Summary of null hypothesis

Zero hypothesis, H0 is a generally accepted fact; it is contrary to the alternative hypothesis. Researchers are committed to rejecting, abolishing or refuting the null hypothesis. The researchers put forward an alternative hypothesis that they thought explained a phenomenon and then tried to reject the null hypothesis.

The famous zero hypothesis in history is that the earth is flat. Later scientists tried to prove that the hypothesis was wrong under this assumption which was generally considered correct in the early stage.

Accordingly, its alternative hypothesis is that the earth is round.

Why zero (null)

In this case, the word “null” means that researchers are trying to nullify such a generally accepted fact. This does not mean that the assumption itself is null! (the word should be called “nullifiable hypothesis” to reduce confusion).

Null means: nullifiable. Can, or allowed to be nullified

The short answer is that the null hypothesis is the research method needed as a scientist; it’s part of the scientific process. Science uses a series of processes to prove or disprove theories to ensure that no new hypothesis is flawed. Including null and void assumptions is a safeguard to ensure that your research is flawless. It is considered very bad by the scientific community not to include zero hypothesis in your research. If you are going to prove an alternative hypothesis without considering it, you are likely to let yourself fail. At least, your experiment may not be taken seriously.

give an example

Long ago, people believed that the world was flat.
Zero hypothesis H0: the world is flat.
Alternative hypothesis H1: the world is round.
Several scientists, including Copernicus, began to refute the null hypothesis. This eventually leads to the rejection of null hypothesis and the acceptance of alternative hypothesis. Most people accepted it! What would have happened if Copernicus had not refuted it but only proved a substitute? No one will listen to him. In order to change people’s minds, he must first prove that they are wrong.

How to put forward zero hypothesis

Example question: the researchers believe that patients with knee surgery would have a longer recovery period if they received physical therapy twice a week instead of three times a week. The average recovery time was 8.2 weeks.

Step 1: find out the hypothesis from the question. This assumption is usually hidden in the question, sometimes a statement of what you want to happen in the experiment. The assumption of the above question is “I expect an average recovery period of more than 8.2 weeks.”
Step 2: transform the hypothesis into mathematics. Remember that the average is sometimes written as μ.

H1：μ> 8.2

Subdivided into H1 (hypothesis): μ (mean) & gt; (greater than) 8.2

Step 3: explain what will happen if the assumption fails. If the recovery time does not exceed 8.2 weeks, there are only two possibilities, that is, the recovery time is equal to or less than 8.2 weeks.

H0：μ≤8.2

It is decomposed again to H0 (null hypothesis): μ (mean value) ≤ (less than or equal to) 8.2

But what happens if researchers don’t know?

Sample question: researchers are studying the impact of aggressive exercise on patients undergoing knee surgery. Treatment is likely to shorten the recovery time, but it may also make the treatment worse. The average recovery time was 8.2 weeks.

Step 1: explain what happens if the experiment doesn’t make any difference. It’s a zero hypothesis – nothing will happen. In this experiment, if there was no response, the recovery time would remain at 8.2 weeks.

H0：μ= 8.2

That is, H0 (null hypothesis): μ (mean) = (equal to) 8.2

Step 2: find alternative hypotheses. The substitution hypothesis is opposite to the null hypothesis. In other words, what happens if our experiment does something?

H1：μ≠8.2

That is H1 (alternate hypothesis): μ (average) ≠ (not equal to) 8.2

This is how to state the null hypothesis!
https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/null-hypothesis/