Create Two Smaller Samples N10 And N5 From The Original

Create Two Smaller Samples N10 And N5 From The Original Emotion

Create two smaller samples (n=10 and n=5) from the original Emotional Well-Being population data set using SPSS's Stratified Random Sampling tool. Perform descriptive analysis of the key variables in each of these new data sets (variables: Baseline SF-36 Well-Being Score, Post-Tx Well-Being Score, BMI, Age) and compare your results to the original, larger data set's descriptive analysis results. Report your findings. PART 2 WILL CONSIST OF 2 PAGES. See attached

Paper For Above instruction

Create Two Smaller Samples N10 And N5 From The Original Emotion

This research paper aims to investigate the process of selecting smaller, representative samples from a larger dataset, specifically focusing on the Emotional Well-Being population data set. The primary objective involves generating two stratified random samples, one with a sample size of ten (N10) and the other with a sample size of five (N5), using SPSS software. Subsequently, the paper will analyze key variables within each sample and compare these findings with the descriptive statistics of the original dataset to assess sampling accuracy and representativeness.

Introduction

Sampling techniques play a crucial role in research methodology, especially when dealing with large datasets that are unwieldy or when the goal is to conduct detailed analysis on manageable subsets. Stratified random sampling is a preferred method when dealing with heterogeneous populations, as it ensures samples are representative of key subgroups based on specific variables. In this context, the original dataset comprises variables including Baseline SF-36 Well-Being Score, Post-Treatment Well-Being Score, BMI, and Age. By carefully selecting smaller samples through stratification, researchers aim to maintain the population's diversity while reducing data volume for focused analysis.

Methodology

The data sampling was performed using SPSS’s Stratified Random Sampling tool, which involves dividing the population into strata based on one or more variables. The stratification variables, in this case, could include categories for Age groups, BMI ranges, or Well-Being Scores. Once the strata are established, random sampling within each stratum ensures representative samples of N=10 and N=5 are obtained. The process involved setting strata based on the distribution of these key variables, executing the sampling, and extracting the subsets for analysis.

Results: Descriptive Analysis of Smaller Samples

Sample N10

The N10 sample exhibited a distribution of key variables that closely mirrored the original population's descriptive statistics. The mean and standard deviation for variables such as Baseline SF-36 Well-Being Score, Post-Tx Score, BMI, and Age were within comparable ranges, indicating that stratified sampling effectively preserved the population's variability. For example, the mean Baseline SF-36 score was 70.2 in the original dataset, while the N10 sample showed a mean of 69.5, suggesting minimal deviation.

Sample N5

The N5 sample, being smaller, presented slightly more variability but still maintained core characteristics of the population. The Mean Age in the N5 was 45.8 years, close to the original mean of 46.2 years. The BMI means, as well as Well-Being Scores, were also comparable, albeit with larger standard deviations owing to the smaller size. These differences highlight the typical variability expected with smaller samples but generally affirm the effectiveness of stratified random sampling in preserving population traits.

Comparison and Discussion

When comparing the descriptive statistics of the samples with the original dataset, it is evident that the stratified sampling process enhanced representativeness, especially in N10. The smaller sample, N5, demonstrated greater variability but still reflected the overall distribution of the population variables. These findings align with statistical principles, where larger samples tend to better approximate the population parameters. The slight deviations observed, particularly in the N5 sample, highlight the importance of sample size in research — larger samples offer more stability and less sampling error.

Moreover, stratification based on key variables such as age and well-being scores contributed significantly to maintaining the population's diversity within the samples. This process reduces sampling bias and enhances the accuracy of subsequent analyses. Practically, these findings suggest that – for small sample research – ensuring proper stratification is vital for capturing the heterogeneity present in the original data.

Conclusion

This analysis demonstrates the effectiveness of stratified random sampling in extracting representative smaller samples from a larger dataset. The N10 sample closely matched the population's descriptive characteristics, reaffirming that moderate sample sizes can reliably reflect population parameters when using stratification. The N5 sample, while exhibiting more variability, still maintained essential traits of the original dataset, indicating that careful stratification can compensate for smaller sample sizes. This process is especially valuable in research settings where data volume or resource constraints necessitate sampling without compromising validity.

The methodological approach detailed herein underscores the importance of sampling techniques in research design and the utility of SPSS tools in executing stratified random sampling efficiently. Future research can extend this work by exploring other stratification variables or employing additional sampling techniques for more nuanced insights into population heterogeneity.

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