When a sample is smaller it is less likely a difference will be found, this means the sample is what?

When a sample is smaller it is less likely a difference will be found, this means the sample is what?

• A. Overpowered
• B. Unbiased
• C. Underpowered
• D. Representativ e

Answer: (C)

Power is the study’s ability to detect a real difference when one exists. A smaller sample reduces power because it increases sampling variability and leads to wider confidence intervals. With less power, a true difference is less likely to be found, which is described as the study being underpowered. This also means a higher risk of a Type II error—failing to reject the null when there is a real effect. An overpowered study would have more power than needed and could detect even tiny differences. An unbiased study refers to absence of systematic error, not the ability to detect differences. A representative sample concerns how well the sample mirrors the population, not the study’s power.

Power is the study’s ability to detect a real difference when one exists. A smaller sample reduces power because it increases sampling variability and leads to wider confidence intervals. With less power, a true difference is less likely to be found, which is described as the study being underpowered. This also means a higher risk of a Type II error—failing to reject the null when there is a real effect.

An overpowered study would have more power than needed and could detect even tiny differences. An unbiased study refers to absence of systematic error, not the ability to detect differences. A representative sample concerns how well the sample mirrors the population, not the study’s power.