Identifying an error means taking a specific claim and showing a mistake. Saying “You cannot do purely deductive reasoning about the real world and expect to get anything meaningful” is not identifying an error. Saying “There exists a child for whom X” is inductive proof of “For all children, X” is ridiculous. It gives a tiny tiny bit of support, but not anything anyone would call a proof, any more than “2+2 = 4″ is proof for “For all X, X+2 = 4.” The paper is making errors, but not that one. If you find one child and prove that he’s not affected by food dye, and you write a paper saying “This child’s behavior is not affected by dye, therefore no children’s behavior are affected by dye”, it will not be published. That was not their intent. I doubt anyone has ever published a paper using the “inductive proof” you think is standard.
In light of the fact that you didn’t read the post closely, didn’t read the paper, and don’t understand how an F-test works, you really should stop being so confident. The claims you’re making require you to have done all three. You are claiming that I interpreted their reasoning incorrectly, and you didn’t read it!
It seems you are confused about how statistics work. When you wish to study if group X has property Y, you take a statistically significant sample from group X and see if this sample has property Y. You then use the results from this sample to conclude whether the group as a whole has property Y (with a high or low probability). And this conclusion is always an inductive conclusion, never deductive.
As reported by you in your original post, their sample did not have the property they were looking for and they therefore concluded that the group as a whole does not have this property. You even reported that their statistics was sound. So, where is the error?
Edit to add: In other words, every statistical study ever done has always had a conclusion of the following form:
There exist a statistically significant sample where this property does (not) hold, therefore the property does (not) hold for the whole group.
Which is just the general form of what you critiqued here:
Translated back into English, this study proved:
There exist children for whom artificial food coloring does not affect behavior.
However, this is the actual final sentence of that paper:
The results of this study indicate that artificial food colorings do not affect the behavior of school-age children who are claimed to be sensitive to these agents.
So, by critiquing this study for being deductively wrong, you are in fact critiquing every statistical study ever done for being deductively wrong. Do you now see the problem with this?
Look, what you’ve written above is based on misunderstanding how an F-test works. I’ve already explained repeatedly why what you’re saying here, which is the same thing you’ve said each time before, is not correct.
This study contains a failure of an F-test. Because of how the F-test is structured, failure of an F-test to prove forall X P(X), is not inductive evidence, nor evidence of any kind at all, that P(X) is false for most X.
I will try to be more polite, but you need to a) read the study, and b) learn how an F-test works, before you can talk about this. But I just don’t understand why you keep making confident assertions about a study you haven’t read, using a test you don’t understand.
The F-test is especially tricky, because you know you’re going to find some difference between the groups. What difference D would you expect to find if there is in fact no effect? That’s a really hard question, and the F-test dodges it by using the arbitrary but standard 95% confidence interval to pick a higher threshold, F. Results between D and F would still support the hypothesis that there is an effect, while results below D would be evidence against that hypothesis. Not knowing what D is, we can’t say whether failure of an F-test is evidence for or against a hypothesis.
And I’ve repeatedly told you that you should’ve focused your critique on this instead of ranting about deduction. The last time I said it, you claimed the following:
There is nothing statistically wrong with the paper.
Now to answer your question:
But I just don’t understand why you keep making confident assertions about a study you haven’t read,
I haven’t been discussing this study, I’ve been trying to help you understand why your critique of it has been misguided.
using a test you don’t understand.
As for this claim you undoubtedly have an interesting “proof” for, I’ve simply avoided confusing you further with a discussion of statistics until you realized the following:
All statistical conclusions are deductively wrong.
A statistical study must be critiqued for it’s misuse of statistics (and obviously, then you must first claim that there is something statistically wrong with the paper).
Identifying an error means taking a specific claim and showing a mistake. Saying “You cannot do purely deductive reasoning about the real world and expect to get anything meaningful” is not identifying an error. Saying “There exists a child for whom X” is inductive proof of “For all children, X” is ridiculous. It gives a tiny tiny bit of support, but not anything anyone would call a proof, any more than “2+2 = 4″ is proof for “For all X, X+2 = 4.” The paper is making errors, but not that one. If you find one child and prove that he’s not affected by food dye, and you write a paper saying “This child’s behavior is not affected by dye, therefore no children’s behavior are affected by dye”, it will not be published. That was not their intent. I doubt anyone has ever published a paper using the “inductive proof” you think is standard.
In light of the fact that you didn’t read the post closely, didn’t read the paper, and don’t understand how an F-test works, you really should stop being so confident. The claims you’re making require you to have done all three. You are claiming that I interpreted their reasoning incorrectly, and you didn’t read it!
It seems you are confused about how statistics work. When you wish to study if group X has property Y, you take a statistically significant sample from group X and see if this sample has property Y. You then use the results from this sample to conclude whether the group as a whole has property Y (with a high or low probability). And this conclusion is always an inductive conclusion, never deductive.
As reported by you in your original post, their sample did not have the property they were looking for and they therefore concluded that the group as a whole does not have this property. You even reported that their statistics was sound. So, where is the error?
Edit to add: In other words, every statistical study ever done has always had a conclusion of the following form:
There exist a statistically significant sample where this property does (not) hold, therefore the property does (not) hold for the whole group.
Which is just the general form of what you critiqued here:
So, by critiquing this study for being deductively wrong, you are in fact critiquing every statistical study ever done for being deductively wrong. Do you now see the problem with this?
Look, what you’ve written above is based on misunderstanding how an F-test works. I’ve already explained repeatedly why what you’re saying here, which is the same thing you’ve said each time before, is not correct.
This study contains a failure of an F-test. Because of how the F-test is structured, failure of an F-test to prove forall X P(X), is not inductive evidence, nor evidence of any kind at all, that P(X) is false for most X.
I will try to be more polite, but you need to a) read the study, and b) learn how an F-test works, before you can talk about this. But I just don’t understand why you keep making confident assertions about a study you haven’t read, using a test you don’t understand.
The F-test is especially tricky, because you know you’re going to find some difference between the groups. What difference D would you expect to find if there is in fact no effect? That’s a really hard question, and the F-test dodges it by using the arbitrary but standard 95% confidence interval to pick a higher threshold, F. Results between D and F would still support the hypothesis that there is an effect, while results below D would be evidence against that hypothesis. Not knowing what D is, we can’t say whether failure of an F-test is evidence for or against a hypothesis.
And I’ve repeatedly told you that you should’ve focused your critique on this instead of ranting about deduction. The last time I said it, you claimed the following:
Now to answer your question:
I haven’t been discussing this study, I’ve been trying to help you understand why your critique of it has been misguided.
As for this claim you undoubtedly have an interesting “proof” for, I’ve simply avoided confusing you further with a discussion of statistics until you realized the following:
All statistical conclusions are deductively wrong.
A statistical study must be critiqued for it’s misuse of statistics (and obviously, then you must first claim that there is something statistically wrong with the paper).