Why does decreasing the probability of making a type one error increase the probability of making a type two error? [2 sentences]

Decreasing the probability of making a Type I error (rejecting a true null hypothesis) requires setting a lower significance level (α), which makes it harder to reject the null hypothesis. This increases the likelihood of failing to reject a false null hypothesis, thereby increasing the probability of making a Type II error (β).

Would you like further details or examples? Here are five related questions to consider:

1. What is the relationship between Type I and Type II errors in hypothesis testing?
2. How does sample size impact the probabilities of Type I and Type II errors?
3. What role does statistical power play in balancing Type I and Type II errors?
4. How can one minimize both Type I and Type II errors simultaneously?
5. What are the consequences of prioritizing the reduction of Type II errors over Type I errors in research?

**Tip:** Increasing the sample size is one way to reduce both Type I and Type II errors.

Why does decreasing the probability of making a type one error increase the probability of making a type two error?

Explore why decreasing the probability of a Type I error (rejecting a true null hypothesis) in hypothesis testing increases the likelihood of a Type II error (failing to reject a false null hypothesis). This explanation covers the balance between significance level, statistical power, and error probabilities. Suitable for undergraduate statistics students.

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