Null and Alternative Hypothesis

The null hypothesis (H0) suggests that there is no statistical significance in a given set of observations. This implies that any kind of deviation or importance you see in a data set is only the result of chance.

This is considered to be true until analytical evidence proves it wrong and replaces it with a different, alternative hypothesis (H1). The null hypothesis is the commonly accepted truth that research may nullify; it is the idea waiting to be tested.

Null Hypothesis Example

In the world of finance and investing, hypothesis testing is used to test relationships between factors that may affect returns or performance. The null hypothesis suggests that results are random, while investors search for a relationship that, if identified, could be used to create better performance.

For example, one investor's null hypothesis might be: Stocks in the S&P 500 index that have P/E ratios above 20 will have no difference in annual returns as stocks in the S&P 500 index with PE ratios below 20.

This sets up an opportunity for another analyst or investor to disprove this null hypothesis to form an alternative hypothesis.

For example, an alternative hypothesis to this would be: Stocks in the S&P 500 index that have P/E ratios above 20 wll enjoy higher annual returns than stocks in the S&P 500 index with P/E ratios below 20.

When to Reject Null Hypothesis

The null hypothesis is tested by formulating the opposite idea, the alternative hypothesis, and then applying observational data that leads to acceptance or rejection of the null hypothesis.

While testing a null hypothesis requires inputting data into a complex stastical formula or software, the basic goal is to see if the data shows enough of a difference from the null hypothesis to support the alternative hypothesis.

Statisticians and analysts may use the p-value to measure the strength of the significant difference, and thus find out if the null hypothesis may be rejected.