Suppose that a researcher normally uses an alpha level of .01 for hypothesis test, but this time uses an alpha level of .05. What does this change in the alpha level do to the amount of power? What does it do to the risk of a Type I error?
There are two types of error, Type I and type II. Type I (alpha) error is the probability of rejecting Ho when it is really true. Type II (beta) error is the probability of accepting Ho when it is actually false. Power is 1-beta.
Changing alpha from .01 to .05 increases your risk of Type I error and decreases your risk of Type II error, thus increasing power.
I hope this helps. Thanks for asking.
To understand the effects of changing the alpha level on power and the risk of a Type I error, let's start by defining these concepts:
1. Alpha level (α): The significance level or alpha level is the predetermined probability of making a Type I error, which is rejecting a true null hypothesis.
2. Power (1-β): The power of a statistical test is the probability of correctly rejecting the null hypothesis when it is false. In other words, it is the probability of avoiding a Type II error, which is failing to reject a false null hypothesis.
Now, if a researcher normally uses an alpha level of .01 for hypothesis testing but switches to an alpha level of .05, here's what happens:
1. Power: Increasing the alpha level from .01 to .05 generally increases the power of the test. This means that the test becomes more capable of detecting a true effect or rejecting a false null hypothesis. By using a higher alpha level, the researcher is allowing for a greater chance of finding evidence against the null hypothesis.
2. Risk of Type I error: By increasing the alpha level, the researcher also increases the risk of committing a Type I error. A Type I error occurs when the null hypothesis is rejected, despite it being true. In this case, with an alpha level of .05, the researcher is accepting a higher probability of incorrectly rejecting a true null hypothesis compared to the usual alpha level of .01.
To summarize, increasing the alpha level from .01 to .05 increases the power of the test but also increases the risk of a Type I error. The researcher becomes more likely to detect true effects but also more likely to incorrectly reject the null hypothesis. It's important for researchers to consider the trade-off between power and the risk of Type I errors when selecting an appropriate alpha level.