Questions: Why is sample size important?

The answer is: Larger sample size increases the likelihood that the results of a study are not due to random chance.

Explanation for each option:

1. Relationships between variables can be determined only using a large sample size.

   • This statement is incorrect. While a larger sample size can provide more reliable results, relationships between variables can still be determined with smaller sample sizes, though the results may be less reliable and more prone to random error.

2. Researchers will always draw the right conclusions about a set of data if the sample size is large enough.

   • This statement is incorrect. A large sample size reduces the likelihood of random error, but it does not guarantee that researchers will always draw the right conclusions. Other factors, such as study design, data collection methods, and analysis techniques, also play crucial roles in the accuracy of conclusions.

3. Larger sample size increases the likelihood that the results of a study are not due to random chance.

   • This statement is correct. A larger sample size reduces the impact of random variation and increases the reliability of the results, making it more likely that the findings reflect true relationships rather than random chance.

4. Legitimate scientific studies can be performed using only a large sample size.

   • This statement is incorrect. Legitimate scientific studies can be performed with both large and small sample sizes, depending on the context and research question. However, larger sample sizes generally provide more reliable and generalizable results.

5. Statistical significance is best achieved with a small sample size.

   • This statement is incorrect. Statistical significance is more easily achieved with larger sample sizes because they provide more power to detect true effects and reduce the likelihood of Type I and Type II errors. Small sample sizes often lack the power to detect significant effects, leading to less reliable results.