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Researchers conducting clinical trials desire effective treatments. Therefore, errors should be avoided as much as possible.
Power is defined as “1-β,” which is the probability that “a treatment that is actually effective is judged to be effective” (Figure 1).
[Figure 1] Test of significance level α (two-sided)
In this study, we explain power using a test of the population mean as an example.
What does power mean
Power is “the ability to determine that the test is effective,” that is, how good the test is.
Since it is the probability of not making a type II error, it is the complement of β (1-β). Generally, statisticians desire a value of 0.8 (80%). This implies that if the test is performed 100 times, the original difference can be detected 80 times (Figure 2).
[Figure 2] Two types of errors and power in statistical significance tests
| Truth/ Test result | Determined that there is no difference (adopting null hypothesis) | Determined that there is a difference (rejecting the null hypothesis) |
| There is really no difference | Correct decision | Type I error(α) |
| There is a real difference | Type II error(β) | Correct decision (1-β) [power] |
The value of the test statistic is strongly influenced by n and power. In general, the higher the value of n and power, the higher the test statistic, and, conversely, the lower the n value and power, the lower the test statistic.
Even if the null hypothesis shows a meaningful difference, if the value of n or power is small, the value of the test statistic will not be large and will result in “no significant difference.”
Conversely, even if the difference in the null hypothesis is small, if the number of n or power is large, it will be “significant.” However, swallowing such test results could be dangerous. Therefore, after determining the sample size and power, it is necessary to repeat the test using that sample size.
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