Research Background
Statistical analysis aims to investigate the patterns found in the variables under study and provide a foundation for making informed, sound decisions with reduced and systematic bias. This paper evaluates the results of a descriptive statistical analysis performed simultaneously across several variables. Descriptive statistics encompasses many tools, including measures of central tendency, confidence intervals, methods for variability, and frequency distributions — the choice of a particular focus depends on the distribution itself and the desired outcomes of the analysis.
The focus of the work is set on examining several different variables. These include the age of respondents in the survey population (continuous), the highest school grade completed (continuous), race and ethnicity (nominal), currently employed (nominal dichotomous), and family income (continuous). As follows, the dataset comprises both quantitative and qualitative variables, requiring different descriptive analysis tools.
Age
The present analysis is structured so that each of the five variables used, or more specifically, the results of their analyses obtained with SPSS, is discussed sequentially; once the individual analyses are completed, general conclusions are drawn for the whole sample. First, the analysis’s indicator of interest was the respondents’ age. The mean age of individuals in the sample was 36.64 (SD = 6.20) years.
Notably, among the 1,000 participants surveyed, the youngest was 19.39 years old, and the oldest was 49.43 years old. This gives a range of 30.05 years. The calculated standard deviation indicates that, on average, the age of each of the thousand respondents differs from the mean (M = 36.64) by 6.20 years (Shi et al., 2020). This indicates a slight variation in the data.
From the collected results, it is also acceptable to assess the tendency of the age distribution to be normal. On the one hand, the calculated skewness is generally close to zero, confirming the distribution’s proximity to normality. On the other hand, the histogram of age shows that a standard curve does not poorly approximate the distribution. In other words, strictly speaking, the age distribution is not perfectly normal, but it has a clear tendency to be so.
School Grade
Second, the highest school grade completed was also analyzed to obtain the sample’s average perceptions. It was shown that the mean of the highest school grade completed is 11.28 (SD = 1.56), which indicates, on the one hand, a mean deviation of each respondent’s value from the mean (M = 11.28) by a value equal to 1.56 and, on the other hand, a relatively low spread of data.
The number of values was 989, indicating 11 missing records in the whole sample compared to the age distribution. The minimum value of the variable was one, and the maximum value was 16. In this case, the tendency towards normality is also observed, as the skewness (-.727) is still close to zero, and the standard curve fits the distribution of the indicator well.
Family Income
Third, concluding the analysis of continuous numerical variables, we should focus on family income. This variable has been measured quantitatively, with higher values indicating greater family financial wealth and vice versa. The descriptive analysis showed that the mean family income for the sample of 895 was $1,172.59 (SD = $788.153). In this case, the standard deviation is closer to the mean, suggesting a departure from normality and increased variation in the data.
However, the histogram and skewness index (2.030) confirm a right-skewed distribution (Turney, 2023). The minimum family income in the sample was $0.00, while the maximum was $6,593.00. This implies that, unlike the previous two continuous variables, the family income variable is not normally distributed.
Race and Ethnicity
We also studied two qualitative variables with categorical levels, which could not be assessed using central tendency and variability measures. In addition, if the distributions of these variables had been visualized, bar charts would have been appropriate rather than histograms (Boels et al., 2019). Fourth, the variable race and ethnicity, which, as the name suggests, assesses the respondent’s ethnicity, was used for analysis.
The sample was shown to have 998 values, indicating that 2 records were missing and were not included in the calculation of relative frequencies. The dominant portion of the sample (80.5%, n = 803) was represented by “Black, not Hispanic”, 12.8% (n = 128) characterized themselves as “Hispanic”, 5.3% (n = 53) were “White, not Hispanic”, and the remainder of the responding sample (1.4%, n = 14) was represented by other ethnicities not listed among the options. This implies that the majority of the sample was assigned to Black respondents.
Current Employment
Fifth, unlike the previous variable, current employment had only two levels and could thus be categorized as a binary variable. This indicator asked respondents whether they were employed at the time of the survey and offered only two responses: yes or no. As last time, the total number of respondents was 998, resulting in 2 missing values.
For example, the majority of the sample (54.7%, n = 546) reported not being employed at the time of the survey. In contrast, 45.3% (n = 452) of participants responded affirmatively to this question, indicating that a smaller proportion of the sample was employed. Strictly speaking, this leads to two results. On the one hand, participants were unemployed when they took the survey. However, the differences between the two proportions may not have been significant; thus, such conclusions should be made with caution.
References
Boels, L., Bakker, A., Van Dooren, W., & Drijvers, P. (2019). Conceptual difficulties when interpreting histograms: A review. Educational Research Review, 28, 1-23.
Shi, J., Luo, D., Weng, H., Zeng, X. T., Lin, L., Chu, H., & Tong, T. (2020). Optimally estimating the sample standard deviation from the five‐number summary. Research Synthesis Methods, 11(5), 641-654.
Turney, S. (2023). Skewness | definition, examples & formula. Scribbr.