Sample size

Definition

Sample size refers to the number of observations or data points included in a statistical sample, which is used to make inferences about a larger population. A well-chosen sample size is crucial because it influences the accuracy and reliability of statistical conclusions, affecting the power of hypothesis tests and the confidence intervals around estimates. Balancing sample size with cost and feasibility is also an important consideration in research design.

5 Must Know Facts For Your Next Test

1. Larger sample sizes generally lead to more accurate estimates and narrower confidence intervals, which enhances the reliability of statistical results.
2. A small sample size can increase the risk of sampling error, leading to potentially misleading conclusions about the population.
3. In inferential statistics, determining an appropriate sample size often involves considering the expected effect size, significance level, and desired power of the test.
4. Sample size calculations can help researchers avoid wasteful over-sampling or under-sampling in their studies, optimizing resource use.
5. In many cases, ethical considerations may limit the feasible sample size in studies involving human subjects.

Review Questions

• How does sample size impact the reliability of statistical conclusions drawn from a study?
  • Sample size plays a critical role in determining the reliability of statistical conclusions because larger samples tend to provide more accurate estimates of population parameters. This accuracy arises from reduced variability and narrower confidence intervals. In contrast, smaller samples can lead to greater sampling error and less confidence in the results, making it harder to generalize findings to the larger population.
• Discuss how one might determine an appropriate sample size for a research study and what factors need to be considered.
  • Determining an appropriate sample size involves several factors such as the expected effect size, significance level (alpha), and desired statistical power (often set at 0.80 or 80%). Researchers may also use formulas or software for power analysis that take these elements into account. Additionally, practical considerations such as budget constraints, time limitations, and ethical implications must also influence decisions about how large a sample should be.
• Evaluate how varying sample sizes can affect the outcomes of hypothesis testing in inferential statistics.
  • Varying sample sizes can significantly affect hypothesis testing outcomes by altering both Type I and Type II error rates. Larger sample sizes typically provide more information, which can lead to better detection of true effects (reducing Type II errors) while maintaining control over Type I errors. Conversely, small samples might fail to reveal significant relationships even if they exist due to insufficient power, thereby impacting researchers' interpretations and subsequent decisions based on those tests.

Related terms

Population: The entire group of individuals or instances about whom we want to draw conclusions.

Sampling Error: The difference between the sample statistic and the actual population parameter due to the randomness of selecting a sample.

Power Analysis: A method used to determine the minimum sample size required for a study to detect an effect of a given size with a certain degree of confidence.