Can someone clearly explain Type I vs Type II errors? I keep mixing them up.

This is one of the most frequently confused topics in CFA Level I Quant, so you're definitely not alone. Let me give you a framework that makes it impossible to mix them up.

The Core Definitions:

Memory trick: Type I = I ncorrectly reject. The "I" in Type I matches the "I" in "incorrectly reject."

The Probability Connection:

• P(Type I error) = alpha (the significance level you choose, typically 0.05)
• P(Type II error) = beta
• Power of the test = 1 - beta = probability of correctly rejecting a false H_0

Worked Scenario:

Meridian Technologies claims its new trading algorithm generates an average daily return of 0%. You suspect it actually generates positive returns, so you set up:

• H_0: mu = 0%
• H_a: mu > 0%
• Significance level: alpha = 0.05

You collect 60 days of data and compute a test statistic of 2.15. The critical value at 5% (one-tailed) is 1.645.

Since 2.15 > 1.645, you reject H_0 and conclude the algorithm generates positive returns.

Scenario A — Type I error: If the algorithm actually does NOT generate positive returns (H_0 is true), but your sample happened to show unusually high returns by chance, you committed a Type I error. You sounded a false alarm.

Scenario B — Type II error: Now imagine a different researcher runs the same test but with only 15 observations. They get a test statistic of 1.40 and fail to reject H_0. If the algorithm truly DOES generate positive returns, this researcher committed a Type II error. They missed the real signal because the sample was too small.

Key Relationships for the Exam:

• Increasing alpha reduces beta (and vice versa) — there's a tradeoff
• Increasing sample size reduces BOTH types of error
• A more powerful test has a lower probability of Type II error

For more hypothesis testing practice, explore our CFA Level I question bank where we walk through dozens of testing scenarios step by step.