What Makes Analyzing Survey Data Different?

When most students begin to study statistics, they are generally taught formulas which assume that all of the observations they are analyzing had an equal probability of being selected into the sample. The reason for this assumption is that, given simple random selection, estimation of statistics of interest (e.g. means, regression coefficients, etc.) is straightforward. In addition, assuming equal selection probabilities makes it possible to calculate a statistic’s variance (a measure of the precision of an estimate) without much difficulty.
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