Page 9 - statistical mathematics

Parametric statistics

Parametric statistics is a branch of statistics which assumes that sample data comes

from a population that can be adequately modeled by a probability distribution that

has a fixed set of parameters. Conversely a non-parametric model does not assume

an explicit (finite-parametric) mathematical form for the distribution when

modeling the data. However, it may make some assumptions about that

distribution, such as continuity or symmetry.

Example:

The normal family of distributions all have the same general shape and are

parameterized by mean and standard deviation. That means that if the mean and

standard deviation are known and if the distribution is normal, the probability of

any future observation lying in a given range is known.
Suppose that we have a sample of 99 test scores with a mean of 100 and a standard

deviation of 1. If we assume all 99 test scores are random observations from a
normal distribution, then we predict there is a 1% chance that the 100th test score

will be higher than 102.33 (that is, the mean plus 2.33 standard deviations),

assuming that the 100th test score comes from the same distribution as the others.

Parametric statistical methods are used to compute the 2.33 value above, given 99

independent observations from the same normal distribution.

Nonparametric statistics

Nonparametric statistics is the branch of statistics that is not based solely on

parametrized families of probability distributions (common examples of

parameters are the mean and variance). Nonparametric statistics is based on either

being distribution-free or having a specified distribution but with the distribution's

parameters unspecified. Nonparametric statistics includes both descriptive statistics