  # Statistical Hypothesis Testing

## What is Statistical Hypothesis Testing?

Statistical hypothesis testing is the formal process of accepting or rejecting assumptions made about a population parameter. The hypotheses are chosen by looking at two sets of random variables, or a random sample from a model, and then testing the probability that any difference between the two sets is caused by either chance/error or non-random influence. Unlike other forms of scientific hypotheses, there are only two possible statistical assumptions a researcher can make:

• The null hypothesis, expressed by H

0, is the assumption that the sample observations only differ because of random chance or sampling error.

• The alternative hypothesis, expressed by H1 or Ha, is the exact opposite. This assumes the sample observations are not affected by sampling errors or chance and instead are influenced by some non-random cause.

## How do you Conduct a Statistical Hypothesis Test?

1. State the null or alternative hypothesis mathematically so that if one is true, the other must be false.

2. Choose and calculate a test statistic, for example the mean score, proportion, t statistic or z-score.

3. Decide on a decision threshold value to apply to the test statistic. This is usually a particular significance level using the P-value (probability of conducting another test with a result just as extreme) or region of acceptance (similar to p-value, but with a range of values) methods.

4. Reject the null hypothesis, thereby accepting the alternate, if the test statistic returns a result below the significance level of your decision rule. If the result is higher than the significance level, then fail to reject the null hypothesis, thereby rejecting the alternate.

This significance level approach is not foolproof, which is why hedging terms such as “reject” and “fail to reject” are used to describe the test results. There are two possible errors that can occur:

Type I errors are rejecting a null hypothesis when it is true, expressed by alpha (α).

Type II errors are failing to reject a null hypothesis that is false, expressed by beta (β).