Type I and Type II Errors - Informal Interpretation

Informal Interpretation

In non-technical terms, a Type I error exists when I falsely assert a condition which does not exist. For example, I may toss a coin 10 times; if each time it comes up heads I may initially conclude it is a weighted coin but further tosses demonstrate only 50% heads. My initial conclusion would represent a Type I error in my assertion that heads are more likely than tails with that coin. A Type II error exists when I fail to identify a difference when one exists. Let's say I wonder whether men are taller than women, measure the next 10 men and the next 10 women and find no difference in height, so assert there is no height difference between the genders. If I then measure the next 100 men and women and then the next 1000 men and women and each time find the average height of men is greater than the average height for women, I might conclude that my earlier conclusion had been incorrect (due to 10 being too small a sample), so a Type II error. Both examples, though, demonstrate that one usually needs additional information to determine whether an assertion is in error. That is, one generally cannot know at the time one makes an assertion based on statistics whether one is making the assertion in error. What is important is to be clear when one makes an assertion based on statistics that there is a chance that assertion will be an error. The general convention is to allow a 5% chance for a Type I error and a 20% chance of a Type II error, although specific situations may dictate other chances for one or the other type of error.

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