Market leader acquisition strategy and employee management integration analysis

WidgeCorp

A null hypothesis is what is being tested. Essentially, when one runs a statistical test, the objective of the test is to prove the null hypothesis. If the null hypothesis is not proved, then the alternative hypothesis is proved. A good example of this would be trying to test drinking water from a well to prove that it is safe. Let's say that the cutoff for safety is 100 parts per million of a specific element. We cannot tell by looking at it whether or not the water is safe, so we must test it. The null hypothesis is that the water is safe; in other words the null hypothesis is that the water will have under 100 ppm of the element. We run the test on the water and it shows 140 ppm.

This means that the null hypothesis was not proven -- the 140 ppm is higher than 100pm and the null hypothesis was that it would be lower. As a result, the alternative hypothesis has been proven. The alternative hypothesis is that the water is not safe. We can set the null hypothesis to anything that makes sense -- the alternative hypothesis is essentially the opposite of that. It is important to remember, however, that the scenario must fit. The null and alternative hypotheses must be mutually exclusive and they must be the only two options available -- otherwise rejecting the null hypothesis would not prove the alternative hypothesis.

With statistical techniques, the actual numbers could be quite a bit more complicated, but the underlying principle of the null and alternative hypotheses is the same. The null hypothesis is what we are testing for. If we do not find it, then we cannot accept the null hypothesis and we must accept the alternative hypothesis.

There are two types of errors that we can have. A Type I error is a false positive and a Type II error is a false negative. We need to be aware of these errors because there are business implications. Consider the water example, and assume we are a restaurant and we take that well water and serve it to our customers. In the Type I error we have rejected the null hypothesis wrongly. Say the water was actually 40 ppm and our reading was 140 ppm. If we are a restaurant using that well, we would have deemed the water unsafe and spent money on bottled water needlessly. The Type I error therefore cost us money.

A Type II error fails to reject a false null hypothesis. In this scenario, our reading was 40 and the actual was 140. So we thought the water was safe but it was not. In this case, we would have given the water to our customers and poisoned them. As you can see, the Type II error also costs us money. Both types of errors are costly to business, which is why we run statistical tests on confidence so that we know what the likelihood of either type of error might be.