One of them relates to creating a single value which can be treated as if it had arisen from a standard normal distribution (zero mean, unit variance).
[citation needed] The first meaning is as an alternative name for the standard score or z score, 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 of some hypothesis, such as a difference in means.
[citation needed] The second meaning of normal score is associated with data values derived from the ranks 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 of the same rank in a sample of standard normal random variables of the same size as the observed data set.