Psychological tests (III)

When the measurements are all very similar, the reverse is true. All values are very near to the average, and the average is consequently a good predictor. To take into account these variations, several measures can be used to qualify the average. The simplest is the range, which is the difference between the highest and the lowest values. Still, the standard deviation is preferred for theoretical reasons. It is calculated as the square root of the mean of the squared deviations with respect to the average.

Normal distribution

By using tests, certain human characteristics can be sampled and expressed as numerical values. These values can then be plotted to obtain a statistical graph, the histogram, which is usually utilized to show statistical distributions. When this is done, it is customarily to find that the graph can be approximated by a curve with the form of a bell. There exists a mathematical curve (a curve defined by an equation) that has the form of a bell: it is called the 'normal curve' because, besides appearing in many natural phenomena, it can be shown that in repeated careful measurements the errors have a frequency distribution that follows this curve.

The normal curve is also called the bell curve or the Gaussian curve, because Carl F. Gauss used it to analyze errors in astronomical observations. This curve was discovered independently in the 18th century by the French mathematicians Abraham de Moivre and Pierre Simon de Laplace. Its usage was promoted by the Belgian scientist Adolphe Quetelet.

Because so many observable biological characteristics follow a normal distribution, it has become common to presume that this always happens, but it is not true. There are two other distributions that frequently appear in observed data: the binomial distribution and the Poisson distribution. This fact has to be taken into account when applying certain statistical tests, like the t-test, which assume that the population has a normal distribution. In the case of a very large number of observations, other distributions (as the binomial distribution) tend to the normal distribution and can be approximated by it.

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