Z Score

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Z Score - short version

(1) Statistical measure that quantifies the distance a point is from the mean in terms of standard deviations.

(2) The observed value of the z statistic.

Z Score - long version

The z-score also known as standard score, z-values, z-scores, normal scores, and standardized variables; the use of "Z" is because the normal distribution is also known as the "Z distribution", indicates how many standard deviations an observation or datum is above or below the mean. It is a dimensionless quantity derived by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing; however, "normalizing" can refer to many types of ratios; see normalization (statistics) for more.

The z-score is most frequently used to compare a sample to a standard normal deviate (standard normal distribution, with μ = 0 and σ = 1), though they can be defined without assumptions of normality. The z-score is only defined if one knows the population parameters, as in standardized testing; if one only has a sample set, then the analogous computation with sample mean and sample standard deviation yields the Student's t-statistic. The standard score is not the same as the z-factor used in the analysis of high-throughput screening data, but is sometimes confused with it.


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