The term normal score is used with two different meanings in
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
. 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). 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 mean ...
or
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 mean ...
, 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.
Import ...
of the same rank in a sample of
standard normal random variables 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 In statistics, rankits of a set of data are the expected values of the order statistics of a sample from the standard normal distribution the same size as the data. They are primarily used in the normal probability plot, a graphical technique for ...
, 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.
See also
*
Normalization (statistics)
In statistics and applications of statistics, normalization can have a range of meanings. In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging ...
*
Normal probability plot
The normal probability plot is a graphical technique to identify substantive departures from normality. This includes identifying outliers, skewness, kurtosis, a need for transformations, and mixtures. Normal probability plots are made of raw d ...
*
Q–Q plot
In statistics, a Q–Q plot (quantile-quantile plot) is a probability plot, a List of graphical methods, graphical method for comparing two probability distributions by plotting their ''quantiles'' against each other. A point on the plot co ...
References
Nonparametric statistics