You might have encountered it in class or during researches you have made — hypothesis testing. After the establishment of a problem and a question you want answered with regards to it, hypothesis testing essentially involves the following steps, (putting the technicalities aside),

• Forming a guess conjecture, the alternative hypothesis, Ha, based on your prior belief founded upon available information with regards to the problem at hand. The alternative hypothesis is a statement of the outcome you are expecting from your experiment.
• Setting up a null hypothesis, Ho, which is a complete negation of the alternative hypothesis you’ve formulated.
• Gathering information, and
• Analyzing whether or not the information collected provides sufficient evidence to reject the null hypothesis. This would then entail strong evidence in favor of the alternative hypothesis

An often overlooked yet highly important part of this procedure is the null hypothesis. Let’s explore how it fits in the mold of statistical tests of hypothesis.

What is the Null Hypothesis?

The null hypothesis is the antithesis to the alternative hypothesis. It is a hypothesis of no effect. In other words, it posits that what has been observed can be attributed to chance, instead of a significant effect.

How does rejection of the Null support the Alternative?

Statistical tests of hypothesis work by assuming that the null hypothesis is true. If in the experiment, what we have observed does not deviate so much from what we would expect if the null hypothesis indeed was true, we cannot dismiss the possibility that the null hypothesis is indeed true.

However, take the case that the evidence shows significant departures from the expected behavior if the null hypothesis was true. This means our observations effectively contradict our  assumption. We can therefore dismiss, or in other words, reject the null hypothesis.

Recall though that we have set up the null hypothesis in such a way that it is the exact opposite of the alternative. Given that we have assumed a scenario where everything that is exactly not the alternative hypothesis is true and having shown that such an assumption is invalid, we are compelled to treat our observations as evidence in favor of the alternative hypothesis.

An Illustration

For instance, if we want to know if a new medicine formulation has a significant effect on the healing rate of a certain disease compared to the old formulation. Our hypotheses would be set-up this way,

H₀: There is no significant difference in effect between the old and new medicine formulation.

H_a: There is a significant difference in effect between the old and new medicine formulation.

Now, we assume that the null hypothesis is true. We collect information from a sample of test subjects. One group took the old formulation, the other group took the new one. We will test if the assumption will hold up.

Upon data collection and analysis, we have two possible scenarios:

1. Your data contradicts your initial assumption of no effect. You observed that those who took the new formulation have significantly higher healing rates. Because of this, you are compelled to reject Ho. The evidence is in favor of the proposition that there is a significant difference in treatment effect between the old and new formulations.
2. Your data shows that the difference in effect is marginal. Given this, we cannot dismiss the possibility that there is indeed no effect and that the difference we have observed just happened by chance. We cannot reject Ho.

Why Test for the Null Hypothesis?

You might be curious though as to why tests for hypothesis involve testing the null, which isn’t the scenario we’re interested in — it is the exact opposite. Why not instead test for the alternative?

Statistical tests of hypothesis are guided by Popper’s theory of falsification, where he states that while no amount of information can sufficiently prove a statement, even a single piece of information can ultimately disprove it.

Now, having assumed the scenario in which the alternative hypothesis can be disproven, and with observations suggesting that this assumption cannot hold, we have confidence in concluding our findings are in favor of the alternative hypothesis.

An Absolute?

Does this mean that the rejection of the null hypothesis guarantees that the alternative hypothesis is true? Well, no. We just have a strong evidence in favor of it. In conducting a hypothesis test, researchers always attach a certain risk, known as the level of significance that the rejection of the null hypothesis is a wrong decision. While these attached risks are set to be small, it is still a risk of committing the wrong decision.