*2.2. Participants*

The sample consisted of two groups of inhabitants of Eastern Poland (*n* = 452). The first was made up of women (*n* = 226), and the second was made up of men (*n* = 226). The participants were 18–80 years old. Detailed sociodemographic characteristics of the respondents by gender are presented in Table 1.


**Table 1.** Sociodemographic characteristics of the surveyed women and men.

Markings: *M*—mean, *SD*—standard deviation, *t*—value of Student's *t*-test for independent data, *p*—significance level.

The analyzed groups were homogeneous in terms of age, number of children, place of residence, education, marital status and professional activity.

#### *2.3. Physical Activity Measurements*

The Short Form *Physical Activity Questionnaire* (*IPAQ-SF*) was used to measure weekly physical activity. It contains seven questions about the time spent on activities that require vigorous and moderate physical effort, as well as time spent on walks and time spent in the form of passive rest (sitting, lying down). Weekly exercise level can be estimated in MET units (minute/week). It is the product of the activity coefficient for a specific activity, the number of active days and its duration in minutes. On this basis, the level of physical activity of the examined person is determined, which may be: (a) high—from 3 to 7 days of intense physical exertion or at least 1500 MET; (b) sufficient—3 to 7 days of vigorous

physical activity for at least 20 min a day or 5 to 7 days of moderate exercise/walking for at least 30 min a day or 5 to 7 days of any physical activity that in total exceeds 600 MET; (c) insufficient—lack of physical activity or failure to meet the conditions of the two above-mentioned levels [25,50].

#### *2.4. Mental Health Measurements*

The *General Health Questionnaire* (*GHQ-28*) was used to measure mental health. The tool is used to assess mental health, which is divided into four dimensions: somatic symptoms, anxiety and insomnia, social dysfunction and symptoms of depression. The *GHQ-28* enables the identification of people whose mental condition has been subject to a temporary or long-term breakdown as a result of experienced difficulties or as a result of mental illness, and those who are at a significant risk of mental health disorders. The cut-off point is a score of 12 or more. The questionnaire has high internal consistency and validity rates. The values of Cronbach's *alpha* coefficients, calculated in the studied population of women, ranged from 0.76 to 0.82, and in the population of men ranged from 0.76 to 0.83 [51].

#### *2.5. Cognitive Functioning Measurements*

The *Attention and Perceptiveness Test* (*TUS*) version 6/9 was used to measure cognitive functioning in terms of attention and perceptiveness. The tool is used to assess cognitive disorders in three dimensions: perceptual work, perception deficits and attention deficits. The *TUS* enables the identification of people whose cognitive functioning condition has been subject to a temporary or long-term breakdown as a result of experienced difficulties or as a result of illness, and those who are at a significant risk of cognitive disorders. The questionnaire has high internal consistency and validity rates. The values of the absolute stability coefficients (3-week interval between tests), calculated in the studied population of women, ranged from 0.77 to 0.81, and in the population of men ranged from 0.78 to 0.83. The results were converted to sten scores [52].

#### *2.6. Social Functioning Measurements*

To measure social functioning during the COVID-19 epidemic, the *Social Functioning Scale* (*SFS*) was used. This scale was constructed for this study. The tool was developed on the basis of Falvo's [18] concept of social functioning. The *SFS* measures the quality of social functioning during the COVID-19 epidemic in three spheres, which include family and interpersonal and professional relationships. The test contains 21 questions that respondents refer to on a six-point Likert scale. The answers range from *definitely no* to *definitely yes*. The test validation and normalization procedure were carried out on a sample of 700 adults. The content validity coefficients of the *CVR* ranged from 0.96 to 1.00. The theoretical validity was verified by exploratory factor analysis with simple Oblimin rotation and Kaiser normalization and confirmatory factor analysis. Criterion validity was estimated on the basis of the analysis of the correlation matrix with dimensions theoretically related to social functioning: self-esteem, life satisfaction, social support and the results of other tests measuring social functioning. Cronbach's *alpha* coefficients in the group of studied women ranged from 0.81 to 0.88, and in the population of men, from 0.83 to 0.90. The results were converted to sten scores.

#### *2.7. Measurements of Controlled Variables*

For the measurement of controlled variables, a questionnaire created for the needs of the conducted research was used. It consisted of a series of questions about sociodemographic data (gender, age, place of residence, education status, marital status, number of children, professional activity) and the health condition of the respondents.

#### *2.8. Statistical Analysis*

Statistical calculations were performed on anonymized data using IBM SPSS 27 with AMOS software.

The description of the researched sample was based on the calculation of the percentage distribution of the qualitative data frequency, the mean values, standard deviation and minimum and maximum values of quantitative parameters.

The significance level of intergroup differences in terms of qualitative data was verified using the *c*2 test. The reliability of the tests was estimated based on the Cronbach *alpha* measures.

The shape of the variable distributions was estimated on the basis of the Kolmogorov– Smirnov test. Levels of activity of the research subjects were compared using a *c*2 test, while the effect size was determined based on Cramer's *V* value. The verification of intergender differences was carried out using Student's *t*-test for independent data, the statistically significant results of which were supplemented by estimating the size of the effects using Cohen's *d* coefficient.

The characteristics of the physical activity of the respondents, their mental health, cognitive functioning and social functioning were determined on the basis of the mean value, standard deviation and minimum and maximum values.

The estimation of measurement models and the interactive structural model was performed using SEM structural equation modeling in the confirmatory version, in which the *Maximum Likelihood* method was used. The use of an advanced method of statistical analysis made it possible to verify the occurrence and significance of mutual and multifaceted interaction of individual factors forming the structure of physical activity for women and men, shaping the state of mental health and cognitive disorders, as well as social functioning. In the presented models (measurement and structural), the values placed next to the arrows indicate the estimates of standardized coefficients for a given path, while the values above the observable variables represent the constants in the equation. The coefficients for random factors (variables e) are initially arbitrarily set at the level of 1 as non-standardized, and after standardization, their values are equal to 0 and are not presented.

In the work, the boundary point of committing a type I error is 0.05.
