What Is the Null Hypothesis?

Null hypothesis, a statistical term, also known as a null hypothesis, refers to a pre-established hypothesis when performing statistical tests. When the null hypothesis holds, the relevant statistics should obey a known probability distribution.

In statistics, the null hypothesis ( null hypothesis ) is done

When we see the null hypothesis, we will naturally ask, this "hypothesis" is too strange. It is actually called the null hypothesis. Is there any one hypothesis and two hypotheses? In other words, are assumptions measurable by numbers? A way to have a good understanding of this problem may need to mention correlation coefficients, as well as some simple statements about assumptions. When we want to understand whether two events are related, we use the correlation coefficient to measure the degree of correlation between them. It is a value between -1 and 1. when

1 The null hypothesis is generally an intentional overthrow;

2 due to type 1 error

Under the assumption that the null hypothesis is true, determine

It is often assumed that the job of a scientist is to prove the validity of a hypothesis-such as the presence of electrons or a drug that cures cancer. But most of the time, scientists do the opposite: they need to reverse assumptions.

This method has been developed and perfected by scientists for decades, but one afternoon in the early 1920s was particularly noticeable during this historical process. It was an agricultural research station in England and three scientists were drinking afternoon tea. A statistician named Ronald Fisher poured a cup of milk tea to his colleague, Muriel Bristol.

Bristol rejected the cup of tea. She prefers the taste of pouring milk first and then tea.

"How is it possible?" It is said that Fisher replied, "Of course it makes no difference whether milk is poured first or milk is poured later."

But Bristol was firm. She insisted that she could taste the difference.

The third scientist in the conversation, William Roach, suggested that everyone experiment. (This may actually be a moment of scientific collaboration: Bristol and Lodge married in 1923.)

But how to test Bristol's claims? The easiest thing Fisher and Lodge could do was to pour a cup of milk tea so that Bristol wouldn't see it, and then gave her a taste to see if she could guess whether it was milk or tea.

However, even if she is right, it does not necessarily prove that she has a unique appreciation of tea. Considering that there is a 50% probability that she can get it right, she can totally guess the answer by relying entirely on Mongolia.

Years later, Fisher described how such claims should be tested in his 1935 book Design of Experiments. Instead of trying to prove that Bristol can taste the difference between the two teas, he tried to refute the assumption that "Bristol's choice is random." "We can call such hypotheses 'zero hypotheses,'" Fisher wrote. "Zero hypotheses can never be proven or confirmed, but may be denied by experimental means. It can be said that the purpose of each experiment is nothing more than To give the facts a chance to disprove the null hypothesis. "

Fisher outlined a way to refute the null hypothesis that Bristol's choice was random. He will prepare 8 cups of tea, 4 cups of milk first and 4 cups of milk later. Then he would disrupt the order of the cups and let Bristol taste one cup at a time. She needs to divide 8 cups of tea into two groups, one group thinks that milk is put first, and the other is milk later.

It is said that Bristol passed the mark without difficulty and correctly distinguished all 8 cups of tea. Due to Fisher's experimental design, she relied on a guess to classify all 8 cups of tea correctly. Eight cups of tea are divided into two groups and there are a total of 70 different combinations, which means that Bristol has only a 1/70 probability of completely answering the question.

Fisher's test still cannot completely rule out the possibility that Bristol was right. It's just that she is unlikely to guess correctly. He could further reduce this possibility by having Bristol drink more tea, but he could never reduce it to zero.

Since absolute proof is impossible, Fisher is more inclined to consider operability when doing experiments. In the agricultural laboratory he and Bristol worked in, Fisher's job was to analyze data collected over decades to determine whether this information was valuable, for example, to determine what the best formula for crop fertilizers was. Scientists can use this data to design larger experiments to get more accurate results. Fisher doesn't think it makes sense to design an experiment that takes hundreds of years to get results. He believes that when the probability is low to a certain level, it is enough to accept it when it is good.

He believes that 5% is a reasonable threshold. If we assume that a null hypothesis is correct, but find that the probability of observing such data under the null hypothesis is less than 5%, then we can safely "reject" the null hypothesis. In Bristol's case, the probability of her guessing is far less than Fisher's threshold, only 1.4%.

Thanks in large part to Fisher, the null hypothesis has become an important tool for scientific discovery. You can find the shadow of the null hypothesis in every branch of science, from psychology to virology to cosmology. And, scientists continued Fisher's 5% threshold probability. ^[2]