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Notes -
'Null hypothesis' does not mean 'most likely hypothesis'; it means 'the hypothesis that the thing for which we are looking does not exist.'
https://en.wikipedia.org/wiki/Null_hypothesis
I agree that's not the definition of "null hypothesis" and I have never claimed otherwise.
Here is a thought experiment to demonstrate my point:
Suppose that a previously unknown species of bird is discovered; 6 members of the new species are exposed to a high dose of radiation, a level that is known to kill roughly half of birds which are exposed. After the radiation exposure, 2 of the six die within a few weeks. There is a debate over whether or not this new species is invulnerable to radiation. There is no special reason to think that this new species is different from any other species of bird, but for some obscure political reason, there are people who insist that this new species is invulnerable to radiation.
Concerning our experiment, what should the null hypothesis be?
The null hypothesis would be that the value of X (in this case, susceptibility to radiation) does not differ between group A (previously known birds) and group B (the previously unknown species).
Notice that this does NOT agree with your previous definition of "null hypothesis":
Here, the thing we are looking for is a relationship between (1) exposure to radiation of members of the new bird species; and (2) death.
By your own reasoning, the null hypothesis is that this new bird species is not susceptible to radiation. Yes, this is a silly conclusion but that's the point: There's something very wrong with your reasoning.
The 'thing for which we are looking' is usually 'a difference in variable X between group A and group B.
X can be 'rate of disease progression/recovery' with A and B being patients administered a new medication vs. a placebo.
X can be 'susceptibility to radiation' with A and B being species of bird.
X can be 'biological capacity for intelligence' with A and B being human ethnic groups.
It's interesting that you choose the word "usually," it seems to me that this gives you the flexibility to frame the null hypothesis so as to fit your political preferences.
Here's another example:
Ok, Group A is males from Tribe Z; Group B is females from Tribe Z. The variable X is height.
So your reasoning, the null hypothesis is that there is no difference in height between the men and women of Tribe Z.
Agreed?
Yes, that would be the null hypothesis. The observed differences in height, both in the observed tribe members and in human beings in general, is the evidence with which we reject the null hypothesis, but it does not stop being the null hypothesis because it is rejected.
Scientific Study Finds No Significant Difference in Height Between Men and Women in Newly Discovered Tribe
This is a bit confusing. In my hypothetical, the study was strictly limited to a small number of members of Tribe Z. Are you saying that it's permissible to use general knowledge and/or data from outside of the study to make a determination regarding the null hypothesis? Are you saying it's required?
Yes, general knowledge can contribute to a rejection of the null hypothesis. That is why, while for the time being, I do not believe that there is a difference in genetically-determined intelligence between races, I am not claiming that as a sanity-complete proposition. If Omega-the-super-intelligent-computer-with-a-100.00%-track-record-of-being-right were to conclude that such intelligence differences exist, I would conclude that Nature is a racist arsehole and support transhumanism more vigorously, but I would not be compelled to re-evaluate everything I thought I knew the way I would if Ωtsicwa100ptrobr were to state that China does not exist or that the Napoleonic Era didn't happen.
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H0 (null): no difference between populations
H1 (alternative): radiation resistance of the new population > radiation resistance of the reference bird population
This is the typical formulation. Null typically assumes no effect or no difference between the populations being considered.
I tend to agree with you as to this particular example, but consider some of the formulations which have been floating around. Such as the "hypothesis that no relationship exists" Given that we are looking at (1) radiation being administered to the new bird population; and (2) deaths among that population, one could argue that the null hypothesis is that no relation exists between the radiation and the deaths.
I think that your formulation does not necessarily work either. For example, suppose there is an obscure un-contacted tribe of people in some remote rain forest and for whatever reason, the question on the table is whether the male members of the tribe are taller than the female members. Suppose further that we meet (and measure) only 4 members of the tribe -- 2 males and 2 females -- and that both of the males are significantly taller than either female. What's the null hypothesis here? Is it simply "no difference between the populations being considered"?
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Yeah but "intelligence is equally distributed among all human races" is a positive hypothesis of it's own, that's why you are effectively doing what he said.
The null hypothesis is indeed one of a set of competing hypotheses, but it’s typically the one that assumes no difference between populations.
If I want to show that two distributions are statistically different then I start with the assumption that they are not and then set out to disprove that.
Similarly, if I believe the populations are not actually significantly different, I believe it’d still be common to set up a null hypothesis that they are not different and then either confirm or reject the alternative hypothesis.
And what assumption do you use when you want to show that they are the same? It's just a matter of how you formulate your question.
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I would tweak that just a bit: "Intelligence is a unique human attribute in that unlike other heritable human attributes, the alleles for intelligence are distributed equally among all races and ethnic groups."
From this perspective, one can see that the "thing we are looking for" is evidence that intelligence is fundamentally different from other heritable human attributes.
In any event, as suggested by another poster, there is a more serious flaw with the argument, which is that we are being presented with an isolated demand for rigor. For example, there are people out there claiming that underachievement of Group X is largely due to historical treatment of Group X. Using the "null hypothesis" argument, this type of claim should fail even harder.
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As a matter of technical statistical terminology, the null hypothesis when testing two groups for equality is that the relevant average (usually the mean, but median tests exist) is the same for both groups.
The whole point of frequentist statistics is that the test doesn't care about what you believe or what the results mean, its just a handle you can turn and get a publishable paper out 5% of the time (if the null hypothesis is true) and rather more often (if its false). A null hypothesis and a prior are different things that exist in different paradigms.
In this case we know for a fact the averages are not the same, the debate is over the causes.
By stubbornly insisting the averages are the same and there's just something wrong with measurements which show otherwise, the debate over causes can be avoided. As I said, a defense in depth. It's not happening and if it is it's due to racism and even if it's not, we should take from the able to subsidize the unable.
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