Statistical assumptions

Statistics, like all mathematical disciplines does not generate valid conclusions from nothing. Every theorem in mathematics requires a set of assumptions or hypotheses from which its conclusions are derived. [Mathematical proof]?s are procedures for transforming hypotheses into conclusions.

The most common 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)

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