2.1. Research Model
This study was designed within the scope of relational survey models in which possible theoretical causal relationships between athletes' cognitive flexibility, decision making, happiness and forgiveness were examined. Researchers do not intervene in the relationships in relational survey models. The researcher, who can provide clues in relational research, does not look for a relationship related to causes and effects [45].
2.2. Study Group
The study group of the research consists of 623 athletes who are 18 years of age or older and actively engaged in licensed sports as of 2023. As a result of the assumption tests of the Structural Equation Model, which is a multivariate analysis type, it was concluded that the remaining 618 observations were of sufficient size considering the minimum number of observations to be reached [46].
2.3. Data Collection Tools
Forgiveness Decision Scale
The Decision to Forgive Scale, adapted to Turkish culture by Ekşi, Parlak, and Demir Celayir [47], consists of 6 items and a single dimension. The scale, which does not have reverse items, is a 5-point Likert-type scale ranging from Strongly Disagree (1) to Strongly Agree (5). A high score indicates a person's high decision to forgive. For the adaptation study of the Forgiveness Decision Scale to Turkish Culture, 297 pre-service teachers over the age of 18 participated. The Cronbach's alpha reliability coefficient calculated to obtain the reliability evidence of the scale was 0.91, and this value revealed that the scale is a highly reliable measurement tool. In addition, the item-total correlations of the items were examined to obtain evidence of the construct validity of the scale and it was found that these values ranged between 0.59 and 0.84. The correlation coefficients were also found to be statistically significant.
Cognitive Flexibility Scale
The Cognitive Flexibility Scale developed by Bilgin [48] consists of 19 items. The scale items consist of pairs of adjectives (e.g. I can, I cannot, - I am successful, I am unsuccessful). The lowest score that can be obtained from the scale is 21 points and the highest score is 105 points. Reliability and validity were tested using a sample of 637 adolescents. The higher the scores obtained from the scale, the closer the individual is to cognitive flexibility. In the reliability study conducted on the scale, the Cronbach's alpha coefficient for the whole scale was found to be 0.92. The item-total correlations of the items ranged between 0.49 and 0.63. The test-retest correlation coefficient was 0.77 and the halving coefficient was 0.87 over an eight-week interval.
Natural Decision Making Scale
Developed by Sundu and Yaşar, [49] the Natural Decision Making Scale consists of 6 items and one dimension. The Cronbach's Alpha coefficient calculated for the whole scale is 0.80. There are no reverse coded items in the scale, which has a 5-point Likert structure ranging from Strongly Agree to Disagree. Natural decision making, which is the subject of the research, was preferred in the scale created with 554 participants over the age of eighteen who are working in different professions, since it is seen as the process of focusing on and choosing the most appropriate one among various options. In addition, the factor loadings of the Natural Decision Making scale items ranged from 0.68 to 0.87 and all of them were statistically significant.
Happiness Scale
The Happiness Scale developed by Demirci and Eksi [50] has a unidimensional structure consisting of 6 items. The scale, which does not contain any reverse-coded items, has a 5-point Likert structure (1: Not at All Suitable for Me, 5: Completely Suitable for Me). Cronbach Alpha internal consistency coefficient of the scale was calculated as 0.83. The Happiness Scale, which was created to investigate the characteristics of a peaceful and happy life, was conducted with 900 participants over the age of 18. In addition, the test-retest reliability coefficient obtained from the reapplication of the scale to 62 participants at three-week intervals was calculated as 0.73. The factor loadings of the items in the scale ranged between 0.59 and 0.78.
Confirmatory factor analysis (CFA) was conducted to reveal the psychometric qualities of the data collection tools used in this study. The aim of CFA is to discover the factor or factors based on the relationships between variables by revealing the sources of variance and covariance [51]. In order to obtain evidence for the reliability and convergent validity of the scales used in the study, AVE values were calculated and presented in Table 1. According to the research findings, the values calculated for CR, which is the evidence of construct relability, should be above 0.50 [52], the average variance extracted for convergent validity, i.e. AVE, should be in the range of CR≥AVE≥0.50 [53], but in cases where AVE values are less than 0.5, the CR≥0.7 criterion can be accepted for convergent validity. Since all scales included in the analysis were unidimensional, divergent validity evidence such as maximum shared squared (MSV) and average mean square of shared variance (ASV) were not examined.
Table 1. Reliability and Validity Findings of The Scales Used
Scales
|
CA
|
CR
|
AVE
|
CA
|
CR
|
Convergent
Validity
|
Happiness
|
0.87
|
0.84
|
0.49
|
✓
|
✓
|
✓
|
Cognitive Flexibility
|
0.95
|
0.94
|
0.44
|
✓
|
✓
|
✓
|
Natural Decision Making
|
0.70
|
0.70
|
0.40
|
✓
|
✓
|
✓
|
Forgiveness
|
0.86
|
0.86
|
0.54
|
✓
|
✓
|
✓
|
Criteria
|
≥.70
|
≥.70
|
≥.70>CR
|
≥.70
|
≥.70
|
AVE<CR
|
When the results of Table.1 are taken into consideration, it is concluded that all measurement tools used within the scope of the research provide reliable and valid measurements. It can be said that the AVE value obtained in Table 1 is low but acceptable. This is because Fornell and Larcker [53] emphasized that in cases where the CR value is higher than 0.60, AVE less than 0.50 is acceptable and construct validity is sufficient [54].
2.4. Collection of Data
The necessary ethical permission was obtained from the relevant committees before the study. Ethics committee approval was obtained from Mersin University. Voluntary participants were informed that the information received would only be used within the scope of the current study and would remain confidential. Scale forms including demographic information were applied to the participant athletes online for approximately 15 minutes and data were collected.
2.5. Data Analysis
This study was conducted with structural equation modeling (SEM) in order to reveal the mediating relationships of forgiveness in the relationship between cognitive flexibility, decision making and happiness in active licensed athletes. SEM, which is a statistical method that predicts the causal relationships that observed and latent variables may have, puts forward a theoretical framework [55, 56, 57]. The main purpose of SEM is to reveal the relationship patterns of the data obtained as well as the latent variables [58]. SEM, which is widely used to test observed and latent variables and is based on a theoretical foundation [59, 60], is a method that tests and estimates multivariate models in fields such as economics, medicine and psychology [61, 62], and differs from traditional methods by taking into account the measurement errors of the latent variable [63, 16].
Before performing SEM, which is a multivariate statistical technique, assumptions were examined. Within the scope of the assumptions, since the data were collected online, no missing or missing data were found. Then, single and multiple outliers were examined. In this context, the standardized Z values for single outliers ranged between (-3.54, 1.58), and the 445th observation with a value of -4.37 was excluded from the analysis because it produced a single outlier. In this context, since all observations were within the limits of 4 ≥ z ≥ 4 [51], the analysis continued without any single outlier. As a result of the degrees of freedom comparison [64] for the remaining 621 observations, 3 observations (163rd, 390th and 546th) that produced values above the values of Mahalonobis distances (χ23, 0.001=16.27) were excluded from the analysis and the analyses continued with the remaining 618 observations. The hypothesis analyses continued with testing the multicollinearity problem and Variance Inflation Factor (VIF) and Tolerance values were analyzed. In this context, the tolerance values ranged between (0.922, 0.974) and all values were above 0.20; the VIF values ranged between (1.027, 1.084) and all observation values were below 5, indicating that there was no multicollinearity problem among the items [51]. The Durbin-Watson value, which is an additional test for multicollinearity, was obtained as 1.93, and the fact that this value is close to 2 [65] is an indication that the errors are not related to each other.
Testing the measurement model is one of the basic assumptions of SEM analyses. Table.2 presents the goodness of fit and poorness of fit values of the measurement model including all the variables within the scope of the study and the criterion criteria against which these values will be compared.
Table 2. Measurement Model Results
Variables
|
X2 /sd
|
RMSEA
|
SRMR
|
CFI
|
NFI
|
NNFI
|
CFA Measurement Model
|
2555/623
|
0.08
|
0.05
|
0.95
|
0.93
|
0.95
|
Perfect fit
|
≤ 3
|
≤.05
|
≤.05
|
≥.95
|
≥.95
|
≥.95
|
Good fit
|
3≤ x2 /sd ≤ 5
|
.05≤RMSEA≤.08
|
.05 ≤ SRMR ≤.10
|
.90≤CFI <.95
|
90≤NFI<.95
|
90≤NFI<.95
|
Considering the goodness of fit statistics found in Table 2 and the literature criteria, it is observed that the tested measurement models match with excellent and good fit criteria. The testing of measurement models is an important assumption of SEM analysis [66], and the model-data fit evaluation is evaluated in Table 2 by considering excellent and acceptable fit values [67, 68, 69, 70]. It is recommended to report RMSEA, x2 degrees of freedom and significance values, SRMR and CFI values as a minimum in studies based on CFA [70]. The measurement model tested with the dependent, independent and mediator variables in the study matches with excellent fit and good fit indicators.
In this study, which was conducted on the basis of SEM by taking into account the mediation model of Baron and Kenny [71], the status of the relationships between the dependent, independent and mediator variables is taken into account in mediation decisions. In the first stage, the relationship between the dependent and independent variable is tested. This relationship should be significant. In the next stage, the fact that the mediating variable added to the model causes the relationship between the independent and dependent variable to be lost reveals that the mediating variable is full mediation, while only a decrease in the relationship between the independent and dependent variable or a slight decrease in the level of the standardized value reveals that it is partial mediation [72].
Before proceeding with the decision analyses regarding mediation studies, all of the binary relationships between the variables to be considered within the scope of the model must be significant. In this context, the analyses of the binary relationships between the dependent, independent and mediator variables hypothesized for Model-1 and Model-2 are evaluated based on the measurement model outputs and presented in Table 3 and Table 4.
Table 3. Correlations Between Study Variables
Variables
|
Happiness
|
Decision Making
|
Happiness
|
---
|
|
Decision Making
|
.11**
|
---
|
Forgiveness
|
.23**
|
.30**
|
** p < .01
Table 4. Correlations Between Study Variables
Variables
|
Happiness
|
Cognitive Flexibility
|
Happiness
|
---
|
|
CognitiveFlexibility
|
.54**
|
---
|
Forgiveness
|
.23**
|
.14**
|
** p < .01
Therefore, within the scope of mediation, hypotheses 1,2,3,4,5,6,7 of the theoretical models in Figure 1 and Figure 2 were confirmed and the prerequisites for the mediation study were provided.