# Null hypothesis

In statistics, a null hypothesis, often written as ${\displaystyle H_{0}}$,[1] is a statement assumed to be true unless it can be shown to be incorrect beyond a reasonable doubt.[2] The idea is that the null hypothesis generally assumes that there is nothing new or surprising in the population. The most common null hypothesis is the "no-change" or "no-difference" hypothesis (as in "there is no difference between a sample mean and a population mean").[3] When testing whether something works, one would start with the null hypothesis that it will not work. The term was first used by Ronald Fisher in his book The Design of Experiments.[4]

Every experiment has a null hypothesis. For example:

• When performing an experiment to see if a medicine works, the null hypothesis is that it does not work.
• When performing an experiment to see if people prefer chocolate or vanilla ice cream, the null hypothesis is that people like them equally.
• When performing an experiment to see if either boys or girls can play piano better, the null hypothesis is that boys and girls are equally good at playing the piano.

The opposite of a null hypothesis is an alternative hypothesis. Some examples of alternative hypotheses are:

• This medicine makes people healthier.
• People like chocolate ice cream better than vanilla.
• Boys are better at playing the piano than girls.

## References

1. "List of Probability and Statistics Symbols". Math Vault. 2020-04-26. Retrieved 2020-09-22.
2. "Null and Alternative Hypotheses | Introduction to Statistics". courses.lumenlearning.com. Retrieved 2020-09-22.
3. "Introductory Statistics: Null and Alternative Hypotheses". opentextbc.ca. Retrieved September 22, 2020.
4. Oxford English Dictionary: "null hypothesis," first usage: 1935 R.A. Fisher, The Design of Experiments ii. 19, "We may speak of this hypothesis as the 'null hypothesis', and it should be noted that the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation".