Lies, Damn Lies and Inadequate Sample Size

Benjamin Disraeli was the Victorian era Prime Minister of the United Kingdom.  He famously said “there are three kinds of lies: lies, damned lies and statistics”.  He died in 1881.  This was after Sir Francis Galton coined the term standard deviation, but before he popularized concepts like of correlation and the Central Limit Theorem with his publication of Nature in 1889.

Perhaps Disraeli was witness to how misleading statistics could be without an understanding of sample size requirements.  Most people wander about in the same fog that engulfed Disraeli.

The Central Limit Theorem states that a sample size equal to or greater than 30 is required to make credible assertions about a population.  “In practice, the Central Limit Theorem allows us to make inferences about population means relying on the normal distribution when a) the population is normal or b) when n ≥ 30. As a practical matter, the sampling distribution of the mean will be approximately normal when n ≥ 15 and the population is symmetrically distributed. However, appraisers usually know very little about the shape of population distributions of price, property attributes, financing arrangements, and the like. Therefore, the n ≥ 30 criterion generally applies to real property valuation work.”[1]

In general, if the mean and the median of a population differ, the distribution is not normal and you need a sample size of 30 or greater.

[1] Marvin L. Wolverton, PhD, MAI, An Introduction to Statistics for Appraisers (Chicago, The Appraisal Institute)