Response to Reviewer 1:

General comments:

We've tried to answer all the points raised in the study.

Methods:

Reviewer. Line 145: is the sample adequate to validate the study? Suggest the authors look at: https://www.mdpi.com/862272; sample size estimation.

Response:

Sample Size

Initially, data should be gathered from a sufficiently large sample to appropriately conduct subsequent analyses. The necessary sample size to properly perform statistical significance tests has been a significant topic of debate. It appears that the number of variables or items to be assessed will dictate the required sample size to achieve robust outcomes. Past recommendations regarding item-to-response ratios ranged from 1:4 [49] to at least 1:10 [50] for each set of scales to be subjected to factor analysis. Moreover, recent studies have indicated that, in most cases, a sample of 150 observations should be adequate to achieve an accurate solution in Exploratory Factor Analysis, provided that the correlations among items are reasonably strong [51]. For confirmatory factor analysis, it is worth noting that we suggest a minimum sample size of 100 [52].

Moving to another main point, the final factor structure required a sample size that exceeded the "n/q > 5" guideline proposed by Bentler and Chou [53] for factor analysis. In this rule, "n" denotes the number of the sample and "q" the number of parameters estimated in the model. For our final model, we had 18 parameters to estimate. Subsequently, the sample was divided into two sub-samples, n1 = 380 (380/18 > 5) for the Exploratory Factor Analysis (EFA) and n2 = 380 (380/18 > 5) for the Confirmatory Factor Analysis (CFA). This division was done randomly. Our approach aligns with that of the original validation study by Pelletier, Rocchi [41] and is consistent with methods commonly used in similar studies [54-56]. Interestingly, Tabachnick and Fidell [57] indicated that a sample size of 300 provides a reassuring level to address concerns related to statistical power. In line with this, Schönbrodt and Perugini [58] posited that a minimum of 240-250 participants is necessary to achieve a point of stability. Additionally, Hair, Black [59] suggest that a sample size greater than 300 is an ideal threshold for factor analyses, which the current study's sample size exceeds.

Furthermore, results consistent with these have been reported by Hirschfeld, Brachel [60] who similarly noted these findings, suggesting a sample size of over 500 participants to achieve stability. As a result, the desired participant count for this research was set in line with, or above, the recommendations from comparable studies, targeting at least 500 participants (i.e., n ≥ 500).

Reviewer. Line 156: I would suggest removing the history and targeting the instrument. What does the instrument consist of? Is the original instrument attached to this manuscript with items in the same order they were distributed? Pointing at the instrument is highly important.

Response: The administration of the questionnaire was done in 26 October 2021 following the start of the sports season and the end of the health crisis of coronavirus, 800 questionnaires were distributed. We informed the club coordinators of the objectives of the work. The scales were distributed to the teams before the training session. The SMS-II was completed two hours before the start of the athletic competitions. The instructions for the tool were well explained to the athletes. The athletes indicated their age, gender, and sport discipline.

All study participants volunteered and took part in the study anonymously and confidentially. Data collection adhered to the standards set forth by the Declaration of Helsinki and its later amendments. Prior to initiating the data collection process, ethical clearance was secured from the Ethics Committee at the National Center of Medicine and Sports Sciences of Tunisia, with the reference number LR09SEP01. The tool was administered using traditional pen-and-paper techniques.

All participants were duly briefed on the primary aim and objectives of the study. Those aged 18 and above gave their written informed consent prior to filling out the questionnaires. For participants below the age of 18, written informed consent from their legal guardians was a prerequisite for participation.

Reviewer. Line 185: how was the instrument distributed? Penn and paper? Electronic? What kind of software was used? How?

Response: All study participants volunteered and took part in the study anonymously and confidentially. Data collection adhered to the standards set forth by the Declaration of Helsinki and its later amendments. Prior to initiating the data collection process, ethical clearance was secured from the Ethics Committee at the National Center of Medicine and Sports Sciences of Tunisia, with the reference number LR09SEP01. The tool was administered using traditional pen-and-paper techniques.

All participants were duly briefed on the primary aim and objectives of the study. Those aged 18 and above gave their written informed consent prior to filling out the questionnaires. For participants below the age of 18, written informed consent from their legal guardians was a prerequisite for participation.

Reviewer. Line 192: before the data collection or before the beginning of analysis?

Response: Prior to initiating the data collection process, ethical clearance was secured from the Ethics Committee at the National Center of Medicine and Sports Sciences of Tunisia, with the reference number LR09SEP01. The tool was administered using traditional pen-and-paper techniques.

Reviewer. Line 193: how was the parents' permission obtained?

Response: The instructions for the revised Sports Motivation Scale-II (SMS-II) are well explained to the athletes. Athletes will provide their age, gender, and sport. Parental consent will be obtained for non-adult athletes. Verbal informed consent will be obtained from each athlete prior to the start of the two-week study. Participation of all athletes will be voluntary. Prior to administration of the two-day questionnaire, parental consent will be obtained by signing a written parental consent form for all minor participants ([13-18] = 419). Similarly, at the time of scale distribution and after verbal consent from the athletes, all adult participants ([19-30] = 361) will sign the written consent that will accompany the instrument so that they can complete the items. Athletes may refuse to participate in the study if they are unwilling to sign the consent form. We will use this procedure to increase the number of participants in the study. Most athletes refuse to participate in studies when asked to sign a consent form. Consequently, it is necessary to initially communicate verbally with the participants, elucidate the advantages this study offers to the sport, and confirm that there is no risk to the athletes either during or after their involvement. Subsequently, presenting the written consent will secure their participation and minimize the likelihood of refusal.

Reviewer. Line 195: what do the authors mean by the raw data obtained by the participants were analyzed to ensure maximum confidentiality? line 195-197 should be rewritten with clarity in mind?

Response: All study participants volunteered and took part in the study anonymously and confidentially.

Reviewer. Line 204-208: is this not part of the PCA? what was the cutoff for a good fit? Where was the goodness of fit measured? How? (model fit)?

Response: I have eliminated lines 204-208 since they do not pertain to the CPA. The content of lines 204-208 is identical in meaning to that of lines 216-219.

Reviewer. Line 244: what does the instrument quality have to do with the descriptive statistics of the participants?

Response:

Age, gender, and type of sport are factors considered in the sensitivity of the instrument. Geographically, the participants hail from various regions of Tunisia: Tunis in the north accounts for 22.1%, while the central regions of Sfax and Kairouan represent 19.8% and 19.6% respectively. In the south, Gafsa participants make up 21.3%, with Gabes at 17.2%.

Reviewer. Line 258-: how relevant is this analysis to the purpose of this study? Does this mean that the instrument does not measure change from time to time? what is the difference between this analysis and the KMO and Bartlett sphericity test? what is the purpose of this study? was it to measure if participants answered similarly from one time to another time, or to validate a translated questionnaire?

Response: I have removed lines 258-276 because they are irrelevant to this study.

Reviewer. Line 277-281: what is the purpose of line 277-281? does this indicate that the dimensions are related? Ok, why is it important?

Response: lines 277-281 are not important in this study.

Reviewer. Line 285-300 could be changed with the rotational matrix produced by the PCA, and the eigenvalue could be reported with its graph to show the loadings of the items.

Response: The section spanning lines 285-300 has been substituted with the rotation matrix generated from PCA, with the eigenvalues graphed to display the factor loadings.

Figure 1. Scree plots of eigenvalues in factor analyses.

Table 5. Standardized solutions for factor loadings for the sports motivation scale SMS-II.

Ligne 361 (discussion):

Reviewer. It should be presented in the same order as it was tested.

1- Discuss the methodology used to address the problem.

2- discuss the instrument's quality.

3- discuss the Composite scores and their meaning.

4- discuss EFA.

5- DISCUSS CFA

6- discuss Sensitivity analysis

The original version of the SMS, published in 1995, has been used in numerous studies to assess motivation in sports. However, it has received criticism in some studies concerning both the content of the items and its psychometric structure [101, 102]. Experts in the field, Pelletier, Rocchi [41] concluded that some items were unclear, and others did not align with the theory. In a detailed study in 2013, Pelletier, Rocchi [41] refined the SMS down to 18 items and released it as SMS II. Regarding its development, the integrated regulation was included in the revised SMS-II version. These authors have shown that different forms of intrinsic motivation make the scale less reliable. Therefore, it is necessary to add other sub-scales valuing intrinsic motivation for this revised version to strengthen its structure and develop profitability. The scale was designed to assess athletes’ level of motivation for sport regarding SDT [41]. According to Pelletier, Rocchi [41], the 18-item scale successfully tests sports motivation. In this context, the researchers decided to conduct this study to adapt and integrate the 18 items into Tunisian culture. In summary, the results of this study indicated that the Arabic version of the SMS-II is a reliable and valid tool for measuring the level of motivation in sport for athletes from both sexes and different types of sport (individual or team). Overall, we found very good psychometric properties for this adapted instrument. Moreover, the results collected by the EFA showed that this SMS-II scale well suggested the desired theoretical model, with good internal consistency for all the adopted dimensions. The 18 items of the SMS-II justified high reliability and excellent temporal stability. Likewise, the CFA fit indices were good.

To ensure the results of SMS-II, we began with ensuring the normal distribution of the data, which is evident from the results related to skewness and kurtosis. Such the skewness (Sk) and kurtosis (Kr) values provided evidence supporting the assumption of a normal distribution for the data set. Both the Sk and Kr values fell within the acceptable asymmetric range of +2 and −2, confirming data normality. This step was crucial as it ensured that the subsequent statistical analyses, especially those that assume data normality (like PCA), were appropriately applied. Kaiser-Meyer-Olkin (KMO) measure and Bartlett's sphericity test were employed to determine the sampling adequacy. Meeting the criteria for both tests (KMO > 0.6 and a significant p-value for the Bartlett test) was pivotal as it indicated that factor analysis was suitable for this dataset. A test-retest reliability analysis further confirmed the scale's temporal stability with a remarkably high correlation coefficient of 0.935, underscoring the scale's consistency over time.

The scale demonstrated excellent internal reliability across various measures: McDonald’s omega, Cronbach's alpha, and Gutmann λ6. Particularly notable is McDonald's omega (ω SMS-II = 0.841), which, as highlighted in the literature [83], is a superior indicator of internal reliability. This means that the items within the SMS-II consistently measure the intended construct. Given that most parameters showed high correlations with excellent values, this attests to the instrument's quality in measuring the constructs it purports to measure.

Through principal component factor analysis, we uncovered a six-factor solution for the SMS-II version. This suggests that the eighteen items of the scale can be aggregated to create scores for these indices. It is noteworthy that only the first six factors accounted for an impressive 87.66% of the total variance. The results were further corroborated by the scree plot, which indicated a point of inflection after the first factor. This convergence of evidence, from both eigenvalues and the scree plot, strongly underscores the appropriateness of considering the first six principal components for further analysis.

The results of the Exploratory Factor Analysis (EFA), specifically with an orthogonal Varimax type like Kaiser's [66] Varimax criterion, were utilized to identify the underlying factor structure of the SMS-II scale. The findings revealed six primary factors, consistent with the expectations set out by the principal component analysis. The chosen threshold for item retention based on a loading of ≥0.40. In our study, collected results indicated that the Arabic version of the SMS-II scale is a reliable and valid instrument for measuring athletes' motivation in different disciplines. This conclusion is also supported by some research [28, 44-48]. The eigenvalues and the amount of variance accounted for by each factor offer insights into their relative importance. For instance, the first major component (amotivation) accounted for a substantial 30.73% of the total variance, highlighting its significance. By contrast, subsequent factors, while still crucial, accounted for incrementally lesser variance. Factor saturations ranged between 0.872 and 0.952, which is indicative of strong loadings and affirms the suitability of our factor structure.

The CFA serves to test our hypothesized factor structure against the collected data. A good fit between the theoretical model and observed data further strengthens the scale's validity. A suite of fit indices was employed to evaluate the model's goodness-of-fit. The chi-square statistic, χ2, which is sensitive to sample size, returned a value of 144.591 with 120 degrees of freedom and a p-value greater than 0.063. When normalized (χ2/df), the obtained value falls within the acceptable range, resonating with the recommendations of Wheaton, Muthen [92], Hermann, Joreskog [93], and Tabachnick and Fidell [94]. Our CFA results exhibited high values for AGFI, GFI, CFI, NFI, and TLI (NNFI), all surpassing the 0.95 threshold [77, 95-97]. The RMSEA and SRMR, indicators of the model's error, were both below 0.02, signifying a perfect fit, consistent with the values cited by scholars for an acceptable fit [76, 98-100]. The PNFI and PCFI exceeded 0.76, suggesting that the model parsimony is satisfactory. Taken together, these CFA results offer a resounding endorsement of the six-dimensional model for the Arabic version of SMS-II, particularly for our sample of Tunisian athletes.

Sensitivity analysis evaluates how different variables, conditions, or data perturbations might impact the outcomes of a study. Our findings indicates that motivation varies across different age groups and the type of sport (team vs. individual). Particularly, team sports athletes aged 13-18 years exhibited greater motivation compared to athletes in individual sports. Conversely, individual sports athletes aged 19-30 years exhibited a pronounced inclination towards intrinsic motivation and introjected regulation relative to team sports athletes. Furthermore, variables like age, sport type, and gender also manifested discernible effects on motivation dimensions. For instance, age and sport type influenced introjected regulation, while gender played a role in shaping external regulation. The type of sport also affected identified regulation. Interestingly, no significant interaction effects were identified, suggesting that these factors influence motivation dimensions independently. In conclusion, the sensitivity analysis highlights the nuances of motivation across various demographic and sport-related variables, offering a comprehensive view of how different factors motivational affect orientations in athletes.

Finally, the results of our study confirm that there is a Tunisian version of the SMS-II with good psychometric properties, respecting the six-factor structure proposed by Pelletier, Rocchi [41] to measure the level of motivation in sport in Tunisia, which represents a step forward for sport psychology in the creation of a measurement tool for all sport type and for both sexes.

Athletes after age 30 have variety motivations, and it appears that motivations for engagement in sport may vary throughout the lifespan [103]. The athlete's motivations affect performance in sport [104]. In the Arab world, studies that focus on motivation in the context of sport remain rare. It is advisable to use this instrument to learn about the importance of the motivational levels of athletes of both sexes and various ages.

However, our research had some limitations. It was necessary to conduct further validations with other instruments (basic needs satisfaction scale) since the athletes also passed through a continuum of adaptation in the activity (i.e., beginner, expert, or professional) which acted on their response. Arab validation could be influenced by Arab world culture, so it is necessary to share this validation with other countries to accommodate cultural changes and examine the general extensibility of athlete outcomes.

Attachments

Attachment

Submitted filename: Response to Reviewers..docx