| Calling Sequence | Zscore(data)
ZscorePercent(data) | ||||||||||||
| Parameters |
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| Return Type | {list,matrix} | ||||||||||||
| Synopsis | Zscore transforms a vector or matrix of counts into a vector/matrix of normalized variables (ones with expected value 0 and variance 1). This is subtracting the expected value and dividing by the standard deviation. Or Z = (X-E[X])/sqrt(Var(X)). | ||||||||||||
In this way the observations can be measured in "standard deviations away from the mean", which is a simple and useful measure. This is sometimes called the Z-transform, but since the Z-transform has a well established use in power series, we use the name Zscore. | |||||||||||||
If the input is a vector of integers, it is assumed that all the values are counts of events which are equally probable. If the input is a matrix it is assumed that the values are counts of two independent events (columns/rows). In both cases, a binomial distribution is assumed for the counts, i.e. the individual events counted are independent of each other. ZscorePercent is very similar, but instead of returning a normalized variable, it returns a percentage of the expected value, i.e. Z = 100 * (X-E[X])/E[X] | |||||||||||||
| Examples | > Zscore( [8,12,21,7] ); [-1.3333, 0, 3, -1.6667] > print(Zscore( [[3,7,21],[10,15,33]] )); -0.73710648 -0.25050450 0.56887407 0.55192433 0.19114995 -0.47500296 > ZscorePercent( [8,12,21,7] ); [-33.3333, 0, 75, -41.6667] | ||||||||||||
| See also | Cumulative, CumulativeStd, OutsideBounds, ProbBallsBoxes, ProbCloseMatches, Rand, StatTest, Std_Score, TestStatResult | ||||||||||||