Types of Assumptions
Statistical assumptions can be categorised into a number of types:
- Non-modelling assumptions. Statistical analyses of data involve making certain types of assumption, whether or not a formal statistical model is used. Such assumptions underlie even descriptive statistics.
- Population assumptions. A statistical analysis of data is made on the basis that the observations available derive from either a single population or several different populations, each of which is in some way meaningful. Here a "population" is informally a set of other possible observations that might have been made. The assumption here is a simple one, to the effect that the observer should know that the observations obtained are representative of the problem, topic or class of objects being studied.
- Sampling assumptions. These relate to the way in which observations have been gathered and may often involve an assumption of random selection of some type.
- Modelling assumptions. These may be divided into two types:
- Distributional assumptions. Where a statistical model involves terms relating to random errors assumptions may be made about the probability distribution of these errors. In some cases, the distributional assumption relates to the observations themselves.
- Structural assumptions. Statistical relationships between variables are often modelled by equating one variable to a function of another (or several others), plus a random error. Models often involve making a structural assumption about the form of the functional relationship here: for example, as in linear regression. This can be generalised to models involving relationships between underlying unobserved latent variables.
- Cross-variation assumptions. These assumptions involve the joint probability distributions of either the observations themselves or the random errors in a model. Simple models may include the assumption that observations or errors are statistically independent.
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