Parameters and sample statistics

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See also: Analyzing and using data introduction, Statistics of a sample

Mean, standard deviation, variance etc. are all both sample statistics and parameters, depending on the circumstance of their use, which are:

Measures of a population

If one had the necessary information about all the individuals in a population, one could calculate any descriptive parameter, like their average height. These are population parameters.

Measures of a probability distribution

Probability distributions have parameters that describe certain characteristics about the distribution, like its mean.

Measures of an uncertainty distribution

Confidence distributions have parameters that describe certain characteristics about the distribution, like its mean.

Measures of a sample

One can calculate some statistics for any set of values, like their mean. If that set of values is drawn at random from a population or probability distribution, the statistic can be used to estimate the population or probability distribution parameters (the sample mean can be used as an estimate of the corresponding population mean, or probability distribution mean, for example).

Monte Carlo simulation results

The results of a Monte Carlo simulation are effectively samples from the output probability distribution the simulation is trying to determine.

There are therefore five situations in which you will come across terms like mean, standard deviation, percentiles, etc. In each situation they have different meanings and are defined and calculated differently. These links provide an explanation for the most common terms:

  1. Parameters of a population;

  2. Parameters of a probability distribution;

  3. Parameters of an uncertainty distribution;

  4. Statistics of a sample; and

  5. Statistics of Monte Carlo simulation results.

Read on: Parameters of a population