# Hypothesis Testing

## What is 'Hypothesis Testing'

Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to infer the result of a hypothesis performed on sample data from a larger population.

## BREAKING DOWN 'Hypothesis Testing'

In hypothesis testing, an analyst tests a statistical sample, with the goal of accepting or rejecting a null hypothesis. The test tells the analyst whether or not his primary hypothesis is true. If it isn't true, the analyst formulates a new hypothesis to be tested, repeating the process until data reveals a true hypothesis.

## Testing a Statistical Hypothesis

Statistical analysts test a hypothesis by measuring and examining a random sample of the population being analyzed. All analysts use a random population sample to test two different hypotheses: the null hypothesis and the alternative hypothesis. The null hypothesis is the hypothesis the analyst believes to be true. Analysts believe the alternative hypothesis to be untrue, making it effectively the opposite of a null hypothesis. This makes it so they are mutually exclusive, and only one can be true. However, one of the two hypotheses will always be true.

If, for example, a person wants to test that a penny has exactly a 50% chance of landing heads, the null hypothesis would be yes, and the null hypothesis would be no, it does not. Mathematically, the null hypothesis would be represented as Ho: P = 0.5. The alternative hypothesis would be denoted as "Ha" and be identical to the null hypothesis, except with the equal sign struck-through, meaning that it does not equal 50%.

A random sample of 100 coin flips is taken from a random population of coin flippers, and the null hypothesis is then tested. If it is found that the 100 coin flips were distributed as 40 heads and 60 tails, the analyst would assume that a penny does not have a 50% chance of landing heads, and would reject the null hypothesis and accept the alternative hypothesis. Afterward, a new hypothesis would be tested, this time that a penny has a 40% chance of landing heads.

## Four Steps of Hypothesis Testing

All hypotheses are tested using a four-step process. The first step is for the analyst to state the two hypotheses so that only one can be right. The next step is to formulate an analysis plan, which outlines how the data will be evaluated. The third step is to carry out the plan and physically analyze the sample data. The fourth and final step is to analyze the results and either accept or reject the null.