SIP Report SP2024 (1)

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Statistics

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Feb 20, 2024

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MATH 1308/1309 Charting Sociodemographic Waters: A Statistical Expedition Introduction This statistical inquiry aims to derive meaningful insights from the GSS2022 dataset, utilizing various key variables. The primary purpose is to analyze and draw conclusions about the identified population, shedding light on aspects such as work, marital status, education, happiness, health, and financial satisfaction. The original data source for this investigation is the General Social Survey 2022 (GSS2022). The population under consideration includes respondents from diverse demographic backgrounds, contributing to a comprehensive understanding of societal trends. One major finding of this inquiry reveals intriguing patterns in the relationships between education levels, financial satisfaction, and the overall well-being of the surveyed individuals. Methods This study is fundamentally an observational analysis, specifically a cross-sectional study. The data utilized for this investigation originate from the General Social Survey 2022 (GSS2022). The source data were collected through a meticulously structured survey questionnaire administered to a diverse sample of individuals across different demographics and social strata. This cross-sectional design allows for a snapshot view of a broad population at a specific point in time. The variables examined in the findings section encompass a range of sociodemographic aspects, including: WRKSTAT (Work Status): Qualitative variable. Describes individuals' employment status with categories such as "Work Full Time," "Work Part Time," and others. MARITAL (Marital Status): Qualitative variable. Captures individuals' current marital status, including categories like "Married," "Widowed," and "Never Married." CHILDS (Number of Children): Quantitative variable. Represents the count of children, allowing for numerical analysis. EDUC (Education Level): Quantitative variable. Indicates the education level attained by respondents on a numerical scale from 0 to 20. HAPPY (Happiness): Qualitative variable. Gauges overall happiness levels with categories such as "Very Happy," "Pretty Happy," and "Not Too Happy." HEALTH : Qualitative variable. Assesses general health status with categories such as "Excellent," "Good," "Fair," and "Poor." SATFIN (Financial Satisfaction): Qualitative variable. Measures satisfaction with present financial situations, including responses like "Pretty Well Satisfied," "More or Less Satisfied," and "Not Satisfied At All." Page 1 of 12

MATH 1308/1309 SEXBIRTH1 (Sex at Birth): Qualitative variable. Indicates recorded sex at birth, categorized as "Male" or "Female." TOTALINCENTIVE : Quantitative variable. Represents the total incentive for each case, allowing for numerical analysis. Each variable's classification as qualitative or quantitative is justified based on its inherent nature and the type of information it contributes to understanding the respondents' characteristics. This distinction ensures a comprehensive and accurate exploration of the dataset in the subsequent findings. Findings The variables assessed were MARITAL, CHILDS, HEALTH, and TOTALINCENTIVE  Numerical Summaries of Quantitatice Variables: CHILDS represents the count of children individuals have within the dataset. The mean (1.93) is slightly higher than the median (1.5), indicating a right-skewed distribution. The right-skewed distribution, as evidenced by the higher mean than median, suggests the presence of a few respondents with relatively more children. TOTALINCENTIVE represents the total incentive for each case within the dataset. The mean (124) and median (122) are close, suggesting a relatively symmetric distribution. This indicates that the incentive values are evenly distributed around the center, with no Page 2 of 12 Column Mean Std. dev. Min Q1 Median Q3 Max CHILDS 1.9333333 2.0073312 0 0 1.5 3 8 Column Mean Std. dev. Min Q1 Median Q3 Max TOTALINCENTIVE 124 51.816822 52 87 122 162 200

MATH 1308/1309 significant skewness. The standard deviation (51.82) indicates moderate variability in the total incentive values.  Relative Frequency distribution of Qualitative variable: RelativeFrequency table results for MARITAL: Count = 60 MARITAL Relative Frequency Divorced 0.16666667 Married 0.36666667 Never Married 0.33333333 Separated 0.016666667 Widowed 0.11666667 Most Frequent Response: The most frequent marital status is "Married" with a relative frequency of 0.3 36666667 . This indicates that a significant portion of the sampled population is currently married. Least Frequent Response: The least frequent marital status is "Separated" with a relative frequency of 0.016666667 . This suggests that separation is less common among the respondents. Relative Frequency table results for HEALTH: Count = 60 HEALTH Relative Frequency Excellent 0.25 Fair 0.16666667 Good 0.5 Page 3 of 12

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MATH 1308/1309 HEALTH Relative Frequency Poor 0.083333333 Most Frequent Response: The most frequent health status is classified as "Good" with a relative frequency of 0.5. This indicates that a significant portion of the sampled population perceives their health as good. Least Frequent Response: The least frequent health status is categorized as "Poor" with a relative frequency of 0.083333333. This suggests that a smaller proportion of respondents consider their health to be poor, indicating a generally positive perception of health among the sampled individuals.  Graphical summaries : Frequency Histogram for CHILDS Page 4 of 12

MATH 1308/1309 The frequency histogram for the variable CHILDS illustrates the distribution of the number of children among respondents. The histogram visually represents the count or frequency of each distinct value or range of values.The majority of respondents have fewer children, with peaks around 0, 1, and 2. There is a noticeable decline in frequency as the number of children increases. The distribution is right-skewed, indicating that a significant proportion of respondents have a relatively smaller number of children, while fewer individuals have larger families. The histogram effectively conveys the shape of the distribution, highlighting the prevalence of respondents with one or two children compared to those with more, and provides a visual representation of the diversity in family sizes within the sampled population.  Relative Frequency bar chart for variable: WRKSTAT The relative frequency bar chart for the variable WRKSTAT, visually represents the distribution of work statuses among respondents. Each bar corresponds to a specific work status category, and the height of the bar reflects the relative frequency of that category. In this specific distribution: Page 5 of 12

MATH 1308/1309 "Work Full Time" has the highest relative frequency, indicating that a substantial portion of respondents is employed full time. "Retired" is also prominent, suggesting a significant number of respondents are retired. "Keeping House" and "Work Part Time" have noticeable relative frequencies, indicating that some individuals are primarily engaged in housekeeping or working part-time. "In School" has a lower relative frequency, suggesting a smaller proportion of respondents are currently pursuing education. This visual representation enhances the understanding of the distribution of work statuses within the sampled population, providing insights into the prevalence of different employment and activity categories. Variable Trends BOXPLT FOR TOTALINCENTIVE ACROSS THE VARIABLE SEXNOW1 Page 6 of 12

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MATH 1308/1309 Summary statistics for TOTALINCENTIVE: Group by: SEXNOW1 BOXPLOT TREND FOR TOTALINCENTIVE ACROSS THE VARIABLE HAPPY Page 7 of 12 SEXNOW1 Min Q1 Median Q3 Max IQR Female 52 87 127 200 200 113 Male 52 87 112 152 200 65

MATH 1308/1309 Summary statistics for TOTALINCENTIVE: Group by: HAPPY HAPPY Min Q1 Median Q3 Max IQR Not Too Happy 52 52 102 200 200 148 Pretty Happy 52 87 122 157 200 70 Very Happy 62 102 127 144 200 42 Comparing Shape: For SEXNOW1: Both male and female boxplots have similar shapes, indicating comparable distributions. For HAPPY: The boxplots for different happiness levels show varying shapes. "Not Too Happy" has a larger spread, while "Very Happy" has a narrower spread. Comparing Center (Median): For SEXNOW1: Females have a higher median (127) compared to males (112), indicating that females, on average, have higher TOTALINCENTIVE values. For HAPPY: The medians increase from "Not Too Happy" (102) to "Pretty Happy" (122) to "Very Happy" (127), suggesting an association between happiness and incentive levels. Comparing Spread (IQR): For SEXNOW1: Females have a larger interquartile range (IQR) of 113 compared to males with an IQR of 65, indicating more variability in incentive values among females. For HAPPY: "Not Too Happy" has the largest IQR (148), followed by "Pretty Happy" (70) and "Very Happy" (42), indicating decreasing variability with increasing happiness levels. Page 8 of 12

MATH 1308/1309 Outliers: For SEXNOW1: There are no obvious outliers for both males and females based on the provided summary statistics. For HAPPY: No specific information about outliers is provided, but you can identify outliers by comparing individual data points against the whiskers in the boxplots. In summary , these comparisons suggest that there are differences in the distribution of TOTALINCENTIVE based on the variables SEXNOW1 and HAPPY. Females tend to have higher median incentive values, and there is an indication of decreasing variability in incentive levels with increasing happiness. Further detailed examination with the actual boxplots may reveal additional insights. Social Impact Variables such as "Childs" (number of children), "TotalIncentive" (total incentive received), "Marital" (marital status), "Health" (self-reported health status), "Wrkstat" (work status), "Educ" (educational level), "Satfin" (satisfaction with financial situation), "Sexnow1" (gender), and "Happy" (self-reported happiness level). Analyzing these variables can provide insights into social trends within the identified population. Childs : The "Childs" variable indicates the number of children for each individual. The distribution of this variable may reflect trends in family size within the population. A low number of children might suggest a trend toward smaller families, possibly influenced by social and economic factors such as changing attitudes towards family planning and career priorities. TotalIncentive : "TotalIncentive" represents the total incentive received by individuals. The distribution of incentives can provide insights into the economic well-being of the population. Higher incentives may indicate better financial opportunities or benefits, while lower incentives may suggest economic challenges. This could reflect broader economic trends or government policies affecting financial support. Marital : The "Marital" variable classifies individuals into categories such as "Never Married," "Married," "Widowed," and "Divorced." Examining the distribution of marital status can reveal trends in relationship patterns within the population. For instance, a high proportion of married individuals may suggest stability and traditional family structures, while a significant number of divorced or never-married individuals could indicate changing social norms. Page 9 of 12

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MATH 1308/1309 Health : "Health" reflects self-reported health status. Analyzing this variable can provide insights into the overall health of the population. A high percentage reporting good or excellent health may indicate a generally healthy population, while a higher proportion reporting poor health may raise concerns about potential health challenges within the community. Wrkstat : "Wrkstat" categorizes individuals based on their work status, such as "Work Full Time," "Retired," or "Unemployed." This variable can illuminate employment trends within the population, shedding light on the prevalence of retirement, full-time employment, or unemployment. Changes in work status may reflect shifts in the economy or job market. Educ : The "Educ" variable indicates the educational level of individuals. Analyzing the distribution of education levels can offer insights into the educational attainment within the population. A higher percentage of individuals with advanced degrees may suggest a well-educated population, potentially impacting socioeconomic factors and career opportunities. Satfin : "Satfin" measures satisfaction with financial situations. Examining this variable can provide information on the economic well-being and financial satisfaction of the population. Higher satisfaction levels may indicate economic stability, while lower satisfaction levels may highlight financial challenges. Sexnow1 : "Sexnow1" categorizes individuals by gender. Analyzing the gender distribution can reveal demographic patterns and gender imbalances within the population. Understanding gender demographics is crucial for addressing social issues related to gender equality and representation. Happy : The "Happy" variable represents self-reported happiness levels. Analyzing this variable can provide insights into the overall well-being and contentment of the population. Higher reported happiness levels may suggest a satisfied and content community, while lower levels may indicate potential areas of concern or dissatisfaction. In summary , a detailed analysis of these variables allows for a comprehensive understanding of social trends within the identified population, covering aspects such as family dynamics, economic well-being, employment patterns, education levels, and overall happiness. To draw more meaningful comparisons, historical data and external sources should be referenced to contextualize the findings and identify any significant shifts or trends over time. Conclusion The statistical inquiry conducted on the provided dataset offers valuable insights into various aspects of the identified population, such as family structure, economic well-being, health, and overall happiness. By examining variables like marital status, educational levels, work status, and self-reported health, the inquiry provides a comprehensive snapshot of the social dynamics within the community. Page 10 of 12

MATH 1308/1309 These inferences are meaningful for several reasons. Firstly, understanding family structures and sizes informs policymakers and community leaders about potential shifts in societal norms, guiding the development of family- oriented programs or support systems. Additionally, insights into economic well-being and work status are crucial for addressing issues related to employment opportunities and financial stability within the community. Moreover, the self-reported health status and happiness levels shed light on the overall well-being of individuals. This information is pertinent for healthcare professionals and community organizations in tailoring health and well-being initiatives to address specific needs and challenges within the population. To enhance the meaningfulness of the statistical inquiry, comparisons with established surveys, such as the General Social Survey (GSS), or other relevant studies can be beneficial. The GSS, conducted by the National Opinion Research Center (NORC) at the University of Chicago, provides a comprehensive view of the social trends and attitudes in the United States. By aligning findings with such benchmark data, the statistical inquiry gains contextual relevance and allows for a more robust understanding of how the identified population compares to broader social trends. In a community context, the results of this inquiry can serve as a foundation for evidence-based decision-making. Policymakers, local authorities, and community organizations can use these insights to tailor interventions, allocate resources effectively, and address specific needs identified within the population. By incorporating historical data and findings from established surveys, the statistical inquiry gains credibility and becomes a powerful tool for shaping policies and initiatives that promote the well-being of the community. Page 11 of 12

MATH 1308/1309 References StatCrunch. (2019). Pearson Education Inc. https://www.statcrunch.com/app/index.html? dataid=4548301# The General Social Survey. (2021). General Social Survey 2022 (GSS2022.) [Data set]. NORC at the University of Chicago. https://gss.norc.org/pages/GSS50.aspx Page 12 of 12

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