Type I and Type II error rates are interrelated. This is due to the fact that the Type II error rate is inversely related to the significance level (the Type I error rate), which affects statistical power.
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The tradeoff between Type I and Type II errors is thus significant:
- Lowering the significance level reduces the likelihood of Type I errors, but raises the likelihood of Type II errors.
- A test’s power can be increased to reduce Type II error risk while increasing Type I error risk.
The graph below illustrates this trade-off. Two curves can be seen:
- The null hypothesis distribution displays every outcome you could get if the null hypothesis were correct. Any point on this distribution where the conclusion is correct does not require rejecting the null hypothesis.
- The alternative hypothesis distribution displays every outcome that could be attained in the event that the alternative hypothesis is correct. Any point on this distribution where the correct conclusion is to reject the null hypothesis.
Where these two distributions cross over, Type I and Type II errors happen. The Type I error rate is represented by the blue shaded area by alpha, and the Type II error rate is represented by the green shaded area by beta.
