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 innacurate conclusions.

The most commonly applied statistical assumptions are:

  1. independence of observations from each other (see statistical independence)
  2. independence of observational error from potential confounding effects
  3. exact or approximate normality of observations (see normal distribution)
  4. linearity of graded responses to quantitative stimuli (see linear regression)