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A type 1 error (alpha) is when a statistic calls for the rejection of a null hypothesis which is factually true. This is unavoidable: statistically speaking, even purely random events will occasionally produce non-random seeming results. A type 1 error is called a false positive because it forces the researcher to make a 'positive' statement that something odd is happening, when in fact nothing is happening except an excess of chance (in the same way that your family doctor means that something odd is going on with your body when she tells you that a test came back positive).

A type 2 error (beta) is when a statistic does not give enough evidence to reject a null hypothesis even when the null hypothesis should factually be rejected. Increasing the power of the test (by increasing sample size, or making new assumptions) can help to minimize the likelihood of this error. A type 2 error is a false negative, for the same reasons as above - the researcher is forced to say that nothing interesting is happening.

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Q: What are the differences between Type 1 errors and Type 2 errors?
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