What is a Type I error? Explain how the cumulative Type I error affects your decision making. How is the two independent sample t-test different from ANOVA?
1. What is a Type I error?
There are two kinds of errors that can be made in significance testing:
(1) A true null hypothesis can be incorrectly rejected (Type 1 error)
(2) A false null hypothesis can fail to be rejected (Type II error). Type II error (the Type II error rate) is designated by the Greek letter beta (ß). A Type II error is only an error in the sense that an opportunity to reject the null hypothesis correctly was lost. It is not an error in the sense that an incorrect conclusion was drawn since no conclusion is drawn when the null hypothesis is not rejected.
A Type I error is an error where a conclusion is drawn that the null hypothesis is false when, in fact, it is true. This is an error of "seeing too much in the data."
"Type I errors are generally considered more serious than Type II errors. The probability of a Type I error (α) is called the significance level ...
This solution explains Type I error and how the cumulative Type I error affects decision making. It also explains how the two independent sample t-test is different from the ANOVA.