Sample size (n N)

How to read it

OpenStax’s Introductory Statistics uses both letters in one passage: a population’s squared deviations are divided by N, “the number of items in the population”, and a sample’s by n − 1, “one less than the number of items in the sample”. Penn State’s STAT 500 course notes say that n “will always equal sample size”. n turns up in many formulas because the reliability of a sample depends on it: OpenStax gives the standard deviation of the sampling distribution of the mean as the standard deviation of the original distribution divided by the square root of n, and notes that n is the number of values averaged together, not the number of times the experiment is done.

Also searched as: n in statistics, n N, population size symbol, sample size symbol.

N for the sample

In NIST’s Engineering Statistics Handbook a capital N is the number of data points in the sample: it writes the mean as the sum of the values divided by N, and the sample variance with N − 1. Jeff Miller’s history of statistical symbols records the same habit in the early biometric literature, where the number of units was usually written N, as in Student’s 1908 paper “The Probable Error of a Mean”. Which N a formula means depends on the book.

n in Fisher’s books

In R. A. Fisher’s Statistical Methods for Research Workers (1925, with 13 later editions) n is not the sample size. Fisher used n for the number of degrees of freedom, following Karl Pearson’s chi-square paper of 1900, and so wrote n′ for the number of observations, Miller explains; his chapter on correlation speaks of samples where n′ = 10. Statisticians who disliked Fisher’s n chose the Greek letter ν (nu) for degrees of freedom, and ν is in M. G. Kendall’s Advanced Theory of Statistics (1943).