There exist children for whom artificial food coloring does not affect behavior.
The whole point of inductive reasoning is that this is evidence for artificial food coloring not affecting the behavior of any children (given a statistically significant sample size). You cannot do purely deductive reasoning about the real world and expect to get anything meaningful. This should be obvious.
They measured a difference between the behavior of the test and the control group. They chose an F-value that this difference would have to surpass in order to prove the proposition that food color affects the behavior of all children. The specific number they chose requires the word “all” there. The differences they found were smaller than the F-value. We don’t know whether the differences were or were not large enough to pass an F-value computed for the proposition that food color affects all but one child, or most children, or one-fifth of all children.
Where, exactly, is the evidence that artificial food color doesn’t affect the behavior of any children?
Why would I critique them for finding values smaller than the F-value? The values were smaller than the F-value. That means the test failed. What I then critiqued was their logical error in interpreting the test’s failure.
Where, exactly, is the evidence that artificial food color doesn’t affect the behavior of any children?
Since your post is the first time I’ve heard of this: I have no idea, but I assume google has the answer.
I mean where in the paper. There is no evidence in the paper that artificial food color doesn’t affect the behavior of any children.
Your claim that they are using inductive logic shows that you didn’t understand the paper. Your response that I should have critiqued their not finding a high enough F-value shows you really don’t have the first clue about what an F-test is. Please learn a little about what you’re critiquing before you critique it so confidently in the future.
What I then critiqued was their logical error in interpreting the test’s failure.
No, what you (originally) critiqued was the lack of rigorous deductive reasoning in their statistical analysis, as shown by both your introduction and conclusion solely focusing on that. Even whatever point you tried to make about the F-values was lost in a rant about deduction.
I mean where in the paper. There is no evidence in the paper that artificial food color doesn’t affect the behavior of any children.
In your own words you stated the following:
Translated back into English, this study proved:
There exist children for whom artificial food coloring does not affect behavior.
And that sentence (if true as you claim) is inductive evidence for their conclusion. How many times do I have to tell you this?
Your claim that they are using inductive logic shows that you didn’t understand the paper.
All statistical reasoning is inductive reasoning. You claiming the opposite shows that you don’t understand statistics.
Your response that I should have critiqued their not finding a high enough F-value shows you really don’t have the first clue about what an F-test is.
Since you completely missed my point, I’ll try again: Focus on critiquing what’s statistically wrong in this paper, not what’s deductively wrong. I simply chose that sentence as it seemed to be the most coherent one in your response.
Now, you seem to be under the assumption that I am defending this paper and it’s conclusion, so let me make it clear that I do not. I have neither read it, nor plan to. I merely found you attacking a statistical analysis for being deductively wrong, and chose to try and help you clear up whatever misunderstanding you had about statistics being a part of deductive reasoning.
I’m guessing you’ve recently started learning about discrete mathematics, and seek to apply your new knowledge on quantifiers to everything you come across. Don’t worry about being wrong, almost everyone goes through such a phase.
Since you completely missed my point, I’ll try again: Focus on critiquing what’s statistically wrong in this paper, not what’s deductively wrong. I simply chose that sentence as it seemed to be the most coherent one in your response.
So you chose a sentence without understanding it.
There is nothing statistically wrong with the paper.
I merely found you attacking a statistical analysis for being deductively wrong, and chose to try and help you clear up whatever misunderstanding you had about statistics being a part of deductive reasoning.
The error is not in the statistical analysis. The error is in the deductions they made when interpreting it. You are claiming that logic and statistics are like oil and water, and can never co-occur in the same paper. This is incorrect.
I’m guessing you’ve recently started learning about discrete mathematics, and seek to apply your new knowledge on quantifiers to everything you come across. Don’t worry about being wrong, almost everyone goes through such a phase.
As I mentioned in my post, I used to teach logic at a university. So now you have also proved you didn’t read my post. And you have proved you don’t know the difference between logic and discrete math. So know we know that you
don’t know what an F-test is
didn’t read the whole post
don’t know the difference between logic and discrete math
And I also kinda doubt you read the paper. Did you?
I’m sorry that LessWrong has made you stupider, by giving you false confidence to speak with authority on matters you are ignorant of.
As to being wrong, identify an error in anything I’ve said, instead of spouting platitudes about induction without any connection to specific facts and arguments.
The error is in the deductions they made when interpreting it.
And the whole point of science is that it is built on inductive (and not deductive) reasoning.
You are claiming that logic and statistics are like oil and water, and can never co-occur in the same paper. This is incorrect.
Well, I’ll give you points for creativity in your straw man, at least.
As I mentioned in my post, I used to teach logic at a university.
So, you were a TA then?
So now you have also proved you didn’t read my post.
No, it merely “proves” that I skimmed the personal biography part of your post in favor of focusing on your actual content.
don’t know what an F-test is
Please tell me how you “proved” this.
And you have proved you don’t know the difference between logic and discrete math.
Well, every course in discrete mathematics usually has at least a lesson or two on logic and quantifiers. I just assumed you learned it in such a setting since then you would have had an excuse to not understand it properly (as opposed to having spent an entire course focused solely on logic).
And I also kinda doubt you read the paper. Did you?
Funny how you use the fact that I skimmed the non-essential parts of your original post as proof that I didn’t read any it, and then goes on to completely ignore what I wrote here:
Now, you seem to be under the assumption that I am defending this paper and it’s conclusion, so let me make it clear that I do not. I have neither read it, nor plan to. I merely found you attacking a statistical analysis for being deductively wrong, and chose to try and help you clear up whatever misunderstanding you had about statistics being a part of deductive reasoning.
I also find your usage of the word “proof” very interesting for someone who claims to have taught logic.
I’m sorry that LessWrong has made you stupider, by giving you false confidence to speak with authority on matters you are ignorant of.
Do you always insult people who try to help you? It might help your future discussions if you don’t take criticism so personally.
As to being wrong, identify an error in anything I’ve said,
I have already done so numerous times. Maybe you should try to read my arguments instead of just skimming and assuming?
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).
The whole point of inductive reasoning is that this is evidence for artificial food coloring not affecting the behavior of any children (given a statistically significant sample size). You cannot do purely deductive reasoning about the real world and expect to get anything meaningful. This should be obvious.
They measured a difference between the behavior of the test and the control group. They chose an F-value that this difference would have to surpass in order to prove the proposition that food color affects the behavior of all children. The specific number they chose requires the word “all” there. The differences they found were smaller than the F-value. We don’t know whether the differences were or were not large enough to pass an F-value computed for the proposition that food color affects all but one child, or most children, or one-fifth of all children.
Where, exactly, is the evidence that artificial food color doesn’t affect the behavior of any children?
Then this is what you should have critiqued in your post. Ranting about their inductive reasoning being deductively wrong gets you nowhere.
Since your post is the first time I’ve heard of this: I have no idea, but I assume google has the answer.
Why would I critique them for finding values smaller than the F-value? The values were smaller than the F-value. That means the test failed. What I then critiqued was their logical error in interpreting the test’s failure.
I mean where in the paper. There is no evidence in the paper that artificial food color doesn’t affect the behavior of any children.
Your claim that they are using inductive logic shows that you didn’t understand the paper. Your response that I should have critiqued their not finding a high enough F-value shows you really don’t have the first clue about what an F-test is. Please learn a little about what you’re critiquing before you critique it so confidently in the future.
No, what you (originally) critiqued was the lack of rigorous deductive reasoning in their statistical analysis, as shown by both your introduction and conclusion solely focusing on that. Even whatever point you tried to make about the F-values was lost in a rant about deduction.
In your own words you stated the following:
And that sentence (if true as you claim) is inductive evidence for their conclusion. How many times do I have to tell you this?
All statistical reasoning is inductive reasoning. You claiming the opposite shows that you don’t understand statistics.
Since you completely missed my point, I’ll try again: Focus on critiquing what’s statistically wrong in this paper, not what’s deductively wrong. I simply chose that sentence as it seemed to be the most coherent one in your response.
Now, you seem to be under the assumption that I am defending this paper and it’s conclusion, so let me make it clear that I do not. I have neither read it, nor plan to. I merely found you attacking a statistical analysis for being deductively wrong, and chose to try and help you clear up whatever misunderstanding you had about statistics being a part of deductive reasoning.
I’m guessing you’ve recently started learning about discrete mathematics, and seek to apply your new knowledge on quantifiers to everything you come across. Don’t worry about being wrong, almost everyone goes through such a phase.
So you chose a sentence without understanding it.
There is nothing statistically wrong with the paper.
The error is not in the statistical analysis. The error is in the deductions they made when interpreting it. You are claiming that logic and statistics are like oil and water, and can never co-occur in the same paper. This is incorrect.
As I mentioned in my post, I used to teach logic at a university. So now you have also proved you didn’t read my post. And you have proved you don’t know the difference between logic and discrete math. So know we know that you
don’t know what an F-test is
didn’t read the whole post
don’t know the difference between logic and discrete math
And I also kinda doubt you read the paper. Did you?
I’m sorry that LessWrong has made you stupider, by giving you false confidence to speak with authority on matters you are ignorant of.
As to being wrong, identify an error in anything I’ve said, instead of spouting platitudes about induction without any connection to specific facts and arguments.
And the whole point of science is that it is built on inductive (and not deductive) reasoning.
Well, I’ll give you points for creativity in your straw man, at least.
So, you were a TA then?
No, it merely “proves” that I skimmed the personal biography part of your post in favor of focusing on your actual content.
Please tell me how you “proved” this.
Well, every course in discrete mathematics usually has at least a lesson or two on logic and quantifiers. I just assumed you learned it in such a setting since then you would have had an excuse to not understand it properly (as opposed to having spent an entire course focused solely on logic).
Funny how you use the fact that I skimmed the non-essential parts of your original post as proof that I didn’t read any it, and then goes on to completely ignore what I wrote here:
I also find your usage of the word “proof” very interesting for someone who claims to have taught logic.
Do you always insult people who try to help you? It might help your future discussions if you don’t take criticism so personally.
I have already done so numerous times. Maybe you should try to read my arguments instead of just skimming and assuming?
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).