Alpha level is the odds a researcher is willing to take to commit a Type I error
In instances where Type I or false positive findings are deleterious to patients, a small alpha level such as .01 or .001 can be chosen. This makes significant treatment effects much harder to detect. With these alpha levels, researchers take on the risks of 1 in 100 and 1 in 1,000, respectively, of committing a Type I error.
When multiple hypotheses are tested concurrently, such as when multiple statistical tests are run at the same time using the same statistical test, the chances of committing a Type I error increase DRASTICALLY. If you were to test five hypotheses using an alpha value of .05, then the odds of committing a Type I error increase to 5 in 20 or 25%. This phenomenon is often accounted for using a Bonferonni corrected alpha value to be used for significance. Simply divide the alpha level by the number of hypotheses being tested to yield the new alpha level that needs to be achieved to denote statistical significance. For example, .05 / 5 = .01. So, when testing my five hypotheses, unless the test statistic falls in the critical area outside of .01, it is not statistically significant.
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