Descriptive Analysis (Age and Gender):
Here, we present the results of the Descriptive Analysis, featuring measures of central tendency and dispersion. The analyzed sample is characterized by a majority in the age range of 66–75 years (53.3%), followed by 56–65 years (33.3%), with minimal representation in the groups of 46–55 and 76–85 years (6.7% each). This inclination towards older ages limits the generalization of results to a wider range of ages and underscores the importance of considering the effect of this bias in data interpretation. Additionally, a gender imbalance is observed, with 60% women compared to 40% men, which may influence the generalization of findings to populations with more balanced gender distributions. This female predominance demands detailed analysis to ensure the validity of the identified trends, highlighting the need for adjustments in future analyses that consider these disparities in both age and gender (Tables 1–2).
Table 1. Age Frequencies
Table 2. Gender Representation in the Sample
Reliability: Cronbach's Alpha Results for Each Scale.
Based on the information analyzed previously and considering that the survey items are designed to measure similar constructs (overall well-being), we will calculate Cronbach's Alpha to assess the internal consistency of the items (Table 3).
Table 3. Reliability Analysis (Cronbach's Alpha)
A Cronbach's Alpha of 0.580 indicates moderate to low reliability. Generally, an alpha value above 0.7 is considered acceptable in social research, although values between 0.6 and 0.7 may be permissible in the early stages of research. The slightly higher value of the alpha for standardized items suggests that standardizing the items could improve internal consistency. With 41 items, the scale is quite extensive. The means and standard deviations of the items vary, indicating different levels of agreement among participants.
Indeed, the scale shows moderate to low internal consistency. This could indicate that some items are not effectively measuring the same construct of well-being among the group of older adult students, as concluded when analyzing means and modes. Cronbach's Alpha is a measure of internal consistency or reliability of a questionnaire. A Cronbach's Alpha value of .580, although moderately low, is not unusual in social sciences, especially in studies involving human attitudes and perceptions, which tend to be more subjective and variable. In this regard, variability in the ages of respondents could contribute to a lower Cronbach's Alpha. Differences in life stages could significantly influence how individuals respond to questions about their well-being, relationships, and self-perceptions. Each age group may have different perspectives and experiences affecting how they answer the questionnaire's questions.
Indeed, a person's priorities, concerns, and values can change significantly throughout their life. For example, younger individuals might be more focused on career development and relationships, while older individuals might reflect more on life satisfaction and deep personal connections. On the other hand, life's accumulated experiences can alter one's self-perception and perception of relationships. Older individuals may have a more nuanced perspective or accept aspects of their lives that younger ones are still exploring or challenging. Third, the quantity and quality of social relationships tend to change with age. Younger people might have wider but shallower social networks, while older individuals might have smaller but deeper networks.
These differences can lead to greater variability in responses among age groups, which could reduce the internal consistency of the questionnaire measured by Cronbach's Alpha (Table 4).
Table 4. Summary Item Statistics
Comparisons and Correlations: T-Test/ANOVA Results.
Given our interest in comparing responses between different groups, that is, comparing well-being according to age or gender, we will use the T-Test (for two groups) or ANOVA (for more than two groups).
T-Test by Gender
A series of independent sample t-tests have been conducted to compare the means of two groups by gender, across a variety of items related to the well-being and attitudes of older adult students in class. The groups are divided by gender (1 = men and 2 = women). The initial observation is that there are significant differences by Gender. Indeed, on several items, there are statistically significant differences between the two groups (Table 5).
Table 5. T-Test Results for Each Item with Significant Differences
The bar chart in Fig. 1 demonstrates how, indeed, the T-test analysis has identified several items where there are statistically significant differences between men and women. For instance, item 8, which relates to having people who listen, shows a higher mean for men, indicating that in this study they feel a stronger lack of social support than women do. This is supported by a significance level of p = 0.004, statistically significant, suggesting that the observed difference is unlikely to be due to chance.
For item 11, which deals with the ability to build a comfortable home and lifestyle, women have a higher mean, indicating greater satisfaction in this aspect compared to men, with a significance of p = 0.017.
Similarly, in item 12, women showed greater activity in carrying out self-proposed projects, with a significance of p = 0.009, suggesting that women may be more engaged or have greater autonomy in project activities.
Items 26 and 30 showed higher means for men, suggesting that men may more often experience a lack of close and reliable relationships and a tendency not to attempt significant improvements or changes in their lives, with a significance of p = 0.021 in both cases.
Finally, items 37 and 38 reflect higher means for women, indicating that they feel they have developed more as persons and that life has been a process of learning, change, and growth, with significances of p = 0.012 and p = 0.007, respectively (Fig. 1).
Figure 1. T-test Analysis of Various Items Showing Statistically Significant Differences Between Men and Women
Effect Sizes:
Effect sizes, such as Cohen's d, indicate the magnitude of these differences. Higher values suggest more pronounced differences between groups. For example, items 8 and 26 show relatively large effect sizes, suggesting notable differences in these aspects between groups. Generally, a Cohen's d of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 or higher a large effect (Table 6).
Table 6. Items with a Large Effect Size (d ≥ 0.8)
The Forest Plot graph in Fig. 2 displays the effect sizes for five different items and evaluates the differences between men and women. Thus, Item 8 ("I don't have many people who want to listen to me when I need to talk") shows a Cohen's d effect size of 1.18934, which is considered large by conventional standards. This indicates a notable difference between genders in the perception of having social support to be heard, being more pronounced in men according to the study results.
Item 26 ("I haven't experienced many close and trusting relationships"), with a Cohen's d of 1.39596, also represents a large effect. This suggests a marked difference between men and women in the experience of close and trusting relationships, with a greater impact on the male group.
Meanwhile, Item 30 ("It's been a long time since I stopped trying to make major improvements or changes in my life"), with an effect size of 1.30744, also reflects a substantial difference between genders, where men report more frequently that they have stopped trying to make significant improvements or changes in their lives.
Lastly, items 37 and 38 have effect sizes smaller than 0.8 and, therefore, are not considered large according to the given classification. Although the outcome on these items might still be relevant, the differences between genders are not as pronounced as in the previous items (Fig. 2).
Figure 2. Forest Plot graph showing the effect sizes for five different items assessing the differences between men and women.
The violin plot in Fig. 3 provides a visual representation of the magnitude of differences between men and women for various items. The plot shows that items 8, 26, and 30 have wider distributions of simulated effects, implying a greater certainty that the observed differences are robust and consistent. Items 37 and 38 feature narrower distributions centered close to zero, indicating that any differences between groups are less pronounced and subject to greater variability or uncertainty (Fig. 3).
Figure 3. Violin Plot on a visual representation of the magnitude of differences between men and women for various items.
ANOVA for Comparing Three or More Groups (Age Ranges)
We have already mentioned the ANOVA results earlier when discussing how variability in age could explain alterations in the sample's reliability. Here, we'll explore other approaches.
The ANOVA results reveal areas where perceptions or experiences significantly vary between groups, as well as areas where differences are not significant. By analyzing the ANOVA study items that showed significant differences (Sig. < 0.05), we can gain valuable insight into the areas where the evaluated groups differ in their experiences or perceptions.
The heatmap graph in Fig. 4 visualizes the levels of statistical significance of items, measured through an ANOVA. Each row of the heatmap represents a survey item, and the color of each row corresponds to the p-value obtained in the ANOVA for that specific item. Darker colors (deep blue) indicate a higher p-value and, therefore, lesser statistical significance; lighter colors (red) represent lower p-values, indicating greater statistical significance (Fig. 4).
Figure 4. Heatmap of the statistical significance levels of a series of items, measured through an ANOVA.
When examining the graph, several points stand out. Certain items show lighter colors, indicating a p-value lower than 0.05, and therefore, statistical significance. This evidence suggests significant differences in how different groups have responded to these items. Specific items with significant differences include items 2, 8, 9, 11, 12, 22, 29, 34, and 35, indicating that perceptions and experiences related to these questions vary significantly among the compared groups.
Items 2 ("I often feel lonely because I have few close friends with whom I can share my concerns") and 26 ("I have not experienced many close and trusting relationships") have p-values of 0.025 and 0.041, respectively, suggesting that feelings of loneliness and the quality of close relationships may significantly vary between age groups.
Items 9 ("I tend to worry about what other people think of me") and 34 ("I do not want to try new ways of doing things; my life is fine as it is") with p-values of 0.026 and 0.027, respectively, reveal that concerns about others' opinions and resistance to change also significantly vary among groups.
Items like 12 ("I am an active person in carrying out the projects I set for myself") and 17 ("I feel good when I think about what I have done in the past and what I hope to do in the future") with p-values of 0.011 and 0.002 show significant differences in how individuals from different age groups feel about their activity and life satisfaction.
Thus, items on Loneliness and Social Relationships (Items 2, 26) focus on feeling lonely and lacking close and trusting relationships. The significant differences suggest some groups may experience more loneliness or have fewer intimate relationships compared to others. This could be influenced by factors such as age, lifestyle, or cultural differences (Fig. 5).
Items related to Concerns About Others' Opinions (Items 9, 34) address worry about what others think and resistance to trying new ways of doing things. The significant differences indicate some groups might be more susceptible to social influence or more resistant to change than others (Fig. 5).
Items on Attitude Toward Life and Achievements (Items 12, 17, 22, 29, 35) relate to activity in carrying out projects, satisfaction with past and future achievements, depression due to daily demands, clarity in life goals, and the importance of new experiences. The significant differences could reflect variations in motivation, resilience to stress, and openness to new experiences among the groups. This may be related to differences in education, economic situation, or mental health (Fig. 5).
Figure 5. Sequence diagram showing significant differences between groups in terms of loneliness, concern about others' opinions, and attitude toward life and achievements.
The presence of significant differences in these items highlights areas where the experiences and perceptions of individuals vary considerably between groups. This can be crucial for understanding the specific needs of each group. It's important to analyze these results within the broader framework of our research and consider how differences between groups might be affected by a variety of factors, including, but not limited to, demographics, socioeconomic, and cultural context.
Now, by analyzing the ANOVA items that did not show significant differences (Sig. ≥ 0.05), we can gain a deeper understanding of the aspects in which the evaluated groups have similar experiences or perceptions (Fig. 6). Thus, the items of Expression of Opinions and Self-Assessment (Items 3, 4, 10, 21), relate to confidence in expressing opinions and evaluating one's own life choices. The lack of significant differences suggests that, regardless of the group, people may have similar levels of confidence in their opinions and in how they assess their life decisions.
On the other hand, the items of Life Satisfaction and Self-Perception (Items 1, 5, 7, 18, 19, 31), address aspects such as satisfaction with past life, self-assurance, and personality perception. The absence of significant differences indicates that these feelings may be consistent across different groups, suggesting that factors like self-esteem and overall life satisfaction might not be strongly influenced by the variables that differentiate the groups.
The items of Social Relationships and Support (Items 14, 32), focus on the perception of friendships and trust in relationships. The similarity between the groups suggests that experiences related to social support and the quality of friendships do not vary significantly among them.
The items of Managing Responsibilities and Change (Items 6, 28, 33, 38, 39), explore how people handle responsibilities, their openness to change, and proactivity in improving their life situation. The lack of differences indicates that these aspects of daily life management and attitude toward change are similar among the groups.
The items of Self-improvement and Personal Growth (Items 13, 36, 37), address the perception of self-improvement and personal development. The similarity in results suggests a widespread tendency among the groups toward how they view their personal growth over time.
The items of Facing Challenges and Setting Goals (Items 23, 29, 30), relate to the clarity of life goals and attitudes toward facing challenges and changes. The absence of statistically significant differences could indicate that most individuals, regardless of their group, have similar levels of ambiguity or clarity regarding their goals and their willingness to address life changes.
Therefore, the lack of significant differences in these items is evidence that certain human experiences and perceptions might be universal or less influenced by the specific variables that differentiate the groups in the study (Fig. 6).
Figure 6. Sequence diagram showing how the evaluated groups share similarities across various categories based on the lack of significant differences in the ANOVA items.
To interpret the implications of the ANOVA results within the context of our research, it's crucial to consider the general theme and specific objectives of the study, as depicted in Fig. 7. On one side, there are Areas with Significant Differences (Sig. < 0.05). These items point to aspects where the experiences or perceptions of the groups significantly differ. For example, Loneliness and Intimate Relationships (Item 2), where differences in loneliness may suggest variations in the quality of social relationships among the groups. Concerns about Others' Perceptions (Item 9), where some groups may be more affected by external opinions than others. Activity in Personal Projects (Item 12), where differences in proactivity could reflect variability in motivation or resources among the groups. Lastly, Well-being and Life-related Depression (Items 17 and 22), may indicate differences in overall emotional well-being and how groups manage daily stress.
On the other side, there are Areas without Significant Differences (Sig. ≥ 0.05). Items without significant differences suggest that the experiences or perceptions in these areas are relatively similar among the groups. This implies that certain aspects of human experience or attitudes are more universal or less affected by the variables that differentiate the groups in the study.
Figure 7. Mind map to interpret the implications of the ANOVA results within the research context.