Statistically significant is a term that is often bandied about. What does it really mean? Why is it important?

First–why is it important?

It is important because it helps the evaluator make decisions based on the data gathered.600px-FUDGE_4dF_probability.svg

That makes sense–evaluators have to make decisions so that the findings can be used. If there  isn’t some way to set the findings apart from the vast morass of information, then it is only  background noise. So those of us who do analysis have learned to look at the probability level (written as a “p” value such as p=0.05). The “p” value helps us determine if something is true, not necessarily that something is important.

probability of occurringSecond–what does that number really mean?

Probability level means–can this  (fill in the blank here) happen by chance? If it can occur by chance, say 95 times out of 100, then it is probably not true.  When evaluators look at probability levels, we want really small numbers. Small numbers say that the likelihood that this change occurred by chance (or is untrue) is really unlikely. So even though a really small number occurs (like 0.05) it really means that there is a 95% chance that this change did not occur by chance and that it is really true. You can convert a p value by subtracting it from 100 (100-5=95; the likelihood that this did not occur by chance)

Convention has it that for something to be statistically significant, the value must be at least 0.05. This convention comes from academic research.  Smaller numbers aren’t necessarily better; they just confirm that the likelihood that true change occurs more often. There are software programs (Statxact for example) that can compute the exact probability; so seeing numbers like 0.047 would occur.2007-01-02-borat-visits-probability

Exploratory research (as opposed to confirmatory) may have a higher p value such as p=0.10.This means that the trend is moving in the desired direction.  Some evaluators let the key stakeholders determine if the probability level (p value) is at a level that indicates importance, for example, 0.062. Some would argue that 94 time out of 100 is not that much different from 95 time out of 100 of being true.

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