In statistics, a standard score indicates by 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).
Standard scores are also called 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". They are 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 though the two are often conflated.
Read more about Standard Score: Calculation From Raw Score, Applications, Standardizing in Mathematical Statistics
Famous quotes containing the words standard and/or score:
“When Freedom, from her mountain height,
Unfurled her standard to the air,
She tore the azure robe of night,
And set the stars of glory there;”
—Joseph Rodman Drake (1795–1820)
“Gargantua, at the age of four hundred four score and forty- four years begat his son Pantagruel, from his wife, named Badebec, daughter of the King of the Amaurotes in Utopia, who died in child-birth: because he was marvelously huge and so heavy that he could not come to light without suffocating his mother.”
—François Rabelais (1494–1553)