# Statistics Hypothesis Testing

This tutorial explains the concepts of hypothesis testing in statistics.

## Hypothesis Testing

Many text book uses the court case example to explain hypothesis testing. In the U.S. (but not all countries), the court finds evidence to prove the defendant guilty, instead of proving the defendant innocent.

There are two hypothesis for a court case:

1. The defendant is guilty – when we have a theory and try to prove it, the hypothesis is called H1

2. The defendant is innocent –  the alternative of H1 (you can simply interpret as something is normally true, i.e. everyone should be innocent) , the hypothesis is called H0 (Null hypothesis)

We don’t prove someone is innocent because we have assumed so, we just need to see if there is enough evidence to prove the defendant guilty.

If there is enough evidence, we say: There is enough evidence to conclude that the defendant is guilty

If there is not enough evidence, we say: There is not enough evidence to conclude that the defendant is guilty, but we cannot say the person is innocent

## Hypothesis Testing Errors

As we try to prove defendant  is guilty, an innocent person may be judged guilty (which is very serious) or a guilty person is judged innocent. Using the statistics terminology to describe these two errors:

1. Type I Error / False Positive (probability is α): We found enough evidence to conclude the defendant is guilty, but it turns out the person is innocent. α is the level of significance we allow to reject null hypothesis.

2. Type II Error / False Negative (probability is β): We could not find enough evidence to conclude the defendant is guilty, but it turns out the person is guilty

The term Power describes the probability of rejecting a false null hypothesis. Specifically, it is the probability that a randomly selected sample will show that the null hypothesis is false.when the null hypothesis is indeed false.

## Examples of Hypothesis Testing

Given μ = 100, if we try to prove population mean >100, then

H0: μ = 100

H1: μ < 100

If we try to prove population mean ≠100, then

H0: μ = 100

H1: μ ≠100

## Outbound References

http://www.sagepub.com/sites/default/files/upm-binaries/40007_Chapter8.pdf