Colored Vegetables and Stroke
A study of colored vegetables and the risk of stroke was done. Although the investigators did not see any effect on stroke of consumption of green, orange, red, yellow, or purple vegetables, they concluded that "High intake of white fruits and vegetables may protect against stroke."
Suppose that for each pair of color groups, we wished to test whether the stroke risk was different. For instance, is it different for green vs. orange? For green vs. red? Suppose there are 10 different pairs to be compared.
Suppose that, for each pair, we perform a hypothesis test with a significance level of 10%. Assume that in truth, there are no differences between any of the pairs.
By chance alone, how many of the hypothesis tests would you expect to appear significant (and thus lead us to mistakenly believe that there was a difference)?
(Source: Oude Griep, et al . 2011. Colors of fruit and vegetables and 10-year incidence of stroke. Stroke 42(11), 3190-3195.)