09 September 2016

What are type I and type II errors?

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Testing  of hypothesis is widespread not only in statistics, but also in the natural and social sciences. When we do a hypothesis test, two types of errors are possible these errors are termed as experimental errors. They are Type-I or Type-II errors. It is important to understand both these effects in order to  manage error and report it, for the right interpretation of conclusion from a experiment.

Decision made
Null Hypothesis is actually
Reject Null
Type I error
Correct rejection
Fail to reject Null
Correct decision
Type II error
Type I errors occurs when we reject a true null hypothesis - 
The Type I error occurs when a the null hypothesis (H0) is rejected in favor of the research hypothesis (H1), when in reality the 'null' is correct. Type I errors are equivalent to false positives. For example, suppose there is a test that is used to detect a disease in a person. If a Type I error occurs in the test, it means that the test will say the person is suffering from that disease even though he is healthy. Type I errors can be controlled. The value of alpha, which is related to the level of significance that we selected has a direct bearing on type I errors. Alpha is the maximum probability that we have a type I error. For a 95% confidence level, the value of alpha is 0.05. This means that there is a 5% probability that we will reject a true null hypothesis. 
Type II errors happen when we fail to reject a false null hypothesis -
Type II error occurs when we do not reject a null hypothesis that is false. It is equivalent to false negatives.  From the above said example of a medical test for a disease, if a Type-II error occurs, then it means that the test will not detect the disease in the person even though he is actually suffering from it.The probability of a type II error is given by the Greek letter beta. This number is related to the power or sensitivity of the hypothesis test, denoted by 1 – beta.
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