During hypothesis testing, we make an assumption about a population based on a sample. We then test this assumption using statistical methods. However, there are chances that our test results may not always be precise, and we might encounter errors in our hypothesis testing. These errors are broadly classified into two types, namely Type I and Type II errors.
Type I error:
A type I error is also known as a false positive error. This error occurs when we reject the null hypothesis when it is actually true. In other words, we conclude that there is a statistically significant difference between two groups when there is no difference. Therefore, there is a high chance of making a type I error, and we use the level of significance (alpha) to control this risk.
For example, lets say a pharmaceutical company has developed a new drug for a particular disease. The null hypothesis is that the drug has no effect, and the alternative hypothesis is that the drug has a beneficial impact. If the company rejects the null hypothesis and concludes that the drug is effective based on the sample data, but in reality, the drug has no effect, this will be a type I error.
Type II error:
A type II error is also known as a false-negative error. This error occurs when we fail to reject the null hypothesis when it is actually false. In other words, we conclude that there is no statistically significant difference between two groups when there is a difference.
For example, lets say a company wants to test a product’s durability under different conditions. The null hypothesis is that the durability is the same for all conditions, and the alternative hypothesis is that durability differs with various circumstances. If the company fails to reject the null hypothesis and concludes that the product’s durability is the same under all conditions, but in reality, the product’s durability differs, this will be a type II error.
In quantitative trading and investment, hypothesis testing is a crucial tool to evaluate investment strategies and to estimate the expected returns. A type I error can lead to a false-positive indication of a strategys success, leading to overconfidence and resulting in poor investment decisions. A type II error can cause a false-negative indication of a strategys performance, leading to underestimation of strategy, and missing out on profitable trading opportunities. Therefore, it is critical to understand the differences between type I and type II errors and control these errors to ensure the accuracy of the hypothesis test results.