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Inferential Statistics

October 29, 2010

The essential task of inferential statistics is to determine what can reasonably be concluded about an entire domain of phenomena—a population—on the basis of having examined only a limited sample of instances drawn from that domain.

A ‘sample’ is a relatively small window through which the investigator hopes to see the outlines of some larger, more inclusive reality. In some cases, the glimpse provided by the sample might truly represent the larger reality, while in other cases it might misrepresent it, leading the investigator to erroneous conclusions. This latter possibility derives from the fact that the phenomena of nature are often shot through and through with random variability. While the risk of drawing erroneous conclusions from a limited sample is considerable within any domain of phenomena, it is especially great in those domains that pertain to the mentality, behavior, and biology of living organisms.

At any rate, whenever there is random variability inherent in the phenomena under investigation, there is always the possibility that the observed facts result from nothing other than mere chance coincidence; and until that possibility is rigorously assessed, no conclusions can reasonably be drawn from a sample, one way or the other.

‘Statistical significance’ is the logical and mathematical apparatus by which that assessment is accomplished. This is far and away the most commonly encountered question of inferential statistics within the various fields of scientific research: “Here are some facts that we have extracted from the complex, chance-infused flow of real-world events.

Now that we have them, how confident can we be that they signify anything more than mere chance, mere random coincidence—the luck of the scientific draw, so to speak?”

via Intro Statistical Significance.

Categories: Statistical Concepts
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