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:** | Error | What Happened | Plain English | |-------|--------------|---------------| | **Type I** | Rejected H_0 when H_0 is actually true | **False alarm** — you concluded something is happening when it isn't | | **Type II** | Failed to reject H_0 when H_0 is actually false | **Missed signal** — you concluded nothing is happening when it is | **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.