Null Hypothesis

What is a 'Null Hypothesis'

A null hypothesis is a type of hypothesis used in statistics that proposes that no statistical significance exists in a set of given observations. The null hypothesis attempts to show that no variation exists between variables or that a single variable is no different than its mean. It is presumed to be true until statistical evidence nullifies it for an alternative hypothesis.

BREAKING DOWN 'Null Hypothesis'

The null hypothesis, also known as the conjecture, assumes that any kind of difference or significance you see in a set of data is due to chance. The opposite of the null hypothesis is known as the alternative hypothesis.

Null Hypothesis versus Alternative Hypothesis 

The null hypothesis is the initial statistical claim that the population mean is equivalent to the claimed. For example, assume the average time to cook a specific brand of pasta is 12 minutes. Therefore, the null hypothesis would be stated as, "The population mean is equal to 12 minutes." Conversely, the alternative hypothesis is the hypothesis that is accepted if the null hypothesis is rejected.

For example, assume the hypothesis test is set up so that the alternative hypothesis states that the population parameter is not equal to the claimed value. Therefore, the cook time for the population mean is not equal to 12 minutes, rather, it could be less than or greater than the stated value. If the null hypothesis is accepted or the statistical test indicates that the population mean is 12 minutes, then the alternative hypothesis is rejected. And vice versa.

Hypothesis Testing for Investments

For example, Alice sees that her investment strategy produces higher average returns than simply buying and holding a stock. The null hypothesis claims that there is no difference between the two average returns, and Alice has to believe this until she proves otherwise. Refuting the null hypothesis would require showing statistical significance, which can be found using a variety of tests. Therefore, the alternative hypothesis would state that the investment strategy has a higher average return than a traditional buy-and-hold strategy.

The p-value is used to determine the statistical significance of the results. A p-value that is less than or equal to 0.05 is usually used to indicate whether there is strong evidence against the null hypothesis. If Alice conducts one of these tests, such as a test using the normal model, and proves that the difference between her returns and the buy-and-hold returns is significant, or the p-value is less than or equal to 0.05, she can then refute the null hypothesis and accept the alternative hypothesis.