The study included 365 university students from various universities across Algeria, comprising 157 males (43%) and 208 females (57%). The age distribution was as follows: 261 participants (71.5%) were aged between 18–30 years, and 104 participants (28.5%) were aged between 31–45 years (M = 1.28, SD = 0.452). Regarding education level, 182 participants (49.9%) were undergraduate students, and 183 participants (50.1%) were graduate students. Regarding employment status, 169 (46.3%) were employed, while 196 (53.7%) were unemployed.

We estimated the sample size based on the number of parameters used in our statistical analysis, specifically for confirmatory factor analysis (CFA) and exploratory factor analysis (EFA). According to the general rule of thumb of ten participants per parameter, we focused on two scales: the Flourishing Scale (FS) with 8 items and the Satisfaction with Life Scale (SWLS) with 5 items, totaling 13 items. Therefore, the minimum required sample size was determined to be 130 participants. Our actual sample size of 365 participants exceeds this minimum, ensuring sufficient statistical power and reliability for both CFA and EFA. This estimation aligns with the guidelines provided by MacCallum et al. (1996).

Data were collected online through a structured electronic questionnaire designed using Google Forms. The questionnaire included demographic questions (gender, age, education level, and employment status), the Flourishing Scale (FS), and the Satisfaction with Life Scale (SWLS). Participants were informed about the study’s purpose, assured of the confidentiality of their responses, and instructed to answer honestly. Participation was voluntary. The questionnaire link was distributed via social media platforms, such as Facebook (targeting university student groups), and through email. The study was conducted between August and November 2024.

The Flourishing Scale (FS), developed by Diener et al. (2010) and later validated in Arabic by Al-Dossary (2021), evaluates participants' psychological well-being. This scale comprises 8 items, each rated on a 7-point Likert scale ranging from 1 (strongly disagree) to 7 (strongly agree). Higher scores signify greater levels of flourishing. An example of an item is, "I lead a purposeful and meaningful life."

The Satisfaction with Life Scale (SWLS), created by Diener et al. (1985) and translated into Arabic by Abdallah (1998), measured participants' overall life satisfaction. This scale includes five items, with responses scored on a 7-point Likert scale from 1 (strongly disagree) to 7 (strongly agree). An example of an item is, "In most ways, my life is close to my ideal."

Data analysis was conducted using IBM SPSS Statistics (Version 27.0; IBM Corporation, 2020) for descriptive statistics and exploratory factor analysis (EFA), and IBM AMOS (Version 24.0; Arbuckle, 2016) for confirmatory factor analysis (CFA). Data screening included assessments of skewness and kurtosis, adhering to thresholds of ±2 and ±7, respectively, to evaluate normality (Kline, 2015).

EFA was performed using Principal Component Analysis (PCA), with the Kaiser-Meyer-Olkin (KMO) test for sampling adequacy (≥ 0.70) and Bartlett’s Test of Sphericity (p < .05) to determine the suitability for factor analysis (Hair et al., 2019). Factors were retained based on eigenvalues greater than 1 and cumulative variance exceeding 60% (Field, 2018).

CFA was used to validate the factor structure, utilizing various fit indices: the chi-square to degrees of freedom ratio (χ²/df ≤ 3; Hair et al., 2019), the Comparative Fit Index (CFI ≥ 0.90), the Tucker-Lewis Index (TLI ≥ 0.90), the Root Mean Square Error of Approximation (RMSEA ≤ 0.08; Steiger, 1990), and the Standardized Root Mean Square Residual (SRMR ≤ 0.08; Hu & Bentler, 1999). Reliability was assessed using Cronbach’s alpha (≥0.70; George & Mallery, 2003) and composite reliability (CR ≥ 0.70; Fornell & Larcker, 1981), with convergent validity supported by an average variance extracted (AVE) of at least 0.50.

The measurement invariance of the three-factor model was evaluated across gender and age using a sequential approach. Model comparisons focused on changes in χ²/df, CFI, RMSEA, and SRMR, with a change in CFI (ΔCFI) of less than 0.01 considered evidence of invariance (Cheung & Rensvold, 2002). Additionally, Pearson’s correlation assessed item correlations for the Flourishing Scale (FS) and the relationship between flourishing and life satisfaction, with a correlation coefficient (r) of 0.30 or higher indicating moderate to strong convergent validity (Cohen, 1988). Differences across demographic variables were analyzed using independent samples t-tests and one-way ANOVA (Cohen, 1988).

Descriptive statistics were calculated for the items of the FS – Algerian Version, as presented in Table 1. The mean scores for the items ranged from 4.75 to 5.76, with standard deviations between 1.36 and 1.61, indicating moderate variability in responses. Skewness values ranged from -1.22 to -0.67, and kurtosis values ranged from -0.31 to 1.19. These values fall within the acceptable thresholds of ±2 for skewness and ±7 for kurtosis (Kline, 2015), suggesting that the data distribution for all items approximates normality. This supports the appropriateness of the data for subsequent statistical analyses, including factor analysis.

Exploratory factor analysis (EFA) was conducted using principal component analysis (PCA) to evaluate the scale's structure. Results indicated excellent sampling adequacy (KMO = .898) and significant sphericity (χ² = 1154.840, df = 28, p < .001), confirming the suitability of the data for factor analysis. A single factor was extracted, explaining 60.71% of the total variance. Factor loadings ranged from .59 to .78, with communalities between .35 and .60, indicating that most items contributed substantially to the extracted factor. These results support the unidimensionality of the scale and its validity for measuring the intended construct.

The confirmatory factor analysis (CFA) revealed a marginally acceptable model fit for the initial model with a chi-square statistic (χ² = 78.941, df = 20, p < .001) and a chi-square to degrees of freedom ratio (χ²/df = 3.947). Fit indices, including RMSEA (.09; 90% CI [.070, .111]), SRMR (.04), GFI (.947), CFI (.948), and TLI (.927), provided mixed evidence of validity, with RMSEA suggesting potential misfit. Factor loadings ranged from .53 to .75, indicating strong relationships between the latent construct and its indicators.

Examination of modification indices indicated improved model fit when the error covariance was freed between Items 1 and 2, both driven by social relationships that foster purpose, share variance beyond the flourishing factor, justifying the adjustment. The revised model yielded a chi-square statistic (χ² = 66.015, df = 19, p < .001) and a chi-square to degrees of freedom ratio (χ²/df = 3.474). Fit indices improved with RMSEA (.08; 90% CI: .061–.105), SRMR (.03), GFI (.958), CFI (.959), and TLI (.939). Factor loadings remained consistent, ranging from .53 to .75, further supporting the validity of the refined model. See Figure 1 for the revised CFA model.

Reliability analysis confirmed good internal consistency with a Cronbach’s alpha of .87, composite reliability (CR) of .87, and average variance extracted (AVE) of .46.

The inter-item correlations for the FS-Algerian version (Table 2) demonstrate positive and statistically significant relationships among all eight items at p < 0.01, with Pearson correlation coefficients ranging from .46 to .76. These results indicate strong internal consistency, supporting the unidimensional structure of the scale. Overall, the findings confirm the scale's reliability and its suitability for assessing flourishing as a cohesive construct.

The measurement invariance of the three-factor model was evaluated for gender and age as shown in Table 3, the model fit indices were satisfactory for both groups. For gender, the χ²/df values ranged from 2.44 to 2.63, with CFI values between .924 and .950, and RMSEA values slightly above the ideal cutoff. For age, the χ²/df values ranged from 2.24 to 2.50, with CFI values between .936 and .952, and RMSEA values from .058 to .064. These results support the invariance of the three-factor model across gender and age.

To assess the concurrent validity of the Flourishing Scale, a significant positive correlation was found between the Satisfaction with Life Scale (SWLS) and flourishing, with a Pearson correlation coefficient of r = .46 (p < .01). This indicates a moderate positive relationship, suggesting that higher levels of life satisfaction are associated with greater flourishing within the study sample.

The impact of demographic variables—gender, age, education level, and work status—on flourishing was analyzed. Gender differences showed no significant effect, with men (M = 41.53, SD = 8.085) and women (M = 41.97, SD = 9.258) having similar flourishing scores, t(363) = -0.472, p = .637. Age groups (18–30 years, 31–45 years) also did not show significant differences, t(363) = -0.728, p = .467. No significant differences in flourishing were found between undergraduate (M = 41.15, SD = 8.483) and graduate students (M = 42.40, SD = 9.015), t(363) = -1.359, p = .175. Similarly, work status did not show significant differences, with employed participants (M = 42.69, SD = 8.377) reporting slightly higher flourishing scores than unemployed participants (M = 40.99, SD = 9.031), t(363) = 1.845, p = .066. These results suggest that demographic variables do not significantly affect flourishing in the sample.

This study demonstrated strong psychometric properties for the Flourishing Scale (FS) in the Algerian context, but certain limitations should be addressed. The sample was limited to university students, restricting the generalizability of the findings to other populations. Future research should validate the FS across broader demographic and cultural groups. The cross-sectional design also limits causal inferences, highlighting the need for longitudinal studies to assess the stability of flourishing and its interactions with related constructs over time.

Additionally, exploring the FS's relationship with culturally specific constructs and using qualitative approaches could enhance its contextual relevance. Further investigations into measurement invariance across diverse subgroups, such as rural versus urban populations, would ensure its reliability across Algeria’s demographic diversity. Addressing these gaps will strengthen the scale’s applicability and contribute to a deeper understanding of well-being in diverse settings.

This study validated the Flourishing Scale (FS) within the Algerian context, confirming its reliability and construct validity as a measure of psychological well-being. The FS demonstrated a robust unidimensional structure, strong internal consistency, and meaningful correlations with other well-being indicators, reinforcing its applicability in non-Western settings. By adapting and validating the scale for university students, this research bridges an important gap in understanding flourishing in culturally specific contexts and provides a practical tool for assessing well-being. The findings underscore the scale’s versatility across demographic groups and its potential for broader applications. Future studies should expand its use across different populations and explore its connections with constructs like resilience and work-life balance to deepen its relevance in promoting psychological health.