Using a sample to infer the characteristics of a population

Usually you cannot study the whole population, so every time you gather data from a sample you are “working in the dark” because the sample may not be very representative of that population. You have to take every possible precaution, including having a good sampling design, to try to ensure a representative sample. Unfortunately you still do not know whether it is representative! Although it is dangerous to extrapolate to the more general case from measurements on a subset of individuals, that is what researchers have to do whenever they cannot work on the entire population.

This chapter discusses statistical methods for estimating the characteristics of a population from a sample and explains how these estimates can be used for significance testing.

Statistical tests

Statistical tests can be divided into two groups, called parametric and non-parametric tests. Parametric tests make certain assumptions, including that the data fit a known distribution. In most cases this is a normal distribution (see below). These tests are used for ratio, interval or ordinal scale variables. Non-parametric tests do not make so many assumptions. There is a wide range of non-parametric tests available for ratio, interval, ordinal or nominal scale variables.

The normal distribution

A lot of variables, including “geological” ones, tend to be normally distributed.