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:
“This unlettered mans speaking and writing are standard English. Some words and phrases deemed vulgarisms and Americanisms before, he has made standard American; such as It will pay. It suggests that the one great rule of compositionand if I were a professor of rhetoric I should insist on thisis, to speak the truth. This first, this second, this third; pebbles in your mouth or not. This demands earnestness and manhood chiefly.”
—Henry David Thoreau (18171862)
“And theres a score of duchesses, surpassing womankind,
Or who have found a painter to make them so for pay
And smooth out stain and blemish with the elegance of his mind:
I knew a phoenix in my youth, so let them have their day.”
—William Butler Yeats (18651939)