Sample Size

Definition

Sample size refers to the number of observations or data points collected in a statistical study or experiment. It is a crucial factor that determines the reliability and precision of the conclusions drawn from the data.

5 Must Know Facts For Your Next Test

1. The sample size affects the precision and reliability of statistical inferences, with larger sample sizes generally leading to more accurate and reliable results.
2. In experimental design, the sample size is determined based on factors such as the desired level of statistical significance, the expected effect size, and the desired power of the test.
3. The hypergeometric distribution is used to model situations where the sample is drawn without replacement from a finite population.
4. When estimating a binomial proportion, the normal approximation is used, and the sample size calculation depends on the desired margin of error and the expected proportion.
5. The finite population correction factor is used to adjust the standard error of the mean when the sample size is a significant fraction of the population size.

Review Questions

• Explain how sample size is related to experimental design and ethics.
  • In experimental design, the sample size is a critical consideration as it directly impacts the statistical power of the study and the reliability of the conclusions drawn. A larger sample size generally leads to more precise and reliable results, but it also requires more resources and may raise ethical concerns, particularly in studies involving human participants. Researchers must balance the need for statistical rigor with the ethical considerations of minimizing participant burden and ensuring the study is not overpowered, which could lead to the unnecessary use of human or animal subjects. The sample size calculation is a key step in the experimental design process and is often guided by ethical principles, such as the need to minimize risks and maximize the potential benefits of the research.
• Describe how sample size is used in the context of the hypergeometric distribution and estimating the binomial proportion with the normal distribution.
  • The hypergeometric distribution is used to model situations where a sample is drawn without replacement from a finite population. In this context, the sample size is a crucial parameter as it determines the probability of observing a certain number of successes in the sample. The sample size must be carefully chosen to ensure the hypergeometric distribution is an appropriate model for the data and that the statistical inferences drawn are reliable. When estimating a binomial proportion, the normal approximation is used, and the sample size calculation depends on the desired margin of error and the expected proportion. The sample size must be large enough to ensure the normal approximation is valid and that the estimated proportion falls within the desired margin of error with a specified level of confidence.
• Analyze the role of sample size in the context of confidence intervals, hypothesis testing, and effect size calculations.
  • Sample size plays a critical role in the accuracy and reliability of statistical inferences, such as confidence intervals and hypothesis testing. When the population standard deviation is known or the sample size is large, the sample size determines the margin of error and the precision of the confidence interval. In hypothesis testing, the sample size affects the power of the test, which is the probability of detecting an effect if it truly exists. Larger sample sizes generally lead to higher statistical power and more reliable conclusions. Additionally, the sample size is a key factor in calculating effect sizes, such as Cohen's d, which quantify the magnitude of the difference between two groups. The sample size must be sufficient to ensure that the effect size estimate is stable and representative of the true population effect.

Related terms

Population: The entire group of individuals, objects, or measurements of interest that a researcher wants to study or draw conclusions about.

Sampling: The process of selecting a subset of a population to represent the entire population for the purpose of statistical analysis.

Margin of Error: The maximum expected difference between the true population parameter and the sample statistic.