> ... Early introduction of all the foods was not easy but it was safe. Among the infants who did manage to consume the recommended quantity of the allergenic foods there was a two-thirds reduction in overall food allergy.
> For those who fed their infant the recommended amount of peanut there was a significant reduction in peanut allergy, 2.5% in the standard introduction group compared to no cases in the early introduction group (0%).
> There was also a significant reduction for egg allergy- 5.5% in the standard introduction group compared to 1.4% in the early introduction group.
In other words, in the group as a whole when considering all food allergies, the difference was not statistically significant, but that can be attributed to a large number of families in the test group failing to actually perform the test. It sounds like when you control for actually following the instructions there is a statistically significant difference in overall food allergy incidence.
OP took a sentence out of context that said that overall food allergies across the whole group were not reduced by a statistically significant amount. But the authors go on to explain why that was and explain that if you control for real participation in the test then it is significant.
I didn't. There is no context there. It's not the whole group that were not reduced. Read the sentence again:
> food allergy was lower in the group introduced to allergenic foods early but the difference was not statistically significant
Group introduced to allergenic foods early. And of course if you control for kids that don't already display an allergy at the age that they're introducing it, you're going to have a reduced rate of allergy.
There's a reason they're saying it's not statistically significant...
It was statistically insignificant among the whole early introduction group. This includes everyone who may have been randomised into that group but then didn't follow the (quite onerous) regimen that we were given. This was a full schedule of when different foods had to be fed to the baby and how much. We'd have to record whether they had eaten the amount required and so on. Among those who did follow it, the results were significant. Most importantly, there were zero cases of peanut allergy in that group.
How is that proving the hypothesis?