Exploring JASP as a data analysis tool in L2 research: a snapshot

: This paper explores the potential of JASP (Jeffreys’s Amazing Statistics Program, https://jasp-stats.org/) as a robust statistical tool in advancing Second Language Acquisition (SLA) research, with a specific emphasis on its application within the domain of L2 writing. Second language writing proficiency is a complex and multifaceted skill, demanding rigorous empirical investigation to uncover nuanced patterns and insights. JASP, known for its user-friendly interface and advanced statistical capabilities, emerges as a promising instrument for researchers seeking to unravel the intricacies of L2 writing development. The paper begins by providing an overview of the features embedded in JASP and continues to discuss some of the extant research within the field of SLA that implements JASP as a data analysis tool. Follows is a detailed description of the use of JASP in two L2 writing papers, in which the data analysis decisions are discussed. Furthermore, the discussion delves into the practical implications of utilizing JASP in L2 writing research, including its ability to accommodate small sample sizes, handle complex interactions, and facilitate transparent and reproducible analyses. The paper concludes by advocating for the widespread adoption of JASP in SLA research, positing that its integration holds the promise of advancing our understanding of the intricacies of L2 writing development and contributing to the refinement of pedagogical approaches in second language education.


Introduction: Analyzing data in L2 Research
The acquisition of a second language (L2) is a complex process that involves the development of skills in understanding, speaking, reading, and writing in a language other than one's native tongue.L2 learning is not only an academic pursuit but also a vital component of global communication, cultural exchange, and economic activity.In an increasingly interconnected world, proficiency in multiple languages is a valuable asset that can enhance cognitive abilities, cultural understanding, and open doors to international opportunities (Bialystok, 2017).Given this vital significance, the processes involved in second language acquisition (SLA) have been a focal point of research in the field of Applied Linguistics since its origins in the 60s and 70s (Ellis, 2021) and studies have implemented a whole range of research methods, generating an array of data sets to answer the questions concerning L2 learning (Mackey & Gass, 2015).These data sets have been analyzed from both quantitative and qualitative perspectives and as research progressed, so did the ways in which the data was viewed, including for example, mixed-methods studies (Hashemi & Babaji, 2013).
Alongside the development of research methods, comes the progression of data analysis and the need for robust statistical analysis tools.As a result, SLA research has seen a rise in the use of numerous data analysis programmes such as SPSS (https://www.ibm.com/es-es/products/spss-statistics),R-Studio (https://posit.co/download/rstudiodesktop/)and, more recently, JASP (https://jasp-stats.org/).JASP offers both classical and Bayesian analysis procedures, producing results in APA style to facilitate publication within many research fields.Particularly notable is the possibility mentioned of carrying out Bayesian statistical methods, which provide a robust alternative to traditional frequentist approaches (Pfadt, 2022).This framework is pivotal for researchers who wish to seek to incorporate prior knowledge into their analysis, providing a more nuanced and context-rich interpretation of data, which can prove essential in understanding complex language learning processes.

Statistical analysis in studying L2 learning phenomena
Recent advancements in JASP have expanded its utility, particularly in terms of Bayesian analysis.Tutorials have been developed to guide users in applying Bayesian methods to specific statistical tests, such as single-test reliability analysis (Pfadt, 2022), tests of two proportions (Hoffmann et al., 2022), and Bayesian model-averaged meta-analysis (Berkhout et al., 2023).These resources are invaluable for those new to Bayesian methods, offering clear, step-by-step guidance, in a user-friendly software such as JASP.
Additionally, JASP also promotes open science through its integration with the Open Science Framework which aims at ensuring reproducibility and promoting transparency by embedding analysis settings into the results (JASP Team, 2023).The educational potential of JASP is further underscored by its application in diverse fields.This versatility demonstrates JASP's adaptability and relevance across various academic disciplines.

JASP as a data analysis tool: advantages and limitations
JASP stands out in the realm of statistical analysis due to its free and open-source nature, which democratizes access to advanced statistical tools.Unlike proprietary software like SPSS, JASP is accessible to all researchers, which is particularly beneficial for those in underfunded institutions or countries.Its user-friendly interface is designed to be intuitive for users familiar with other statistical packages, thereby lowering the barrier to entry for conducting sophisticated analyses (Kelter, 2020).
One of the significant advantages of JASP is its integration of both frequentist and Bayesian statistical methods, both described in more detail below.This dual capability allows researchers to not only test hypotheses but also to incorporate prior knowledge and beliefs into their analyses, providing a more nuanced understanding of L2 learning phenomena (Quintana & Williams, 2018).However, one limitation of JASP is that, being a newer software, it may not yet have the same breadth of advanced features or the extensive user community that more established programs like SPSS or R have.Notwithstanding, over time, it will likely begin to gain more attention as an alternative data analysis tool.
Another advantage is JASP's commitment to open science.It encourages transparency and reproducibility by allowing researchers to share their data and analysis procedures directly through the software.This feature is particularly relevant in the context of L2 learning research, where reproducibility is crucial for validating findings across diverse linguistic and cultural contexts.Despite these strengths, JASP's limitations include a smaller range of available statistical tests compared to more mature statistical packages.Additionally, while JASP is improving its documentation and online resources, the support available may not be as extensive as that for other tools, potentially leading to a steeper learning curve for some of the more complex analyses (Brydges & Gaeta, 2019), something which we believe will be overcome throughout the following years, given its ever-increasing popularity within the field of L2 research.
In general, the adoption of JASP within the academic community has been steadily increasing, as evidenced by its use in a variety of research fields, including L2 learning.Its impact is particularly notable in promoting the principles of open science and reproducible research.By providing a platform that is both accessible and capable of sophisticated analyses, JASP is lowering the barriers to conducting high-quality statistical research (JASP Team, 2023).
The impact of JASP is also evident in the way it has facilitated a shift towards Bayesian statistical methods in the social sciences.As previously mentioned, Bayesian methods offer a different perspective on data analysis, one that is increasingly being recognized for its ability to handle complex models and incorporate prior information.JASP has been instrumental in this shift by providing tools that make Bayesian methods more accessible to researchers who may not have a strong background in statistics (Wagenmakers et al., 2018) and has contributed to a higher use of these methods within the field of second language research, as detailed in the following section.

JASP in L2 research
JASP is particularly relevant for L2 learning research due to its comprehensive range of statistical tests, which are pertinent for analyzing language learning data.It includes tests for ANOVA, ANCOVA, repeated measures ANOVA, and MANOVA, among others, which are commonly used in L2 research to assess the impact of different instructional methods and learning conditions on language acquisition outcomes (Plonsky, 2013;2014).Developed at the University of Amsterdam, JASP has been financially supported by several universities and research funds, reflecting its credibility and the trust the academic community places in it (JASP Team, 2023).As mentioned above, its design facilitates the application of both frequentist and Bayesian inference, allowing for a more nuanced understanding of L2 learning phenomena.Bayesian inference, in particular, is valuable in L2 research for its ability to incorporate prior knowledge into the analysis, providing a richer context for interpreting results (Quintana & Williams, 2018).JASP's applicability in L2 learning research extends beyond its comprehensive range of statistical tests.It plays a crucial role in analyzing language learning data, especially in studies focusing on the effectiveness of different instructional methods and learning conditions (Wagenmakers et al., 2018).Its robust capabilities in ANOVA, ANCOVA, repeated measures ANOVA, and MANOVA are particularly useful for such assessments.
JASP was developed to be a more accessible and open alternative to proprietary statistical software, and its application in L2 research is growing.It has been used to analyze data in studies examining a range of diverse variables, including speech fluency (Chau et al., 2022), L2 writing (Mazgutova & McCray, 2023), L2 motivation (Zalbidea et al., 2022), and digital game-based language learning (Dixon et al., 2022) to mention a few.Follows is a summary of how some of this research within the field of SLA which has implemented JASP as a data analysis tool.
The integration of JASP in second language (L2) learning research has been a progressive step towards more transparent and accessible statistical analysis.Kelter (2020) highlights the seamless transition researchers can make from traditional statistical packages like SPSS to JASP, thanks to its aforementioned user-friendly, point-and-click interface.
Given the ease JASP presents for researchers, SLA research has seen an increase in its implementation.However, despite some researchers referencing the statistical package they have used for their study, it remains an uncommon practice within the field.That is, many researchers fail to detail the software used and when carrying out the literature review on JASP in L2 learning research for the current paper, it became apparent that this is an issue throughout the field.Notwithstanding, there are a number of research papers that include essential information on the software used and how they implemented it.
As JASP provides the opportunity for carrying out Bayesian analysis, Chau et al. (2022) carried out five Bayesian repeated measure ANOVAs using JASP.This decision was made "in order to attend to the inference crisis of the social and behavioral sciences", by providing additional information via Bayesian methods, to complement the testing that relies on p-values.The values in their research were interpreted according to Norouzian et al.'s (2019) Classificatory Scale.The data analysis provided by JASP proved to be decisive in demonstrating that pronunciation instruction did not play a role on speed fluency improvement for the participants under study (11 native English speakers from the USA).
In line with the research mentioned (Chau et al., 2022), Zalbidea et al. (2023) also implemented Bayesian analysis using the EBICglasso procedure in JASP.Zalbidea et al. (2023) detail the procedures followed and even include specific footnotes on the data analysis potential JASP has for providing information on nodes.The extensive detail provided on the implementation of JASP is uncommon in SLA research and the study by Zalbidea et al. (2023) is one of the very few that includes such rich particulars.JASP was used in this study specifically for examining heritage language (HL) learners' motivational profiles, by modelling the data "into an exploratory regularized partial correlation network" (p.989).The advanced data analysis carried out in this study was able to shed light on psychological network modeling within the specific domain of HL learning motivation, revealing positive connections between the variables analyzed and the HL learners, including intended effort, enjoyment and HL selves.
In line with the research included in this paper, Mazgutova and McCray (2023)  according to Bayes factor hypothesis testing (BHT) -which will be explained in later sections -which is based on a Cauchy value of 0.707.The results from the BHT analysis showed evidence of no difference in terms of the student's engagement with text revisions from Time 1 to Time 2 and the authors explicitly claim that thanks to the BHT method implemented via the use of JASP, they were able to provide a more detailed explanation of the results, especially when compared to more frequentist methods.In addition, they add that the BHT analysis demonstrated that their study, with the specific conditions included, would not likely show different results if replicated in the future and thus, the authors recommend that any future research looking into L2 text revisions over time should include a variety of different variables.
Other research within the field which has used JASP as the data analysis tool has focused on more frequentist models and the inclusion of effect sizes.Dixon et al. (2022) investigated the effectiveness of digital based language learning (DGBLL) by carrying out a meta-analysis on the research that has been carried out on digital games in L2 learning contexts.Their analysis was based on within-group and between-group designs and following Plonksy & Oswald (2014), they selected Cohen's d as the effects size measurement, and followed the benchmarks established.
The authors provide a very thorough description of the data analysis procedure and go into detail regarding the effect sizes and models in question.In terms of the results and the data output provided by JASP, forest plots were created to illustrate the individual effect sizes for each of the studies included in the meta-analysis, as well as to illustrate between and within-group effects.These plots allow the authors to provide visual support for their results which conclude that DGBLL appears to effectively contribute to language learning, especially when compared to non DGBLL instruction.
In conclusion, JASP's role in L2 learning research is multifaceted.It serves as a bridge between traditional statistical methods and modern, open-science practices.Its growing adoption and therefore, its impact reflect a broader movement in the academic community towards more transparent, accessible, and sophisticated statistical analysis.
Owing to its significance thus far within the field of SLA and the opportunities it presents as a reliable and powerful data analysis tool, this study aims to offer a comprehensive description of JASP's utility in L2 research from two distinct perspectives: more traditional frequentist methods in Study 1, and Bayesian methods in Study 2.

Introduction and objectives of the research
The first study described in this paper corresponds to an unpublished doctoral thesis which was carried out in order to respond to two SLA-oriented lines of research.On the one hand, it examined the effects of writing medium on the L2 written accuracy of texts.That is, the research focused on the effect of computer mediated writing versus traditional pen-and-paper writing.On the other hand, the thesis aimed at exploring the effects of three different feedback processing conditions (think-aloud protocols; written languaging; and simultaneous think-aloud protocols with written languaging) on the student's engagement with the feedback and subsequent written production.As the main contribution of the study was empirical, the data collected was analyzed in order to provide empirical evidence on the phenomenon under study.

Methodology and participants
The study followed a pre-test/treatment/post-test design in which a total of thirty-six undergraduate students participated.The students belonged to the fourth year of an English philology degree and were all enrolled on a course on Applied Linguistics.Participants were first invited to complete an Oxford Placement Test (OPT) in order to confirm L2 proficiency homogeneity, which corresponded to an intermediate/high-intermediate level of B2-C1 proficiency (according to the Common European Framework of Reference for Languages).Once they had completed the OPT, they were asked to write an initial text (pre-test) in a 50-minute time-constrained condition.The writing task was the "Fire Chief" task (Gilabert, 2007) which consists in a problem-solving, picture-based task in which students are presented with a drawing of a burning building with a number of people inside, the students are required to detail how they would save the people inside the building, in which order, and justify why.The writing tasks were corrected with direct written corrective feedback (WCF) and given back to the students in order for them to process the error corrections that had been provided.
For the processing stage of the study, participants were divided into three groups according to the manner in which they were asked to process their WCF.Therefore, the first group were asked to think aloud and verbalize their thoughts on the errors and their corrections.The second group were asked to complete a written languaging table and provide relevant information about the errors and their corrections.Finally, the third group were asked to do both of these processing tasks simultaneously.That is, they were asked to complete the written languaging table whilst also verbalizing their thoughts out loud (think-aloud protocols).The final task (post-test) asked participants to return and rewrite their original texts under the exact same conditions as in the pre-test.

Choosing the right statistical approach: why frequentist?
Given the nature of the study, which focused heavily on exploring the effects of written corrective feedback processing on both the levels of depth of processing of the participants, as well as on their L2 written production, decisions had to be made on the data analysis procedures to optimize the wide range of data the research expended.One main criterion which had to be taken into consideration was the small sample size included in the study.As previously mentioned, there were 36 participants included in the research.However, these students were divided into two primary experimental groups; computer-mediated writing and pen-and-paper writing, therefore leaving a small sample of 18 participants per writing condition.In addition, each writing condition processed the feedback provided according to the three feedback processing conditions previously mentioned and thus, the groups were reduced to 6 students per feedback processing condition.Added to the reduced sample size, much of the data collected was qualitative in nature, particularly the think-aloud protocol data and thus, a mixed method approach was essential in order to truly explore the data from each experimental condition in an optimal manner.Given the small sample and the number of variables included within the study, the decision was made to calculate descriptives, including means, standard deviations and 95% CIs, as well as calculating d values (effect sizes) using JASP for the L2 written production, and frequency counts were calculated for the written corrective feedback processing levels across the various conditions.

Analysing the data with JASP
The data collected consisted of the written texts produced in the pre-and post-test, as well as the WCF processing data.Once all data had been collected, the written texts were analyzed in terms of their complexity, accuracy and fluency (CAF) by using manual calculations for accuracy (number of errors/total number of words *100) and fluency (total number of words/total time spent on task) and the online SYNLEX tool (https://aihaiyang.com/software/lca/)for complexity (Ai & Lu, 2010;Lu, 2012).
In terms of the WCF processing data, the think-aloud protocols were transcribed and coded following Leow's (2015) definition of depth of processing (DoP), and the written languaging data was coded according to levels of noticing and engagement, guided by a coding scheme created by Cerezo et al. (2019).For a detailed explanation of the data coding scheme elaborated for the study, see McBride and Manchón (2023).
In terms of data analysis, within-groups analyses were performed on the quantitative data in order to explore the results in terms of the written corrective feedback processing conditions.In addition, between-groups analyses were performed in order to explore the effects of digital versus pen-and-paper writing environments.Given that the number of participants was relatively low, and the thesis included a wide range of variables (WCF processing instruments and two writing conditions), the decision was made to include descriptive measures which were calculated using JASP 0.14.1.In order to carry out the analysis, first the means and standard deviations were calculated for the L2 written CAF measures (as shown in Figure 2).Once we had analysed the data in terms of descriptive statistics, we were then able to carry out independent samples t-tests, and paired sample t-tests in order to compare the means of the various variables under study which included the effects of writing medium (digital vs pen-and-paper) on the L2 written production of the participants (CAF measures), as well as the effects of the WCF processing conditions (think-aloud, written languaging, and simultaneous think-aloud and written languaging) on L2 written products (CAF measures).

Figure 3 Independent Samples T-Test in JASP
In addition, and in order to understand the magnitude of the differences found between the variables analyzed, Cohen´s d effect sizes were also calculated (an option available within JASP, as shown in Figure 3.Following previous research (Plonsky et al., 2021), the effect sizes were interpreted according to the parameters summarized in Table 1 below: The inclusion of effect sizes in the study was motivated by the growing importance of this parameter in SLA research in recent years.Furthermore, given the relatively small sample size and the multitude of variables incorporated in the research design, effect sizes proved to be a valuable tool for producing a robust and dependable interpretation.

Reflections on using JASP for frequentist methods
The output provided by JASP allowed us to provide a solid analysis of the data collected, facilitated by the easily interpretable results this data analysis tool provides.The results are presented in a way that helps users understand the statistical findings, including effect sizes (as in the study carried out), and any other relevant information required.By first examining the descriptive statistics of the variables of interest (writing medium and WCF processing), we were able to obtain an initial sense of the central tendencies and variability in the data.Then, according to the research questions established, we were able to employ the independent samples t-Test, and paired sample t-Tests to assess the significance and practical importance of the results obtained.The effect sizes were essential in obtaining the practical importance of the results as they provided information on the magnitude of the observed effects found in each t-Test carried out.Given that the data belongs to an unpublished doctoral thesis, this paper will not go into any further detail on the specific results found.

Introduction and objectives of the research
The study involved a group of 55 undergraduate students, who participated in a questionnaire developed specifically for this research.This questionnaire, designed to capture students' perceptions and preferences, included questions about their attitudes towards digital and handwritten L2 writing (McBride & Garcés-Manzanera, 2022).It comprised two sections, each with 23 Likert-scale questions, corresponding to the two writing modalities.This dual approach enabled us to compare students' self-reported views on digital versus handwritten L2 writing.Additionally, this approach supported the use of inferential statistics to address our research questions.
As can be seen in Table 2 below, the questionnaire was crafted in Spanish, which was the native language of all the participants.This choice was made to enhance comprehension and avoid any potential confusion due to language barriers.The questions covered a range of topics, including the purpose of writing (whether academic or informal), the participants' confidence in their writing abilities, cognitive factors that might influence the learning effectiveness of writing, and their perceptions regarding the difficulty level of writing in an L2.These diverse aspects were carefully chosen to provide a comprehensive view of how students perceive and interact with different writing formats in a second language setting.The questionnaire for the digital mode was identical except that the references to handwriting (a mano, in Spanish) were replaced with digital writing (por ordenador, in Spanish).Choosing the right statistical approach: why Bayesian?
Typically, L2 research is conducted within a frequentist statistical framework (as in our first study), utilizing traditional statistical tests, with descriptive statistics, or in other cases different from our own, which may based on values such as f and t (for instance, in inferential statistics), the p-value, and increasingly, effect size.However, as highlighted by Norouzian et al. (2019), the prevalent reliance on null hypothesis significance testing has recently come under scrutiny.
Criticisms center on the potential for misleading extrapolations of observed effects to larger populations.
Consequently, Bayesian hypothesis testing is being increasingly considered as a viable alternative in L2 research contexts.The Bayesian statistical approach allows for a more nuanced understanding of the variability in student perceptions as it incorporates both existing evidence and new data.In essence, Bayesian hypothesis testing differs from frequentists methods in that it includes prior beliefs and updates the probability of a hypothesis in light of the new evidence (that is, the data gathered), making it particularly suitable for exploratory studies in educational contexts (see Shikano, 2019or Andraszwicz et al., 2015).
Building on the previous information, we opted for using JASP as a software for the analysis for a number of reasons: (1) JASP offers Bayesian analysis for basic statistical tests, featuring parameter estimation and the Bayes factor hypothesis testing based on the default Cauchy value, which is a weighting scheme (Jeffreys, 1961;Love et al., 2019); (2) the fact that classical counterparts to frequentist methods are present in Bayesian analyses in JASP makes it a more inclusive option.Figure 4 below displays how well incorporated Bayesian analyses are, facilitating the user's and researcher's tasks by incorporating the frequentist (or classical) method with the Bayesian one.

Figure 4 Layout of classical and Bayesian test results in JASP software
In line with the above information, Figure 5 displays the Cauchy value which, in accordance with JASP standards, is set at 0.707.This value is chosen based on the premise that effect sizes are likely to be small in many research scenarios, including SLA and L2 research, where large effect sizes are less common.Such a setting facilitates a non-directional approach in hypothesis testing and offers a versatile alternative (Berkhout et al., 2023).

Figure 5
Interface of JASP software displaying the Cauchy prior scale setting for Bayesian analysis Along these lines, in our study, Bayes factor statistic was used as a substitute to p-value.In fact, Bayes factor is a statistic that "expresses the comparative evidence for one hypothesis (e.g., alternative hypothesis) over another hypothesis (e.g., null hypothesis)" (Norouzian et al., 2019, p. 3).Bayes factor replaces a p-value and is based on a classificatory scale, as seen in Figure 6 which allows us to determine the extent to which our hypothesis is supported by the study data.

Analysing the data with JASP
In our study, we adhered to a data processing methodology in JASP that aligns with the approach outlined in section 3.1.The primary aim of our research was to examine the potential variance in students' perceptions across survey items, particularly comparing traditional writing methods with digital writing techniques in first and third-year students, which was the independent variable in our study.To this end, we employed non-parametric Wilcoxon signedrank tests for within-group comparisons and non-parametric Mann-Whitney U tests for between-group analyses (McBride & Garcés-Manzanera, 2022).Due to the space constraints in this paper, we will concentrate solely on one test to demonstrate the utilization of JASP for conducting our statistical analyses in research.
Delving into the specifics of our first analysis, related to the first research question, several key decisions shaped our approach.We retained the default Cauchy value as set by JASP.This decision was driven by the limited prior research in the domains of SLA and L2 learning, which presented challenges in gathering pre-existing data.In essence, maintaining the default setting appeared to be the most prudent approach.
Furthermore, we configured the Bayesian variant of the non-parametric Wilcoxon signed-rank test to perform 5000 iterations (see Figure 7 below).This decision was based on the premise that a higher iteration count could more accurately reflect the posterior distribution of the model's parameters, thereby yielding more reliable results.Such an approach is indicative of JASP's capability to integrate traditional frequentist tests (like t-tests or Mann-Whitney tests) into a Bayesian framework, offering a more nuanced view of data analysis.To address the initial research question, we utilized JASP for segregating the data into distinct groups.This facilitated the execution of within-group analyses.Specifically, we conducted a Wilcoxon signed-rank test separately for first-year and third-year participants.The process of segregation and analysis in JASP is illustrated in Figure 8.  JASP provides all these additional values -besides the key BF₁₀ -in an attempt to validate the evidence existing to reject the null hypothesis.From the technical perspective, using JASP for Bayesian statistics is a process made easy given the user-friendly software interface, but equally important, because of the output it produces.Likewise, when the results of this study were presented at a conference, which required a more visual presentation of the data, a series of plots were devised by JASP: Prior and Posterior plot (Figure 10 and Bayes factor robustness check (Figure 11).
The depicted Prior and Posterior plot serves as a visual representation of a Bayesian statistical analysis, contrasting initial assumptions (prior) against updated beliefs after considering new evidence (posterior).The solid line indicating the posterior distribution peaks distinctly to the left of zero, suggesting a negative effect size.This inference is substantiated by the posterior median at -1.311, with a 95% credible interval stretching from -1.640 to -0.989, confidently excluding zero.Such a distribution conveys a statistically significant negative effect, implying that the observed data substantiates a real underlying phenomenon rather than mere chance.
Complementing the density curves, Bayesian Factor values (BF₁₀ and BF 01 ) quantify the evidence for the alternative hypothesis over the null hypothesis.A strikingly high BF₁₀ value of 554000 robustly favors the alternative hypothesis (H1), while the minuscule BF 01 value of 1.81e-06 diminishes the likelihood of the null hypothesis (H0), almost to the point of exclusion.This strong statistical support for H1 is visually echoed in the accompanying pie chart, where the shaded area predominates, suggesting a negligible chance for H0.The graph summarizes a rigorous quantitative assessment, indicating a substantial and statistically significant negative effect size that aligns with the research hypothesis.The curve on the plot commences with strong support for H1 at a narrow Cauchy prior width, reflected in a high BF₁₀ value.As the prior width increases, indicating a more uncertain and wider range of prior beliefs, the BF₁₀ value decreases, suggesting diminishing evidence for H1.This trend continues until the evidence becomes merely anecdotal at larger prior widths.However, the BF₁₀ value never drops below 1, which would indicate evidence for H0; hence, across all prior widths, the data tends to support H1 more than H0.
A red dot on the curve indicates a specific prior width where the evidence for H1 is particularly strong.This point falls within the 'Strong' category on the evidence scale, which ranges from 'Anecdotal' at the lowest end to 'Very Strong' at the highest.The evidence levels are delineated on the right side of the graph, providing a quick reference to interpret the BF₁₀ values.Overall, the graph communicates that while the strength of the evidence for H1 varies with the choice of prior, it consistently favors H1 over H0 within the observed range.

Reflections on using JASP for frequentist methods
To conclude this section on the use of Bayesian statistics in L2 research and in particular, on L2 writing, it is essential to consider several crucial aspects: Firstly, despite the widespread reliance on p-values, Bayes factors (BF₁₀) provide a more nuanced perspective on the strength of the alternative hypothesis.Unlike the dichotomous nature of significance in frequentist statistics, Bayes factors offer a continuum for evidence assessment, akin to effect sizes, facilitating a more comprehensive understanding of research findings (Norouzian et al., 2018).Secondly, the frequent occurrence of small sample sizes in L2 research underscores the significance of Bayesian statistics.This methodology is particularly effective in addressing the limitations of frequentist approaches, such as susceptibility to Type I and II errors, thereby ensuring more robust and reliable statistical conclusions.

Conclusions
This paper has aimed at demonstrating the capabilities of JASP as a data analysis tool within second language research, more specifically, within studies on L2 writing.As described, JASP is able to provide frequentist analysis for studies which include simple experimental designs, or small sample sizes, by carrying out T-tests, providing descriptive data and effect sizes, for example.That being said, it is common knowledge that many statistical packages are geared toward frequentist analyses, particularly SPSS, which has been widely used in the field of SLA and is well-known for its extensive set of procedures for data analysis.
However, one of the main benefits of JASP is the fact that it is an open-source software, meaning it is freely available for anyone to download, whereas more traditionally used data analysis software tools are commercial products and require a license to be able to access them.Additionally, JASP is equally friendly in terms of user interface, making it more accessible to early career researchers.In terms of Bayesian statistics, JASP stands out for its emphasis on Bayesian methods, which can certainly be advantageous for specific data sets, particularly when dealing with smaller sample sizes or when incorporating prior knowledge.As demonstrated in this paper, JASP was able to provide detailed statistical analyses on the L2 data under study.However, it is important to note that, given the novelty of using JASP in SLA research, and when compared to other tools which have a longer history, JASP does not have a wealth of online and offline resources thus far.That is, despite other tools having a large quantity of tutorials, books, and even online resources for their use, JASP is still an emerging analysis tool for many research fields and although the tool itself provides a range of educational resources, tutorials and explicative documents, there is still a general lack of specific tutorials within the SLA field.
Ultimately the choice between using JASP in favor of any other available data analysis tool will highly depend on the specific requirements of the research in question as well as the researcher's familiarity with statistical methods.
Notwithstanding, with this paper, we want to highlight the versatility of JASP in implementing both frequentist and Bayesian approaches and call for more research to be explicit, not only in the data analysis procedure, but also in the data analysis tools implemented.By doing so, researchers within the field of second language acquisition can gain more insights into the ways in which we, as a field, are carrying out data analysis, and which tools we are able to implement for the specific data in question.
Statistical analysis plays a crucial role in L2 research, as it provides a means to systematically investigate the intricacies of language acquisition.Through statistical methods, researchers are able to analyze data to uncover patterns, test theories, and draw evidence-based conclusions about language learning processes (Larson-Hall, 2016).The use of statistical tools enables the examination of variables such as exposure, instruction, and individual differences (e.g., age, 1.2 Introduction to JASP as a free and open-source statistical software JASP (Jeffreys's Amazing Statistics Program, https://jasp-stats.org/) is a free and open-source statistical software program supported by the University of Amsterdam.It is designed with ease of use in mind, making it accessible to those familiar with programs like SPSS.Its user-friendly interface and extensive graphical capabilities significantly contribute to its popularity in both educational and research settings.

Figure 1
Figure 1 Descriptive Statistics in JASP also use Bayesian methods via JASP to explore revision behavior in L2 writing.Their research collected data via keystroke logging and explored the changes over a one-month period of students writing in an English for academic purposes (EAP) programme.The data collected (L2 written products and keystroke logging evidence) was analysed and their interpretation were based on Norouzian et al. (2019) and Wagenmakers et al. (2018)'s Bayesian method explanations, which envision the results

Figure 2
Figure 2 Descriptive Statistics in JASP

Figure 7
Figure 7Iterations in Wilcoxon signed-rank test

Figure 8
Figure 8 JASP software screenshot showing the data filtering process for within-group análisis

Figure 9
Figure 9Results of the survey questions by first-year undergraduate students(McBride & Garcés-Manzanera, 2022)

Figure 10
Figure 10Prior and posterior plot

Figure 11
Figure 11 Graphical representation of Bayes Factor (BF₁₀) as a function of Cauchy prior width, indicating levels of evidence for hypotheses H1 and H0