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Power of a Statistical Test
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Power of a Test
The probability that the test correctly rejects a false null hypothesis (i.e., it detects an effect when there is one).
p-value
The probability of obtaining a result at least as extreme as the observed data, assuming the null hypothesis is true.
Noncentrality Parameter
A value used in power analysis that reflects the degree to which the null hypothesis is false; related to effect size.
Statistical Significance
The likelihood that a result from data collection is caused by something other than random chance.
Beta (β)
Another term for Type II error rate, the probability of failing to reject the null hypothesis when it is indeed false.
Alternative Hypothesis (H1)
A statement that there is an effect or a difference, opposite to the null hypothesis.
Cohen's d
A measure of effect size indicating the standardized difference between two means.
Power Analysis
A method used to determine the sample size required to detect an effect of a given size with a certain degree of assurance.
Null Hypothesis (H0)
A statement that there is no effect or no difference, and it is what the statistical test aims to reject.
Sensitivity
The ability of a test to correctly identify those with the effect (true positive rate), equivalent to 1 - β.
Type II Error (Beta)
The probability of failing to reject the null hypothesis when it is false (false negative).
Significance Level (Alpha)
The threshold probability for rejecting the null hypothesis, representing the risk of a Type I error.
Effect Size
A measure of the magnitude of the phenomenon of interest, often influencing the power of a test.
Sample Size (n)
The number of observations in a study, affects the power of a test; larger sample sizes generally provide more power.
Type I Error (Alpha)
The probability of rejecting the null hypothesis when it is actually true (false positive).
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