No. I am not attacking the inductive argument in your points 1-4 above, which is not made in the paper, is not the basis for their claims, and is not what I am talking about.
You speak of the evidence from their study, but apparently you have not looked at the evidence from their study, presented in table 3. If you looked at the evidence you would see that they have a large number of measures of “hyperactivity”, and that they differed between test and control groups. They did not find that there was no difference between the groups. There is always a difference between the groups.
What they did, then, was do an F-test to determine whether the difference was statistically significant, using the assumption that all subjects respond the same way to the intervention. They make that assumption, come up with an F-value, and say, “We did not reach this particular F-value, therefore we did not prove the hypothesis that food dye causes hyperactivity.”
THEY DID NOT ASK WHETHER FOOD DYE INCREASED OR DECREASED HYPERACTIVITY BETWEEN THE GROUPS. That is not how an F-test works. They were, strictly speaking, testing the hypothesis whether the two groups differed, not in which direction they differed.
THERE WAS NO EVIDENCE THAT FOOD DYE DOES NOT CAUSE HYPERACTIVITY IN THEIR DATA. Not even interpreted in a Bayesian framework. They found a difference in behavior, they computed an F-value for 95% confidence assuming population homogeneity, and they did not reach that F-value.
No. I am not attacking the inductive argument in your points 1-4 above, which is not made in the paper, is not the basis for their claims, and is not what I am talking about.
You speak of the evidence from their study, but apparently you have not looked at the evidence from their study, presented in table 3. If you looked at the evidence you would see that they have a large number of measures of “hyperactivity”, and that they differed between test and control groups. They did not find that there was no difference between the groups. There is always a difference between the groups.
What they did, then, was do an F-test to determine whether the difference was statistically significant, using the assumption that all subjects respond the same way to the intervention. They make that assumption, come up with an F-value, and say, “We did not reach this particular F-value, therefore we did not prove the hypothesis that food dye causes hyperactivity.”
THEY DID NOT ASK WHETHER FOOD DYE INCREASED OR DECREASED HYPERACTIVITY BETWEEN THE GROUPS. That is not how an F-test works. They were, strictly speaking, testing the hypothesis whether the two groups differed, not in which direction they differed.
THERE WAS NO EVIDENCE THAT FOOD DYE DOES NOT CAUSE HYPERACTIVITY IN THEIR DATA. Not even interpreted in a Bayesian framework. They found a difference in behavior, they computed an F-value for 95% confidence assuming population homogeneity, and they did not reach that F-value.