Why we should be obligated to use the null hypothesis if it is reasonable
The logic of hypothesis testing is a specific application of decision theory, and it gives a normative or prescriptive idea of optimal decisions under uncertainty.
When we need to take decision/ conclude on hypothesis about a population,
Hypothesis test is a statistical method that uses sample data to evaluate a hypothesis about a population. So, hypothesis test is really a set of rules that if scientists follow, we can be optimal in our decisions.
In Hypothesis test, the null hypothesis states something very specific that in the population , for eg. population mean is 100. So, notice that this makes a specific statement that whatever difference we obtain with observed sample is due to sampling error only (noise).
Null hypothesis has a very critical place in science. We are obligated to use null hypothesis (of observed difference is due to sampling error) if it is reasonable. Because this is the most parsimonious (simple) explanation we can have for any difference obtained, because this explanation makes no statement about anything else happening in the world other than something we know will always happen in the world.
Sampling error
is always going to happen when we take a sample from a population. Our sample
statistics will not match the population parameter. So, sampling error will always be a part of any measurement we make.
So, the null hypothesis says that whatever difference we obtain is simply that
sampling error. We know will always be there.
Why we should be obligated to use the null hypothesis if it is reasonable, goes to Occam's razor philosophy, entities must not be multiplied beyond necessity, is simply a method for deciding between competing explanations (Null and Alternate Hypothesis). Occam’s razor says that we should use the simplest explanation as long as it can reasonably account for whatever we have observed.
The null hypothesis is simply an instantiation of this razor that we should use it if it is reasonable. Purpose of scientistic experiments is to discredit the null hypothesis to say in some way that the null hypothesis isn't reasonable that whatever difference we obtain isn't reasonably attributable to sampling error alone. Remember to do this scientists are going to discredit the null hypothesis because believing the alternative hypothesis will add some entity to the world that is we will be adding to our explanation something other than just sampling error and given our preference for parsimonious explanations in the world we will need some amount of evidence in order to discredit that null hypothesis before we can start believing the alternative hypothesis is true.
Null and Alternate hypotheses are mutually exclusive and exhaustive. If we can discredit one of these hypotheses, specifically the null hypothesis, we will have some reason to believe the other explanation, the alternative hypothesis, is a better explanation for what we have observed.
For instance if we flip a coin a 100 times and get a 100 heads the null hypothesis could be true but it would be a very unlikely event for us to flip a 100 times and get a 100 heads. The null hypothesis could be true but it's not a reasonable explanation given what we know about what happens when we flip coins.
All of statistical inference is like this we need to know if our effect is like the100 heads on 100 coin flips or if it's like 51 heads on 100 coin flips in both cases the null hypothesis could be true but when we get a 100 heads it doesn't seem reasonable to assume it's true
It might seem reasonable to take the alternative hypothesis and make predictions from that but it will be very hard to discredit the alternative hypothesis that the mean after treatment is not equal to a certain value.
In science we try to falsify theories. In hypothesis testing we are in falsify hypotheses, that's the only way we can make good inferences. so we need a hypothesis that we can discredit (ref 2)
The null hypothesis makes a very specific claim that the mean of a population will have a mean of exactly certain value. Further, we know what types of sample means to expect if a population has a mean of certain value. As we knew the characteristics of the sampling distribution in this context (the mean of a sampling distribution of sample means that was equal to whatever population were taking samples from and we also knew the standard deviation of the sampling distribution of sample means that is the standard error) and to figure out these characteristics we only need to know the population mean we're trying to estimate. Thus, to have an idea of what types of sample means we would expect to get we need certain value, which is if the null hypothesis is true.
Reference:
'Module 1:7 - Statistical Inference I' in "Significantly Statistical Methods' a Free Online Statistics Course with JMP Software. Accessed at Significantly Statistical Methods Online Course | JMP
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