• 1. Estimate the pooled effect size of inquiry-based learning (IBL) on students’ critical thinking skills.

• 2. Investigate whether the effectiveness of IBL is moderated by study characteristics, including control group variations, country, education level, and subject area.

H01: Inquiry based learning has no positive and significant effect on students’ critical thinking.

Ha1: Inquiry based learning has a positive and significant effect on students’ critical thinking.

H02a: The effectiveness of inquiry based learning on students’ critical thinking is not moderated by control group variations.

H02b: The effectiveness of inquiry based learning on students’ critical thinking is not moderated by subject domain.

H02c: The effectiveness of inquiry based learning on students’ critical thinking is not moderated by education level.

H02d: The effectiveness of inquiry based learning on students’ critical thinking is not moderated by country of study.

Ha2a: The effectiveness of inquiry based learning on students’ critical thinking is moderated by control group variations..

Ha2b: The effectiveness of inquiry based learning on students’ critical thinking is moderated by subject domain.

Ha2c: The effectiveness of inquiry based learning on students’ critical thinking is moderated by education level.

Ha2d: The effectiveness of inquiry based learning on students’ critical thinking is moderated by country of study.

The research approach used in this study was a quantitative method integrated with meta-analysis. This method was chosen because it aligns with the objective of this research, which is to analyze the effect size of Inquiry-Based Learning (IBL) on students’ critical thinking skills. The PRISMA protocol was applied in the literature search to ensure the transparency and credibility of this meta-analysis.²⁸

Random effects were applied as the model effect size in this meta-analysis. Since all studies included in this meta-analysis employed experimental designs with contrast groups, the effect size can be estimated using Standardized Mean Difference (SMD). SMD is estimated by dividing the difference between the means in the contrast groups by the pooled standard deviation.²⁹ Furthermore, all studies included in this meta-analysis had different scales. Therefore, SMD was applied to equate the different scales or units of all studies included.^30,31

Among the 57 studies analyzed in this study, ten studies did not report the standard deviation for either the experimental group or the control group. These missing data can be addressed by contacting the writer or checking the attachment of the studies.³² The researcher had emailed them, but there was no response until the data analysis stage. The alternative solution taken was to calculate the pooled standard deviation using the available statistical data in the study such as t-test, z-value, and Mean Squared Error.^29,33

In this meta-analysis, the metafor package, developed by (Viechtbauer, 2010), in the R program (2025.09.1 + 401) was used to estimate the individual effect size and its variance, as well as the standard deviation error. Whereas, JASP (0.96.0.0) was used to analyze the pooled effect, subgroup, sensitivity and publication bias, and produce the forest and funnel plot. The analysis was conducted using the restricted maximum likelihood (REML) estimator, with the Knapp–Hartung (KNHA) adjustment to enhance the precision of standard errors and confidence intervals. The effect size of the studies is then interpreted based on the criteria presented in Table 1 below.

Since Cohen’s d tends to provide a biased population effect size for small samples,³⁴ Hedges’ g was employed due to its bias-correction factor.²⁹ Moreover, Hedges’ g provides a more accurate estimate of how much the IBL approach affects students’ critical thinking skills compared to the other methods.¹⁹

Heterogeneity of the studies was assessed by Cochran’s Q statistic. However, it has limited power to detect true heterogeneity when the number of included studies is small and tends to overestimate when the number of studies is large.³² Therefore, the I² statistic is recommended because it is less dependent on the number of studies and offers a clearer and intuitive interpretation of heterogeneity.^32–35 The tentative categorization values of I² according to Higgins et al. (2003) are 25% (low), 50% (moderate), and 75% (high).

This study began with a systematic collection of relevant literature as data sources through SCOPUS, ERIC, and DOAJ databases. This was done from November 2025 to January 2026.

SCOPUS was selected because it provides credible and high-quality articles. ERIC is one of the most prominent databases for meta-analysis because it provides a wide range of literature in the fields of social and educational sciences,^36,37 whereas DOAJ was considered because it provides full access to high-quality literature.

The literature search was done using the keywords combined with Boolean Operators (AND, OR) to ensure comprehensive coverage of relevant literature as well as enhance search precision.^34,38 The literature search was conducted using the following keywords for each database, as shown by Table 2.

Articles identified from the three databases were screened using database-specific filters. In Scopus, the search was limited to journal articles published within the last ten years, final publication stage, journal article, and English language. In ERIC, the search was limited to peer-reviewed journal articles published within the last 20 years because the database did not provide a “last 10 years” filter option. In DOAJ, the search was limited by publication year within the last ten years. The remaining records are presented in the PRISMA diagram. Metadata from each database were imported into Zotero in RIS format to remove duplicate records and screen article titles and abstracts. Duplicate records may occur because the same article can be indexed in more than one database.

The remaining articles were screened based on the inclusion and exclusion criteria presented in Table 3.

Based on Figure 1, ten studies were excluded because their subjects were focused on teachers. Although the Scopus search was restricted to English-language articles, nine Indonesian-language articles were identified from other databases, particularly DOAJ, which indexes articles in various languages.

A total of 74 studies proceeded to the full-text retrieval stage. At this stage, only open-access and downloadable articles were considered. The downloadable articles were read thoroughly to determine the sufficient amount of substantial data. The eligible articles were then extracted into the coding table.

A total of 51 independent studies were included, yielding 57 study entries. The number of study entries exceeded the number of independent studies because Lue et al (2020)³⁹ reported four statistical datasets, whereas Prayogi et al (2024),⁴⁰ Dewi et al (2021),⁴¹ and Duran & Dokme (2016)⁴² each reported two effect sizes.

Data coding

The substantial data, extracted from post-test data of both experimental and control groups of each study,⁴³ were tabulated into the coding table, which consists of the number of samples, mean, and standard deviation of experimental and control groups.^21,36 In addition, moderator variables such as control group variations, subject area, country and education level were also coded.²⁹ The coding procedures were conducted by two coders to ensure their accuracy and reliability.⁴⁴

The first coder (AH) and the second coder (TSK) independently exctracted all of included studies. The discrepancies were resolved through discussion until consensus was reached. Cohen’s kappa was used to assess inter-coder reliability because the coded variables in this meta-analysis were categorical.⁴⁵

Risk of bias assessment (RoB)

Risk of bias was assessed independently by two reviewers for all included studies using the revised JBI Critical Appraisal Checklist for Quasi-Experimental Studies developed by Baker et al (2024).⁴⁶ This tool was selected because most of the included studies employed quasi-experimental designs. This tool evaluates internal validity (eight items) and statistical conclusion validity (one item). Based on these domains, each study was classified as having a low, moderate, or high risk of bias. Since Baker et al (2024) did not specify explicit criteria for these overall risk categories, we used RoB criteria by Krasny-Pacini et al (2014)⁴⁷ as presented by Table 4. For each included study, each risk-of-bias (RoB) item was rated as “Yes” or “No” and coded as 1 or 0, respectively. An internal validity score was calculated by dividing the sum of all item scores by the total number of RoB items. The resulting score was interpreted according to the criteria presented in Table 4.

Cohen’s kappa was calculated from the initial independent ratings of the two reviewers before consensus discussion.

Coding data

Inter-rater reliability was assessed using Cohen’s kappa for each categorical coding variable. According to the criteria proposed by Landis & Koch (1977),⁴⁵ the results indicated almost perfect agreement between the two coders for subject domain, κ = 0.855, country, κ = 0.856, education level, κ = 0.881, and control group variatons, κ = 0.861. The overall Cohen’s kappa was 0.896, also indicating almost perfect agreement. These findings suggest that the coding procedure was consistent between coders before disagreements were resolved through discussion.

Risk of bias assessment (RoB)

Based on Landis & Koch (1977)‘s criteria,⁴⁵ the resulting Cohen’s kappa coefficient of 0.73 is classified as substantial agreement between the reviewers. Overall, most included studies were classified as low risk. Of the 51 studies assessed, 46 were rated as low risk and 5 were rated as moderate risk. No study was classified as high risk. The studies rated as moderate risk were Maharani et al (2023),⁴⁸ Subagiyo et al (2023),¹⁷ Chususiyah et al (2020),⁴⁹ Nurza et al (2021),⁵⁰ and Wiwik et al (2025).⁵¹ At the effect-size level, 52 of the 57 effect sizes were derived from low-risk studies, while 5 were derived from moderate-risk studies. Overall, these findings indicate that most included studies had adequate methodological quality for meta-analysis, as the majority were classified as low risk and no study was rated as high risk.

The characteristic of each study is presented in Table 5. Overall, the studies involved a total of 3.628 students consisting of 907 elementary school students, 545 junior high school students, 1.205 senior high school students, and 971 higher education students. Based on the group, there were 1.818 students in the experimental group and 1.810 students in the control group.

Figure 2 represents the forest plot that encompasses the substantial statistics data analyzed in this meta-analysis, such as individual effect size along with its study weight and confidence interval (CI), summary effect size, and statistics heterogeneity. It is shown that the summary effect size estimated using a random-effects model is 1,336 with a p-value <0,001. Based on Hedge’s g criteria, this value indicates that IBL has a large and significant effect on students’ critical thinking (CT).

The forest plot also demonstrates that all studies included in this meta-analysis have positive and statistically significant pooled effects, as indicated by confidence intervals (CI) 95% ranged from 1.061 to 1.611 that do not cross the line of zero.^19,52 However, study by Putra et al (2018),⁵³ Poerwanti et al (2022),⁵⁴ Ismail & Isroktum (2025),⁵⁵ Farah et al (2020),⁵⁶ Carracedo (2025),⁵⁷ Arsal (2017)¹⁴ and Lu et al. (2020a)³⁹ show insignificant effect, as indicated by the CI that crosses the zero line.

The summary effect size is based on weighted individual effect sizes of the whole studies, with effect sizes from larger samples weighted more than the effect sizes from smaller samples.⁵² A study by Wulandari et al. (2022)⁵⁸ has the largest contribution to the summary effect size, indicated by the highest study weight of 1.87%. Conversely, the study by Farah and Ayoubi (2020)⁵⁶ gives the lowest contribution indicated by the lowest study weight (1.57%).

The heterogeneity analysis indicated substantial variability among the included studies.^19,34 This was shown by Cochran’s Q and I² tests. Cochran’s Q test shows statistically significant heterogeneity Q (56) = 560.00, p < 0.001. It means that the observed variability in effect sizes cannot be explained solely by sampling error.³⁰ Similarly, the high value of the I² statistic shows that 92.09% of the total variability in effect sizes was caused by real differences between studies rather than random variation. Collectively, these statistics consistently indicate substantial heterogeneity and the subsequent exploration of potential moderator variables.⁵⁹

The findings of this meta-analysis show positive and significant summary effects of the thirty-seven studies regarding the effect of inquiry-based learning on students’ critical thinking skills, with a Hedge’s g = 1.34. Based on Cohen’s d criteria, this effect is classified as a very large effect. It means that students who engage in IBL demonstrate substantially higher critical thinking skills compared to those receiving traditional or other learning models applied in the fifty seven studies. This finding confirms that IBL can be a potential learning model in enhancing student’s critical thinking skills.

This result is larger than that of the previous meta-analysis by Arifin et al. (2025)¹⁹ (g (N = 36) = 1.27; 95% CI [0.78, 1.76]). Despite showing large and significant effects, their meta-analysis was limited only on studies conducted on natural science subjects. In contrast, our meta-analysis covered the studies in the field of natural science, mathematics, social science, and language. Therefore, with the large summary effect size, it can be inferred that IBL is not only effective in natural science learning, but also in mathematics, social science and language. Nevertheless, this meta-analysis confirms the meta-analysis by Arifin et al. (2025)¹⁹ in terms of summary effect and confidence interval. It is shown that the summary effect size of this meta-analysis is still in the range of confidence interval of pooled effect size of their meta-analysis. Therefore, the present meta-analysis is consistent with the previous meta-analysis.

The strong effect of IBL on critical thinking can be explained through its core pedagogical characteristics. Unlike traditional methods, which often emphasize the transmission of factual knowledge, inquiry based learning engages students in some activities enhancing students critical thinking, such as constructing knowledge, explaining, reasoning, questioning, and communicating with their instructor or their peers.⁶⁰ These activities are the substantial component of critical thinking. Overall, the results suggest that teachers should apply IBL in the classroom in order to enhance students’ critical thinking.

Despite a large and significant pooled effect, the individual studies included in this meta-analysis showed considerable variation in effect sizes. For instance, a study by Arsal (2017)¹⁴ shows negligible effect (g = 0.2321; 95% CI [−0.29,0.76]). In contrast, study by Chususiyah et al (2020) shows a very large effect (g = 5.18; 95% CI [3.93, 6.43]).

This finding indicates that the effectiveness of IBL on critical thinking may depend on some factors acting as the moderator variables. Thus, this meta-analysis not only analyse the overall effect size, but also detected the potential moderator variables that are responsible for the variety of effect size across the studies, including control group variations, level of education, subject, and country.

Moderator analysis was conducted to examine the sources of the heterogeneity of effect size,^52,61 that may influence the effectiveness of IBL on critical thinking in this meta-analysis. Since the moderator variables considered in this meta-analysis are categorical moderators, the subgroup analysis was applied to analyze moderator variables.⁶² Recent meta-analysis complements the methodological limitation of the previous meta-analysis by reporting the significance of the subgroup analysis. The subgroups were divided into four groups, i.e., control group variations, subject area, level of education, and country.

The studies included in this meta-analysis compared inquiry-based learning (IBL) with several types of control-group instruction, such as traditional, conventional, expository, cooperative learning, problem-based learning (PBL), project-based learning (PjBL), and communicative language teaching (CLT). Because traditional and conventional instruction are overlap conceptually, we grouped the control-group approaches into two broader categories, that is, teacher-centered learning (TCL) and student-centered learning (SCL). Based on,⁶³ traditional, conventional, and expository instruction were categorized as TCL because these approaches generally place the teacher as the main source of explanation and as the primary controller of learning content, activities, materials, and pacing. Similarly, expository instruction was also included in the TCL category because it is closely related to direct instructional guidance, where teachers explicitly present the concepts and procedures that students are expected to learn.⁶⁴

In contrast, cooperative learning, PBL, PjBL, and CLT were categorized as SCL because they provide more space for students to participate actively in the learning process. According to Goodwin, these approaches typically involve collaboration, discussion, exploration, authentic problem solving, communication, and learner engagement. In the same way, CLT engages students as communicators, negotiators, and contributors through activities such as pair/group work, discussion, role play, and problem solving.⁶⁵ IBL itself is classified as an SCL approach. Therefore, in this subgroup analysis, we examined whether the effect of IBL differed depending on whether it was compared with other SCL instructions or with TCL instructions.

The subgroup analysis showed that the type of control-group learning approach significantly moderated the effect of IBL on students’ critical thinking, Qm (1) = 5.21, p = .022. Studies comparing IBL with TCL produced a larger effect size, k = 42; g = 1.527, than studies comparing IBL with SCL, k = 15; g = 0.779.

These findings suggest that the effectiveness of IBL depends partly on the instructional approach used in the control group. IBL tends to demonstrate a greater effect when compared with teacher-centered approaches. This result aligns with the meta-analysis by Arifin et al. (2025), which found that IBL had a large effect on improving students’ critical thinking skills compared with conventional instruction. In contrast, the effect of IBL was relatively smaller when compared with other student-centered approaches. This result is supported by Wijnia et al (2024),⁶⁶ who found that student-centered, problem-driven approaches such as PBL, PjBL, and CBL had positive effects compared with teacher-centered instruction, but did not differ significantly from one another. Therefore, the smaller effect of IBL when compared with other SCL approaches may be explained by the fact that IBL and other student-centered approaches share several core characteristics, such as active participation, collaboration, problem solving, and knowledge construction.

The studies included in this meta-analysis were conducted across twelve countries. However, seven countries, namely South Africa, Iran, the United States, Malaysia, Ghana, the Philippines, and Spain, were represented by only one study each. To ensure sufficient statistical stability and to prevent the exclusion of these studies from the analysis, they were combined into a single “Other countries” subgroup. The subgroup analysis revealed no statistically significant differences between country subgroups, Qm (5) = 3.33, p = .650, indicating that the effectiveness of inquiry-based learning (IBL) on students’ critical thinking was relatively consistent across national contexts.

All country subgroups showed positive pooled effects of IBL on students’ critical thinking. The largest pooled effect was found in studies conducted in Lebanon, k = 2; g = 1.646; 95% CI [−12.77, 16.06]. Yet, the extremely wide and included zero confidence interval indicates substantial statistical imprecision. Indonesia also showed a large and statistically significant positive effect, k = 40; g = 1.429; 95% CI [1.054, 1.804], followed by Taiwan, k = 3; g = 1.250; 95% CI [0.442, 2.058]. Turkey showed a positive but imprecise effect, k = 3; g = 1.096, 95% CI [−0.834, 3.025], while China also showed a positive estimate, k = 2; g = 1.004; 95% CI [−4.013, 6.021]. Yet, with a wide confidence interval crossing zero indicates substantial statistical imprecision. The “Other countries” subgroup showed the smallest but still positive and statistically significant pooled effect, k = 7; g = 0.983; 95% CI [0.512, 1.453]. Thus, although the magnitude of the pooled estimates varied across countries, the direction of effect was consistently positive.

This finding is consistent with study by Santhosh et al (2023),⁶⁷ who found that study location did not significantly moderate the effectiveness of informal STEM project-based learning. Although Santhosh et al (2023) focused on PjBL rather than IBL, their finding remains relevant because both approaches are student-centered and involve active investigation, problem solving, collaboration, and reflection. These processes are closely related to critical thinking. Thus, the finding provides indirect support that the effectiveness of student-centered learning may depend more on fidelity of implementation than on geographical context.⁶⁸

However, this result should be interpreted cautiously because several country subgroups contained few studies and the number of studies across countries was unbalanced. According to Cuijpres et al (2021),⁶¹ subgroup analyses with small or unequal numbers of studies often have limited statistical power to detect reliable moderator effects.

The subject domains represented in the included studies varied considerably. While some studies reported broad subject domains, others focused on specific subjects, including physics, biology, chemistry, economics, history, mathematics, and psychology. Because psychology, history, and social science were each represented by only one study, retaining them as separate categories would have resulted in their exclusion from the subgroup analysis in JASP. Therefore, all subject areas were grouped into four broader subject domains, that is, natural sciences, social sciences, mathematics, and language learning to ensure adequate subgroup representation and facilitate meaningful comparisons.

The subgroup analysis showed no significant differences in the effect of IBL across subject domains, Qm (3) = 1.43; p = .698. This indicates that subject domains did not significantly moderate the effect of IBL on students’ critical thinking. One possible explanation for this result is that IBL is not designed for a specific subject domain, but can be adapted across different subject areas. This finding is consistent with meta-analysis by Antonio & Prudente (2024),⁴⁴ which found that scientific discipline did not significantly moderate the effect of inquiry-based learning on students’ higher-order thinking skills in science learning. Based on the subgroup effect size, the largest effect was found in language learning, k = 5; g = 1.939; 95% CI [−0.415, 4.294], followed by mathematics, k = 5; g = 1.471; 95% CI [0.863, 2.079], natural science learning, k = 44; g = 1.313; 95% CI [1.072, 1.553], and social science, k = 5; g = 0.901; 95% CI [−1.679, 3.481]. However, the pattern of confidence intervals suggests an important distinction. The effects in natural science learning and mathematics were more precisely estimated, whereas the estimates for language learning and social science were much less precise, as indicated by wide confidence intervals that crossed zero.

One possible explanation for this insignificant result is that IBL is not designed for a specific subject domain, but can be adapted across different subject areas. Kuhlthau (2010)⁶⁹ described inquiry as a way of learning that is increasingly used across all subject areas of the curriculum and emphasized that Guided Inquiry can support students’ learning of curriculum content across subject domains. Similarly, Pedaste et al (2015)⁷⁰ described IBL as a structured inquiry cycle consisting of orientation, conceptualization, investigation, conclusion, and discussion. Thus, when these inquiry processes are implemented appropriately, IBL may support learning across subject domains.

The subjects of the studies analyzed in this meta-analysis were distributed into four levels of education – from elementary school to higher education. The subgroup analysis indicated that IBL produced positive effects on students’ critical thinking across all education levels. The largest effect was observed at the junior high school level (k = 9, g = 1.757, 95% CI [0.728, 2.785]), followed by senior high school (k = 17, g = 1.296, 95% CI [0.868, 1.724]), higher education (k = 16, g = 1.250, 95% CI [0.721, 1.779]), and elementary school (k = 15, g = 1.244, 95% CI [0.595, 1.893]). However, the test of subgroup differences was not significant, Qm (3) = 1.11, p = .774, indicating that education grade did not significantly moderate the effect of IBL on students’ critical thinking.

A possible explanation is that IBL effectiveness may depend more on fidelity of implementation than on students’ education level. A prior meta-analysis by Furtak et al (2012)⁷¹ emphasized that IBL should be understood in terms of the cognitive features of the learning activity and the degree of guidance provided to students. Their meta-analysis also showed that teacher-led inquiry produced stronger effects than student-led inquiry, suggesting that structured guidance is central to effective IBL. Similarly, Öztürk et al (2022)⁷² found that grade level did not significantly moderate the effect of IBL on learning outcomes, while Antonio & Prudente (2024)⁴⁴ reported that IBL positively affected students’ higher-order thinking skills regardless of educational level. Thus, although the point estimates varied across education levels, these differences were not statistically meaningful, suggesting that education grade itself did not systematically explain variation in IBL effectiveness.

The substantial heterogeneity observed in this meta-analysis may be partly explained by several study-level characteristics that were not formally tested as moderators, including implementation fidelity, type of inquiry, intervention duration, and assessment instruments. Previous meta-analysis evidence supports the plausibility of these factors. For example, Antonio & Prudente (2024)⁴⁴ found that the effectiveness of inquiry-based approaches varied across inquiry levels, with open inquiry showing the largest effect size, followed by guided and structured inquiry, although the subgroup difference was not statistically significant. Lazonder & Harmsen (2016)⁶⁸ further showed that the type of guidance can moderate performance success in inquiry learning, indicating that the level and form of instructional support may influence learning outcomes.

Intervention duration may also contribute to heterogeneity. Antonio & Prudente (2024)⁴⁴ reported significant subgroup differences by implementation duration, although the pattern was not strictly linear. This suggests that longer interventions do not automatically produce stronger effects; rather, duration may interact with instructional intensity, student engagement, and implementation quality. Similarly, Lazonder & Harmsen (2016)⁶⁸ treated duration as a moderator by distinguishing single-session from multiple-session inquiry interventions.

Implementation fidelity is another plausible source of effect sizes heterogeneity. Although fidelity was not commonly coded as a formal moderator in previous IBL meta-analyses, related evidence indicates that the quality of instructional support matters. Lazonder & Harmsen (2016)⁶⁸ found positive effects of guidance in inquiry learning, while Alfieri et al (2010)⁷³ showed that enhanced discovery approaches involving feedback, scaffolding, worked examples, and elicited explanations were more effective than unassisted discovery. Therefore, differences in teachers’ adherence to inquiry procedures, scaffolding practices, questioning strategies, and support for evidence-based reasoning may partly explain variability in effect sizes.

Finally, assessment instruments may influence the magnitude of the observed effects. Arifin et al (2025)¹⁹ included evaluation as a subgroup variable in a meta-analysis of IBL and critical thinking, while broader meta-analyses on critical thinking have treated instruments or measuring tools as potential moderators. Researcher-developed or curriculum-aligned assessments may be more sensitive to the intervention content and therefore yield larger effects, whereas standardized critical-thinking instruments may provide more conservative estimates. Taken together, these findings suggest that the remaining heterogeneity in the present meta-analysis should be interpreted as reflecting meaningful differences in how inquiry-based learning was implemented, structured, sustained, and assessed across studies.

Sensitivity analysis was conducted using standardized residual diagnostics and leave-one-out influence diagnostics to assess whether the pooled effect was robust to outlying and influential studies. Following Viechtbauer & Cheung (2010),⁷⁴ outliers and influential cases should be examined in meta-analysis because their presence may affect the validity and robustness of meta-analytic conclusions. The studies by Chususiyah et al (2020),⁴⁹ Poerwanti et al (2022),⁵⁴ and Mitarlis et al (2020)⁷⁵ were identified as potential outliers because their standardized residuals exceeded the absolute value of 3, and they were also identified as influential cases in the diagnostic output. Chususiyah et al. (2020), Poerwanti et al. (2022), and Mitarlis et al. (2020) had standardized residuals of 3.527, −4.081, and 3.697, respectively. Before exclusion, the pooled effect was significant, g = 1.336, 95% CI [1.061, 1.611], with very high heterogeneity, I² = 92.09%. After excluding the three studies, the pooled effect slightly decreased but remained significant, g = 1.285, 95% CI [1.089, 1.480], while heterogeneity decreased to I² = 83.87%. These findings indicate that the main conclusion was robust to the influence of the identified studies, although substantial heterogeneity remained.

In the absence of publication bias or small study effects, the estimated individual effect sizes tend to distribute symmetrically on both sides around the pooled effect size.²⁹ The funnel plot in Figure 3 demonstrates the asymmetrical plot, as indicated by the small studies that tend to distribute on the right side. This pattern suggests potential small-study effects and possibility of publication bias. However, since the interpretation of funnel plot tends to be subjective,⁷⁶ Egger’s Regression test is needed as a further analysis to quantify the asymmetry of the funnel plot.²⁹

The publication bias analysis showed that all of the methods applied to assess the publication bias were statistically significant, as shown by Table 6 below.

Based on Table 6, it is shown that Fail-Safe N shows a very large number, meaning that an extremely high number of unpublished studies with null findings would be required to nullify the observed effect. This suggests that this meta-analysis is statistically robust and not easily overturned by potential missing evidence.⁷⁷ However, robustness alone does not guarantee the absence of publication bias. Kendall’s Tau suggests a systematic association between effect sizes and their variances.⁷⁸ In practical terms, this means that studies with lower precision (typically smaller studies) tend to report larger effects.^79,80 This pattern is widely recognized as small-study effects, which are often linked to selective publication or reporting practices in meta-analysis.²⁹

The asymmetrical funnel plot is confirmed by the Egger’s regression test. A significant result in Egger’s test indicates asymmetry in the funnel plot, suggesting that smaller studies yield systematically larger effect sizes than expected under a symmetric distribution.⁸¹

Since the Egger’s test was statistically significant, the analysis was processed to trim and fill the test to identify the missing studies.⁷⁶ The trim and fill test showed that there were no missing studies found in this meta-analysis, as shown visually in Figure 4. After the trim and fill process, the pooled effect size does not change (g = 1.336; p < .0001; 95% CI [1.074, 1.597]). Moreover, the heterogeneity remains the same (i.e., I² = 92.09%). Figure 3 and Figure 4 above demonstrate the funnel plot before and after the trim and fill. It is shown clearly that the funnel plot is still the same, which shows visually that there were no missing studies in this meta-analysis.

The asymmetrical funnel plot shows that there is a possibility of publication bias in this meta-analysis. The Egger’s Regression test confirms statistically the presence of publication bias shown by the funnel plot. Yet, Trim and Fill analysis showed no missing studies. Funnel plot asymmetry and a significant Egger’s test indicate the presence of small-study effects but do not constitute definitive evidence of publication bias.⁸² Such asymmetry may also arise from between-study heterogeneity, methodological differences, or contextual variations. Moreover, given the limited sensitivity of the trim-and-fill method under heterogeneous conditions, the absence of imputed studies suggests that the observed asymmetry is more likely attributable to study characteristics rather than publication bias alone.⁸³

Regarding the effect of IBL on students’ critical thinking, it is shown that IBL has a large and significant effect on students’ critical thinking. Therefore, for the first research objective the null hypothesis (H01) was rejected and the alternative hypothesis (Ha1) was accepted. Whereas, for the second research objective, the moderator testing showed that only control group variations significantly moderated the effectiveness of IBL on students’ critical thinking. Thus, the null hypothesis (H02a) was rejected and the alternative hypothesis (Ha2a) was accepted. In contrast, subject domain, education level, and country of study did not significantly moderate the effectiveness of IBL on students’ critical thinking. Therefore, the null hypotheses (H02b, H02c, and H02d) were accepted and the alternative hypotheses (Ha2b, Ha2c, and Ha2d) were rejected.

Future research is recommended to examine additional potential moderators that may explain the remaining heterogeneity in the effect of IBL on students’ critical thinking skills, particularly implementation fidelity, type or level of inquiry, intervention duration, and assessment instruments. These variables are important because IBL may produce different effects depending on how consistently inquiry procedures are implemented, how much guidance or autonomy is provided to students, how long the intervention is delivered, and how critical thinking is measured.

Zenodo. Does Inquiry-Based Learning Improve Students’ Critical Thinking? A Meta-Analysis Accounting for Control Group Variations [Data set]. https://doi.org/10.5281/zenodo.21246615.⁸⁴

The project contains the following underlying data:

• • Figure 1 – PRISMA Flowchart.tif

• • Figure 2 – Forest plot.tiff

• • Figure 3 – Funnel plot trim and fill.tiff

• • Figure 4 – Funnel plot.tiff

• • PRISMA 2020 – checklist abstract and review.docx

• • PRISMA 2020 – abstract checklist.docx

• • Script for computating effect size

• • R script Risk of Bias Assessment

• • R script reliability of coding data