When is a Type I error more likely?

When is a Type I error more likely?

• A. alpha level is high
• B. small sample size
• C. power is low
• D. the effect is large

Answer: (A)

The key idea is that a Type I error is a false positive: rejecting a true null hypothesis. The chance of doing that is set by the alpha level you choose. When the alpha level is high, you’re granting yourself more frequent chances to call something significant, which means you’re more likely to end up rejecting a true null by mistake. So increasing alpha directly raises the probability of a Type I error. The other factors affect different aspects: a small sample size tends to reduce power, making it harder to detect real effects (increasing Type II error) rather than increasing false positives. A low power situation similarly raises the risk of missing real effects, not of falsely declaring an effect. A large true effect increases power, making true effects easier to detect and reducing Type II error, without raising Type I error.

The key idea is that a Type I error is a false positive: rejecting a true null hypothesis. The chance of doing that is set by the alpha level you choose. When the alpha level is high, you’re granting yourself more frequent chances to call something significant, which means you’re more likely to end up rejecting a true null by mistake. So increasing alpha directly raises the probability of a Type I error.

The other factors affect different aspects: a small sample size tends to reduce power, making it harder to detect real effects (increasing Type II error) rather than increasing false positives. A low power situation similarly raises the risk of missing real effects, not of falsely declaring an effect. A large true effect increases power, making true effects easier to detect and reducing Type II error, without raising Type I error.