Question

Please provide an example of both a Type I Error and Type II Error. Why is it that increasing the sample size reduces the probability of a Type II error to an acceptable level. Please discuss.

Answer 1

`Hey,

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A type I error occurs when the null hypothesis is true, but is rejected. Let me say this again, a type I error occurs when the null hypothesis is actually true, but was rejected as false by the testing.

Let’s use a shepherd and wolf example. Let’s say that our null hypothesis is that there is “no wolf present.” A type I error (or false positive) would be “crying wolf” when there is no wolf present. That is, the actual condition was that there was no wolf present; however, the shepherd wrongly indicated there was a wolf present by calling “Wolf! Wolf!” This is a type I error or false positive error.

A type II error occurs when the null hypothesis is false, but erroneously fails to be rejected. Let me say this again, a type II error occurs when the null hypothesis is actually false, but was accepted as true by the testing.

A type II error, or false negative, is where a test result indicates that a condition failed, while it actually was successful.   A Type II error is committed when we fail to believe a true condition.

Continuing our shepherd and wolf example. Again, our null hypothesis is that there is “no wolf present.” A type II error (or false negative) would be doing nothing (not “crying wolf”) when there is actually a wolf present. That is, the actual situation was that there was a wolf present; however, the shepherd wrongly indicated there was no wolf present and continued to play Candy Crush on his iPhone. This is a type II error or false negative error.

The smaller the difference you want to detect, the larger the sample size (and the longer the length of time) you require.

That means that they have a slim chance of detecting true positives, even when a substantial difference in conversion rate actually exists.

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