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Sample size is crucial in statistics because it impacts the generalizability and reliability of your results. Larger sample sizes tend to provide more accurate representations of the population, which allows for the use of parametric procedures, while smaller samples often require nonparametric methods due to increased variability and reduced representativeness.

Currently studying the reading proficiency of elementary school students in Richmond County School District (RCBOE). The district has approximately 10,000 elementary students.

Using a sample size calculator, we have determined the required sample size for a 95% confidence level with a margin of error of 5%. Inputting these parameters:

1. Population Size: 10,000
2. Confidence Level: 95% (z-score 1.96)
3. Margin of Error: 5% (0.05)

The sample size calculator indicates that you would need around 370 students to achieve these criteria.

Importance of Sample Size

1. Generalizability: Larger samples more accurately reflect the population, allowing findings to be more confidently generalized.
2. Parametric Procedures: These statistical methods assume normal distribution and require larger sample sizes to meet this assumption.
3. Nonparametric Procedures: Smaller sample sizes may not meet the assumptions of normality, necessitating nonparametric methods. These methods do not assume a specific distribution and are used when data doesn't meet the assumptions of parametric tests.

Lastly, nonparametric methods are used when data does not meet the assumptions required for parametric tests, such as normal distribution or homogeneity of variance. They are more flexible and less powerful but are essential for analyzing data from smaller samples or non-normally distributed data.

Reference:

Singh, K., & Masuku, M. B. (2014). Sampling techniques & determination of sample size in applied statistics research: An overview. International Journal of Economics, Commerce, and Management, 2(11), 1-22.