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The confidence interval for any study is a matter of choice, one that is normally decided upon before the study begins but not always.
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Absoluely true, and studies that use higher confidence levels are the ones that tend to be more reliable. I was speaking generally, however, and in general most studies use 95%.
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The major study from which trans fats results have been taken is the Harvard Nurse’s Health Study, which contains 120,000 participants.
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The study that showed that fats in general are harmless is drawn from the same data.
The important thing to remember about the Harvard Nurses Study is that it is a data dredge. It contains data on thousands of conditions and thousands of factors. The researchers regularly pull data from it and at least once in every twenty tries they find something they can publish.
The negative results it produces are the useful ones, because the size of the study reinforces them so heavily, but they rarely get published.
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0.05 would product one false positive in 20. However, 0.0001 would only product one false positive in 10,000.
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So you have to ask, how many studies have been conducted and how many tests did they involve? If 40 researchers have done an average of 5 studies each, each involving an average of 50 tests, that’s your 10,000 tests and you should see 1 that is significant at 0.0001. And quite a lot that are significant at lesser levels. How much trawling was done through the data, and how many tests carried out, to get the ones you quoted?
I don’t know whether trans-fats are bad or not. I do know that if they are harmful, and if there were a reasonable percentage of them consumed in the studies published in JAMA, they should have swayed at least one of the four results into significance. The odds against them doing so have a lot more than four zeros after them. 
The studies are:
Beresford et al, Low-Fat Dietary Pattern and Risk of Colorectal Cancer, JAMA 295 (6) p 643
Howard et al, Low-Fat Dietary Pattern and Risk of Cardiovascular Disease, JAMA, 295 (6) p 655
Prentice et al, Low-Fat Dietary Pattern and Risk of Invasive Breast Cancer, JAMA, 295 (6) p 629