The Null Hypothesis

26 05 2011

(This post was originally posted at Disjointed Thinking.)

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One of the most accurate ways to describe my religious beliefs (or lack thereof) is by way of a concept known as the “null hypothesis”. Like most atheists, I do not claim that I know God does not exist. I merely claim that there is not enough evidence to justify belief in God. And the best way to illustrate this claim is through the null hypothesis. This is a statistical concept that is used for hypothesis testing in science. Because statistics is not a strong point for many people, I will try to explain it using a minimum of stats jargon; however, some will be required, and I will try to explain what each term means the best that I can. I really feel that this is an important concept to understand when one is trying to assess evidence claims (which happens to us all the time). So hang on for the ride!

Basic Statistics

Normal DistributionWhen I measure a certain phenomenon, such as people’s height, there will always be some variability in the results. And for many phenomena, this variability will result in a bell-shaped curve known as a “normal distribution”. There are some very interesting properties of the normal distribution, but what is important here is that the majority of the cases will be clustered around the mean (the statistical word for “average”), and then fewer cases will occur further away from the mean. So for instance, the mean height for a Canadian adult is about 5’8″ for men and 5’3″ for women.1 So if I randomly selected a Canadian man, he would be most likely to have a height somewhere around 5’8″. Or if I wanted to be more precise, I could say that he is likely to fall between about 4’11” and 6’5″. I’d be very surprised if this randomly selected person turned out to be 8 feet tall. There are very few people who are that tall, so it would be very unusual to have chosen them. So the normal distribution tells us that the most frequent cases occur around the mean, and that cases occurring further away are less frequent.

Hypothesis Testing

So what would I do if someone told me of a town in rural Alberta where all the adult townspeople were over 7 feet tall? I would likely be very skeptical. Such a thing is very unlikely, isn’t it? It’s unusual to find even one person over 7 feet tall, let alone an entire town of both men and women over 7 feet tall! But to be a good scientist, I should hold onto my skepticism but remain open to the possibility that such a strange case is indeed true. I would want to head over to this town and start measuring. But let’s say I don’t have the resources to measure every single individual in the town. I might measure 40 or 50 of them. And perhaps the person who told me this story was exaggerating a little bit, and some were below 7 feet. But I might still ask, “Are the people in this town significantly taller than the general population?” And that is a great question with which to use hypothesis testing.

Null HypothesisWhen scientists want to test a hypothesis, they must come up with two different hypotheses to compare. One of these (known as the alternate hypothesis) is the one they would ideally like to be confirmed; in my case, it is this: “The people in this rural town are statistically taller than the general population.” The other hypothesis is known as the null hypothesis, and in my case it would be the following: “There is no difference in the average height of the people in this rural town and the general population.” But why do we need to compare these two things? Why not just see if the alternate hypothesis is confirmed? The reason is because, like I mentioned earlier, phenomena always have some variability. If I measured the townspeople and found out that they averaged 6’8″, that doesn’t mean that every single person was 6’8″ tall. Some were taller, and some were shorter. So how would I know whether I was finding someactual difference between the townspeople and the general population, or if I just happened to select the 50 tallest people in the town? Hypothesis testing helps us to determine whether we just have a bad sample, or if the normal distribution for the town is actually different from the normal distribution for the general population. Or to put it another way, it helps us distinguish between real differences and random fluctuation. The null hypothesis says, “This is just random fluctuation,” and the alternate hypothesis says, “No, this is a real difference.” Scientists support the alternate hypothesis indirectly by disconfirming the null hypothesis. If the data that scientists collect don’t fit with the null hypothesis, then they have better evidence to support the idea that the alternate hypothesis is true. On the other hand, if the data do fit with the null hypothesis, this doesn’t necessarily mean that the null hypothesis is true; it just means that the data do not contradict it.

The Role of Evidence

Another way to look at the concept of the null hypothesis is to use the analogy of a court case. In the modern justice system, the defendant is considered innocent until proven guilty. The prosecution must provide sufficient evidence to prove his or her guilt. In some ways, this works similar to the null hypothesis. The null hypothesis is assumed to be true until sufficient evidence is provided to demonstrate otherwise. The evidence in favour of the alternate hypothesis must outweigh the evidence in favour of the null hypothesis.2 If I want to prove the statement that the Albertan townspeople are significantly taller than the general population, I have to have sufficient evidence that my measurements are not just a reflection of random variability and then add more evidence suggesting that they are actually due to some real difference in height (whatever the cause of this unusually tall town might be).

Black SwanThe null hypothesis works very similarly when it comes to other types of claims. The statement, “God exists”, is a positive claim about the existence of an entity. So in this case, the null hypothesis would be, “God does not exist.” This works the same as any other positive claim: “Unicorns exist” vs. “Unicorns do not exist”, “It rained yesterday” vs. “It did not rain yesterday”, “Black swans exist” vs. “Black swans do not exist”, and so on. If one wants to prove the truth of these statements, they must provide evidence which is sufficiently inconsistent with the null hypothesis. If I try to prove that it rained yesterday by saying that I held my hand out the window and felt splashes of water, this might be good evidence, unless someone points out that I have a leaky eaves-trough directly above my window. In other words, if my evidence can be shown to be perfectly consistent with the idea that it did not, in fact, rain yesterday, then it should not be used to support the idea that it did rain yesterday. I should provide other evidence to support my claim. Or if I mention that I saw a black swan, but upon further examination it turns out to be a black duck, this is no longer evidence that black swans exist. The fact that the evidence must be thrown out does not prove that black swans don’t exist, but it no longer proves that they do. And if there were absolutely no good evidence to prove that black swans exist, why would anyone believe in them?

The claim that God exists is exactly the same as all these other claims. The burden of proof is always on the person making the positive claim. That person must provide good evidence to demonstrate that the claim is true. And if the evidence they provide is entirely consistent with the null hypothesis (that God does not exist), then the evidence is no good. Again, this does not prove that God does not exist, but if there is absolutely no good evidence to prove that God exists, why would anyone believe in him? This is why the null hypothesis is a crucial concept to grasp. Saying “The evidence does not prove that God exists” is entirely different than saying “The evidence proves that God does not exist”. The null hypothesis is a safe bet that requires other hypotheses to prove themselves to be true before one believes in them. If I went to a random rural town in Alberta, my first assumption would be that their average height is about the same as the average height of the general population. This doesn’t mean that it actually is the case that their average heights are the same, but I have no prior reason to think so until I have evidence to prove otherwise. It would be silly to point to an entirely random town for which one has no prior knowledge and say, “That town is filled with giants.” And it would be even sillier to take measurements of the townspeople, see that they have an average height similar to the general population, and still say, “That town is filled with giants.” As far as I am concerned, however, that is what most believers in God do.

Conclusion

I don’t intend to get into an examination of the evidence for and against the existence of God. I have written an entire ten-part series about just that. The intent of this article was to develop a process for assessing whether God exists. The general process is to assume that God does not exist until one finds sufficient evidence to support the claim that he does. To do otherwise is to choose a position that one likes before even taking a look at the evidence. (It’s like assuming the town is full of giants before even seeing a townsperson.) In many cases where this happens, people do this for emotional reasons. They have some desire to believe a certain thing, and so they make up their mind before they even take a look at the evidence. Such a process is irrational, especially since humans have “tendencies”. We often see patterns that are not there (like people who develop superstitions, for example); we seek out evidence to support the beliefs that we already hold and ignore disconfirming evidence, instead of trying to objectively assess all the evidence; and we often reach conclusions that we like and then make up justifications for them afterwards. The only way to avoid these tendencies is to acknowledge that we suffer from them and then try to minimize them through the use of rigorous processes such as hypothesis testing.

Hypothesis

So when I say that I am a “null hypothesis atheist”, I mean that the evidence for God’s existence is either a) faulty, b) illusory, or c) consistent with the null hypothesis that God does not exist. I do not make the statement, “Therefore, God does not exist.” Instead, I simply say, “There is no good evidence to believe that God exists, and I don’t believe in things with no good evidence.” Sure, God might be out there, hiding behind some distant spiral galaxy or outside of space and time altogether. But I will take the conservative path that tries to minimize irrationality, because such a path is the best process we’ve developed to distinguish fact from fiction.

Notes:

  1. I should note that human height is not technically normally distributed, but rather negatively skewed. I’m using this example for illustrative purposes.
  2. Any statisticians reading this are probably cringing at this point. I understand that this is a distortion of how hypothesis testing actually works. But as an admittedly imperfect analogy, I still think it works well enough for providing non-statisticians with an understanding of the basic reasoning behind the null/alternate hypotheses.
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2 responses

9 03 2017
scientist

You’ve failed to mention one very important aspect of hypothesis testing…setting your alpha level to guard against Type II error (to say there is no god when really there is). Alpha and Beta are set based on the liability of making a type 1 or type 2 error…and to make a Type 2 error here is far worse than the alternative. So to improve the power of a test (1-beta) and to be 100% sure you could guard against making a type 2 error, you would need an infinite sample size. Impossible right? That’s the point. Any good scientist would make the null ‘there is no god’ and guard against making a Type II error.

6 10 2017
Atheistic Null Hypothesis: There is no God/Gods | Damien Marie AtHope

[…] instance, the mean height for a Canadian adult is about 5’8″ for men and 5’3″ for women.1 So if I randomly selected a Canadian man, he would be most likely to have a height somewhere […]

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