# Statistical Assumption

Statistical Assumption

Statistical assumptions are general assumptions about statistical populations.

Statistics, like all mathematical disciplines, does not generate valid conclusions from nothing. In order to generate interesting conclusions about real statistical populations, it is usually required to make some background assumptions. These must be made with care, because inappropriate assumptions can generate wildly inaccurate conclusions.

The most commonly applied statistical assumptions are:

1. independence of observations from each other: This assumption is a common error. (see statistical independence)
2. independence of observational error from potential confounding effects
3. exact or approximate normality of observations: The assumption of normality is often erroneous, because many populations are not normal. However, it is standard practice to assume that the sample mean from a random sample is normal, because of the central-limit theorem. (see normal distribution)
4. linearity of graded responses to quantitative stimuli (see linear regression)