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How does the power of a test change with its level of significance?
The significance level α of the test. If all other things are held constant, then as α increases, so does the power of the test. This is because a larger α means a larger rejection region for the test and thus a greater probability of rejecting the null hypothesis. That translates to a more powerful test.
What affects the power of a test?
The 4 primary factors that affect the power of a statistical test are a level, difference between group means, variability among subjects, and sample size.
What factors affect power?
Bullard also states there are the following four primary factors affecting power:
- Significance level (or alpha)
- Sample size.
- Variability, or variance, in the measured response variable.
- Magnitude of the effect of the variable.
What happens when the power of a test increases?
As the power increases, there is a decreasing probability of a type II error, also called the false negative rate (β) since the power is equal to 1 − β. A similar concept is the type I error probability, also referred to as the false positive rate or the level of a test under the null hypothesis.
What happens when the level of a test is decreased?
Decreasing the level means making α smaller. If you make α smaller, you make β larger and power is 1 − β. It’s easiest to see what’s going on in the context of a power curve, for example, with a one-sample t-test.
How is the false positive rate related to the power of a test?
A similar concept is the type I error probability, also referred to as the false positive rate or the level of a test under the null hypothesis. In the context of binary classification, the power of a test is called its statistical sensitivity, its true positive rate, or its probability of detection . A related concept is “power analysis”.
What does power mean in a test of significance?
Power is the probability of avoiding a Type II error. To help students better grasp the concept, I continually restate what power means with different language each time. For example, if we are doing a test of significance at level α = 0.1, I might say, “That’s a pretty big alpha level.