Thus
the improbability of a given result is derived from its distance, in
standard-deviation units, from theoretical expectation. This distance is
calculated from a simple formula, and is known as the
"z-score." In parapsychology, as in most scientific fields, a
particular result is considered "statistically significant"
when the z-score is 2 or more - meaning, when it falls beyond 95% of the
results expected by chance alone. Given that there are no more than 5
chances out of 100 of obtaining such a result by pure chance, its
improbability is expressed in shorthand as p=.05.
Back to our 100-trial coin-toss example. Theoretical expectation here is
50, the mid-point and peak of the bell-curve. So a score of 50 is
equivalent to a z-score of 0. Scores of 55 or 45 are at 1 sigma (z=1),
and scores of 60 or 40 are at 2 sigma (z=2), with the aforementioned
p=.05. A score of 65 or 35, at 3 sigma (z=3), lies beyond 99.7% of
chance fluctuations, where p =.003; this means there are 3 chances in
1000 that the result is due to chance alone. In general, the higher the
value of Z the lower the p-value; the lower the p-value, the more
confidence we have that the result is really due to something other than
chance.
Even a small deviation from chance can be statistically significant, if
it persists over a large number of trials. We have seen that in a
100-toss experiment 65 tails - a 65% success rate - is equivalent to
p=.003. But in a 1000-toss experiment we would only need 547 tails, or
54.7%, to obtain the same p-value.
Note that very low p-values are expressed in "scientific
notation" - i.e., p = .000001 (1 chance in a million) becomes p=10-6. |
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