Random sampling is a mathematical necessity beyond debate or opinion for valid statistical inferences

This poster aims at reminding researchers of the unignorable fundamental concern of random sampling issue in statistical inferences. Random sampling refers to the process of clearly defining a target population and then a probabilistic sample(s) can be literally taken from the population. More specifically, a target population is the collection of all sampling units relevant to some well-defined research questions and, by some objective chance mechanism, each sampling unit has the equal or known probability to be selected into a sample which is referred to as ‘a random sample’. Therefore, each sample unit can be weighted by the inverse of the selection probability to get unbiased estimates of the parameters that fully define the population. Statistical inferences aim at making justifiable conclusions about a population based on sample data. The random sampling thus becomes a matter of mathematical necessity rather than a matter of debate or opinion for any valid statistical inferential analysis. However, it is a matter of fact that practical and/or ethical factors make it literally impossible in most instances to obtain random samples for real life research. This unavoidable fundamental flaw alone invalidates the generalizability of research findings beyond the sample data on the ground of statistical inferences. Sadly, most textbook authors unduly dismiss (or simply ignore) the concerns of random sampling issue with statistical fables (e.g., ‘your sample of observations can be imagined to come and may be regarded as a random sample’); hence most statistical analysis practices simply assume that the random sampling flaw in statistical inferences is negligible.