How to Express a Hypothesis as a Statistical Statement

Statistical analysis is helpful for tough decisions.

When it comes to statistics, using hypotheses is important. It allows real-world application to problems. Using sample information from populations, hypotheses are used to help with decisions. For instance, statistical hypothesis testing is frequently used by businesses to ensure profitability in operations. It is important to construct the hypotheses in a manner that helps derive the information provided. After constructing a valid hypothesis, it can be tested using statistical analysis, the most common of which is one- or two-tailed testing.

Instructions

1. Create a null hypothesis. The null hypothesis is best described as the results that is not covered by the mechanism you are testing or coincidental results. It is denoted by H0 (H sub 0). Usually the null hypothesis will contain equality or a lack of evident change. For example, let's say you had a car in your front yard. The car had been sitting there for over a year and you wanted to know if you should try to sell it. You don't know if it works, but since it sat idle for a long time, it was accepted that it did not run. However, the key to if you will sell it depends on if it is operational, since the market for dead cars is small.

   The null hypothesis is:

   H0: The car does not work.

2. Find an alternative hypothesis. The alternative hypothesis is what you sought to test. In our example, the alternative hypothesis is that the car is not operational. This is expressed as

   H1: The car is operational.

3. After your hypotheses have been constructed, perform statistical analysis to find the proper decision. The decision is either that you reject the null hypothesis, or you fail to reject the null hypothesis, since conclusions are drawn always in reference to the null hypothesis.

Tips & Warnings

• The current condition of the elements involved, or the state of nature, is something you have no control over. All you can control is the decisions made as a result of the state of nature.

• There are 5 elements needed for any statistical test:

• the null hypothesis;

• an alternate hypothesis;

• the test statistic, or what is tested to help come to the decision;

• the rejection/critical region, or the region under the bell curve where you reject the null hypothesis;

• and the conclusion, or the decision that was made.

• Beware Type I and Type II errors.

• Type I errors occur when you reject a correct null hypothesis.

• Type II errors occur when you fail to reject a null hypothesis that is wrong.

• Type I errors are considered more egregious.

References

• University of Richmond: Stats: Hypothesis Testing. Jones, James.