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Normal Scores

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Normal scores use the ranks of a data set to calculate standard normalquantiles of the same size than the original data set. The aim of this calculation ismainly to compare each sample value with the expected value of the order statisticof the same rank from a standard normal distribution sample of the same samplesize than the original data set. The expected values of theorder statistics of asample from a standard normal distribution are the sorted values in increasingorder. Plots of the original data or sample quantiles versus the quantiles or scoresderived from the standard normal distribution are best known as theNormal Quantile–Quantile plots or Normal Q–Q plots where Q stands forquantile. These plots are commonly used as a simple test for normality ina graphical way. If the data set is a sample from a normal probabilitydistribution, the Q–Q plot should show a linear relationship (Barnnet1975).

The best way to explain how to calculate the normal scores is through an example....

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Normal Scores. Figure 1

References and Further Reading

  • Barnnet V (1975) Probability plotting methods and order statistics. Appl Stat 24(1):95–108

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  • Hyndman RJ, Fan Y (1996) Sample quantiles in statistical packages. Am Stat 50:361–365

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  • R Development Core Team (2007) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0

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© 2011 Springer-Verlag Berlin Heidelberg

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de Guenni, L.B. (2011). Normal Scores. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_604

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