The term normal score is used with two different meanings in statistics. One of them relates to creating a single value which can be treated as if it had arisen from a

standard normal distribution In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu i ...

(zero mean, unit variance). The second one relates to assigning alternative values to data points within a dataset, with the broad intention of creating data values than can be interpreted as being approximations for values that might have been observed had the data arisen from a standard normal distribution. The first meaning is as an alternative name for the

standard score In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured. Raw scores above the me ...

z score In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured. Raw scores above the mea ...

, where values are standardised by subtracting the sample or estimated mean and dividing by the sample or other estimate of the standard deviation. Particularly in applications where the name "normal score" is used, there is usually a presumption that the value can be referred to a table of standard normal probabilities as a means of providing a

significance test A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. ...

of some hypothesis, such as a difference in means. The second meaning of normal score is associated with data values derived from the

rank Rank is the relative position, value, worth, complexity, power, importance, authority, level, etc. of a person or object within a ranking, such as: Level or position in a hierarchical organization * Academic rank * Diplomatic rank * Hierarchy * H ...

s of the observations within the dataset. A given data point is assigned a value which is either exactly, or an approximation, to the expectation of the

order statistic In statistics, the ''k''th order statistic of a statistical sample is equal to its ''k''th-smallest value. Together with rank statistics, order statistics are among the most fundamental tools in non-parametric statistics and inference. Importa ...

of the same rank in a sample of

standard normal random variable In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu is ...

s of the same size as the observed data set.Everitt, B.S. (2002) ''The Cambridge Dictionary of Statistics'' (2nd Edition). Cambridge University Press. {{isbn, 0-521-81099-X Thus the meaning of a normal score of this type is essentially the same as a rankit, although the term "rankit" is becoming obsolete. In this case the transformation creates a set of values which is matched in a certain way to what would be expected had the original set of data values arisen from a normal distribution.

References

Nonparametric statistics

See also

References