So in general, for this experiment, we would define the difference, d, to be:ĭ = thickness after Vit. If an individual had a maximal thickness of 0.92mm before the Vitamin E treatment, and 0.95mm after the treatment, the difference, d, for that individual would be For example, suppose we consider the thickness of plaque (mm) in the carotid artery, referenced in Example 1. When considering dependent samples, we analyze the difference, d, in each matched pair. This will be very important as we progress, because we will need to distinguish between whether the samples are dependent or independent, because the statistical methods will be very different. matched-pair design) Two samples are independent when the individuals in one sample do not determine the individuals in the other sample. In general, two samples are dependent if the individuals in one sample determine the individuals in the other sample. In examples like this, where the indivuaduals selected have no relation to each other, we call the samples independent. of Statistics)ĭiscussion: Unlike in Example 1, the samples in this example are completely unrelated ( two different locations). Does the data suggest that the true mean soil pH values differ for the two locations? (Source: UCLA Dept. Problem: Nine observations of surface soil pH were made at two different locations.
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