Why is a study with insufficient power (too small a sample size) considered problematic?

Why is a study with insufficient power (too small a sample size) considered problematic?

• A. It might fail to find a difference between groups when one actually exists (Type II error)
• B. It increases the chance of a false positive (Type I error)
• C. It automatically overestimates the sample effect size
• D. It guarantees generalizability to the population

Answer: (B)

When a study has insufficient power due to a small sample, its ability to detect a real difference is reduced. Power is the probability that the test will reject the null hypothesis if a true difference exists. With a small sample, there is more sampling variability, standard errors are larger, and the test statistic is less likely to reach the required significance level even when an actual effect is present. That means you’re more likely to miss real differences—a Type II error. The other ideas don’t capture the main issue. The false-positive rate (Type I error) is set by the chosen alpha level and isn’t inherently increased just by having a small sample. While small samples can produce imprecise or unstable effect estimates, they don’t automatically overestimate the effect size or guarantee that results will generalize to the population; generalizability depends more on study design and sampling representativeness. The core problem with low power is the higher chance of failing to detect a real effect.

When a study has insufficient power due to a small sample, its ability to detect a real difference is reduced. Power is the probability that the test will reject the null hypothesis if a true difference exists. With a small sample, there is more sampling variability, standard errors are larger, and the test statistic is less likely to reach the required significance level even when an actual effect is present. That means you’re more likely to miss real differences—a Type II error.

The other ideas don’t capture the main issue. The false-positive rate (Type I error) is set by the chosen alpha level and isn’t inherently increased just by having a small sample. While small samples can produce imprecise or unstable effect estimates, they don’t automatically overestimate the effect size or guarantee that results will generalize to the population; generalizability depends more on study design and sampling representativeness. The core problem with low power is the higher chance of failing to detect a real effect.