indices (CFI= 0.99, TLI= 0.99, RMSEA= 0.07 and SRMR= 0.03). However, the value ofχ2/gl = 2.46 is considered acceptable but should not be considered as it lacks statistical support (Kline, 2016). The evaluation of the other goodness fit indices is prioritized (Abad et al., 2011, Brown, 2015). The one-dimensional structure is validated by the values shown as a whole (Schumacker & Lomax, 2016)

Table 2 EAPESA Goodness of Fit Indexes (n=291) 

Note. χ2 = Chi square; gl=degrees of freedom; CFI= Comparative fit index; TLI= Tucker-Lewis index; RMSEA= Mean quadratic error of approximation; SRMR= Standardized root mean square residual; CI= confidence intervals

Figure 1 shows that the factor loads of the second EAPESA model vary from 0.67 to 0.86, with significant loads (λ > 0.5) (Hair et al., 1999).

Figure 1 CFA path diagrams of EAPESA for model 2 

Measurement invariance by gender

In Table 3, the second model was evaluated by making the comparison according to gender. Consequently, the configural invariance that yielded adequate indices (CFI= 0.97, RMSEA= 0.05, SRMR= 0.04) was used. Also, the metric invariance showed significant values (CFI= 0.97, RMSEA= 0.05, SRMR= 0.05). Likewise, the strong invariance was tested (CFI= 0.97, RMSEA= 0.04, SRMR=0.05) and finally, the strict invariance showed acceptable indices (CFI= 0.96, RMSEA= 0.05, SRMR= 0.06). Likewise, ΔCFI ≤ 0.01 and ΔRMSEA≤ 0.015 provide values that verify the invariance of EAPESA measurement according to gender (Chen, 2007; Cheung & Rensvold, 2002).

Table 3 EAPESA measurement invariance by gender 

Note. χ2=Chi square; gl=degrees of freedom; CFI= Comparative fit index; RMSEA= Mean quadratic error of approximation; SRMR= Standardized root mean squared residual

Internal Consistency

Values for Cronbach's alpha (α = 0.907) and McDonald's Omega (ω = 0.908) coefficients acceptable for the second one-dimensional characteristic model were obtained.


The objective of this research study was to evaluate the confirmatory factor structure and invariance of EAPESA measurement in high school students in Metropolitan Lima.

The analysis of the evidence of internal structure through the EAPESA CFA validated its one-dimensional structure according to the studies carried out by Palenzuela (1983), García et al. (2016) and Navarro-Loli and Domínguez-Lara (2019) for samples in adolescents. These last two research studies maintained the 10 items of the original version and the last research study excluded three items for the final model, respectively. In addition, only the research conducted by Navarro-Loli and Domínguez-Lara (2019) used the WLSMV estimation in the same way with the present research. Likewise, various studies (Del Valle et al., 2018; Dominguez et al., 2012; Dominguez, 2014; Moreta-Herrera et al., 2021) also demonstrated a single-factor structure, but in samples of university students.

The reliability analysis reported acceptable values (α = 0.907 and ω = 0.908). This finding is similar to the study conducted by Navarro-Loli and Dominguez-Lara (2019) with adequate values of α= 0.866 and ω= 0.901, unlike the studies of Palenzuela (1983), García-Fernández et al. (2010) and García et al. (2016) that showed only the Cronbach's alpha coefficient (α > 0.8) and the study conducted by Moreta-Herrera et al. (2021) that showed only the Omega reliability coefficient (ω = 0.91), which was appropriate.

Regarding the findings, the invariance of the EAPESA measurement in high school students according to gender was verified. Concordance in its internal structure was verified for both men and women in the nested configural, metric, strong and strict models, evidencing the inexistence of bias in both groups.

Some limitations for the development of the research study include the number of high school students, and its expansion is recommended for future research. Likewise, the data collection procedure through a digital platform reduces the participation of students in responding to the scale online. Likewise, non-probability sampling was used and it restricts the extension of the results. Another limitation is the scarcity of research studies on samples of high school students for comparison with the internal structure and measurement invariance findings of this study. Consequently, expanding the sample size and opting for face-to-face data collection are advisable, since this will reduce bias when students respond to the instrument.


In conclusion, academic self-efficacy is a relevant factor in student development during their educational stage. The adequate psychometric property of EAPESA is shown to be reliable for application and relevant for its use in further research studies related to the field of educational psychology that help to know the perspectives of academic self-efficacy in high school students to execute strategies that consolidate their school success


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Received: April 25, 2021; Accepted: August 15, 2022; pub: August 31, 2022


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