Null Hypothesis and Alternate Hypothesis

1、Null Hypothesis Overview

零假设，H₀是普遍接受的事实;这与备择假设(alternate hypothesis)正好相反。研究人员努力否定、驳斥零假设。研究人员提出了另一种假设(alternate hypothesis)，他们认为这种假设可以解释一种现象，然后努力拒绝零假设。

The null hypothesis, H0 is the commonly accepted fact; it is the opposite of the alternate hypothesis. Researchers work to reject, nullify or disprove the null hypothesis. Researchers come up with an alternate hypothesis, one that they think explains a phenomenon, and then work to reject the null hypothesis.

2、Why is it Called the “Null”?

The word “null” in this context means that it’s a commonly accepted fact that researchers work to nullify. It doesn’t mean that the statement is null itself! (Perhaps the term should be called the “nullifiable hypothesis” as that might cause less confusion).

3、Why Do I need to Test it? Why not just prove an alternate one?

简单的回答是，作为一个科学家，你必须;这是科学过程的一部分。科学使用一系列的过程来证明或反驳理论，确保任何新的假设都没有缺陷。同时包含零假设和替代假设是确保您的研究没有缺陷的一个保障。在你的研究中不包括零假设被科学界认为是非常糟糕的做法。如果你不加考虑就着手证明另一种假设，你很可能会失败。至少，你的实验不会被认真对待。

The short answer is, as a scientist, you are required to; It’s part of the scientific process. Science uses a battery of processes to prove or disprove theories, making sure than any new hypothesis has no flaws. Including both a null and an alternate hypothesis is one safeguard to ensure your research isn’t flawed. Not including the null hypothesis in your research is considered very bad practice by the scientific community. If you set out to prove an alternate hypothesis without considering it, you are likely setting yourself up for failure. At a minimum, your experiment will likely not be taken seriously.

4、Example

不久以前，人们还认为地球是平的。

零假设，H0:世界是平的。
备择假设:地球是圆的

包括哥白尼在内的几位科学家开始驳斥零假设。这最终导致了null的拒绝和替代的接受。大多数人接受了它——那些没有创建扁平地球社会的人!如果哥白尼没有否定它，而只是证明了它的替代品，会发生什么呢?没有人会听他的。为了改变人们的思维，他首先要证明他们的思维是错误的。

Not so long ago, people believed that the world was flat.
Null hypothesis, H0: The world is flat.
Alternate hypothesis: The world is round.
Several scientists, including Copernicus, set out to disprove the null hypothesis. This eventually led to the rejection of the null and the acceptance of the alternate. Most people accepted it — the ones that didn’t created the Flat Earth Society!. What would have happened if Copernicus had not disproved the it and merely proved the alternate? No one would have listened to him. In order to change people’s thinking, he first had to prove that their thinking was wrong.

5、How to State the Null Hypothesis from a Word Problem

你将被要求把一个应用题转换成统计学中的假设陈述，其中包括一个零假设和一个备择假设。将问题分解为几个小步骤可以使这些问题更容易处理。

You’ll be asked to convert a word problem into a hypothesis statement in statistics that will include a null hypothesis and an alternate hypothesis. Breaking your problem into a few small steps makes these problems much easier to handle.

6、How to State the Null Hypothesis

例子问题:一位研究人员认为，如果膝关节手术患者每周进行两次物理治疗(而不是三次)，他们的恢复期会更长。膝关节手术患者平均恢复时间为8.2周。

Example Problem: A researcher thinks that if knee surgery patients go to physical therapy twice a week (instead of 3 times), their recovery period will be longer. Average recovery times for knee surgery patients is 8.2 weeks. 

step1:从问题中找出假设。假设通常隐藏在一道应用题中，有时是对实验结果的陈述。上述问题的假设是“我预计平均恢复期大于8.2周。

Step 1: Figure out the hypothesis from the problem. The hypothesis is usually hidden in a word problem, and is sometimes a statement of what you expect to happen in the experiment. The hypothesis in the above question is “I expect the average recovery period to be greater than 8.2 weeks.”

Step 2: 把假设转化为数学。记住,平均符号一般为μ。

Step 2: Convert the hypothesis to math. Remember that the average is sometimes written as μ.
H1 : μ > 8.2

Step 3:说明如果假设不成立会发生什么。如果恢复时间不大于8.2周，只有两种可能，即恢复时间等于8.2周或小于8.2周。

Step 3: State what will happen if the hypothesis doesn’t come true. If the recovery time isn’t greater than 8.2 weeks, there are only two possibilities, that the recovery time is equal to 8.2 weeks or less than 8.2 weeks.

H0: μ ≤ 8.2

7、But what if the researcher doesn’t have any idea what will happen?

举例:一名研究人员正在研究激进运动方案对膝关节手术患者的影响。这种疗法很有可能提高康复时间，但也有可能使情况变得更糟。膝关节手术患者平均恢复时间为8.2周。

Sample Problem: A researcher is studying the effects of radical exercise program on knee surgery patients. There is a good chance the therapy will improve recovery time, but there’s also the possibility it will make it worse. Average recovery times for knee surgery patients is 8.2 weeks. 

第一步:陈述如果实验没有任何影响会发生什么。这就是零假设——什么也不会发生。在这个实验中，如果什么都没有发生，那么恢复时间将保持在8.2周。

Step 1: State what will happen if the experiment doesn’t make any difference. That’s the null hypothesis–that nothing will happen. In this experiment, if nothing happens, then the recovery time will stay at 8.2 weeks.

H0: μ = 8.2

第二步:找出另一个假设。替代假设与零假设相反。换句话说，如果我们的实验有所不同会发生什么?

Step 2: Figure out the alternate hypothesis. The alternate hypothesis is the opposite of the null hypothesis. In other words, what happens if our experiment makes a difference?
H1: μ ≠ 8.2

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8、Alternate Hypothesis in Statistics: What is it?

为了理解替代假设(也称为替代假设)是什么，首先需要理解零假设的含义。假设这个词的意思是一个工作陈述。在统计学中，我们感兴趣的是证明一个工作陈述(零假设)是真的还是假的。通常，这些工作报表都是预期为真的东西——某种历史或现有的期望值。“null”这个词可以理解为“没有变化”。零假设，从历史的角度来看，你得到了你想要的。

In order to understand what an alternate hypothesis (also called an alternative hypothesis) is, you first need to understand what the null hypothesis means. The word hypothesis means a working statement. In statistics, we’re interested in proving whether a working statement (the null hypothesis) is true or false. Usually, these working statements are things that are expected to be true — some kind of historical or existing expected value. The word “null” can be thought of as “no change”. With the null hypothesis, you get what you expect, from a historical point of view. 

另一种假设是备择假设。基本上，你要看是否有足够的变化(通过替代假设)来拒绝零假设。

The alternate hypothesis is just an alternative to the null.  Basically, you’re looking at whether there’s enough change (with the alternate hypothesis) to be able to reject the null hypothesis.

9、参考文献

https://www.statisticshowto.datasciencecentral.com/what-is-an-alternate-hypothesis/

https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/null-hypothesis/