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Model-based assumptions. These include the following three types: Distributional assumptions. Where a statistical model involves terms relating to random errors, assumptions may be made about the probability distribution of these errors. [5] In some cases, the distributional assumption relates to the observations themselves. Structural assumptions.
The history of scientific method considers changes in the methodology of scientific inquiry, not the history of science itself. The development of rules for scientific reasoning has not been straightforward; scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the primacy of ...
The discussion of background assumptions can include metaphysical and ontological issues in cases where they have important implications for the proper research methodology. For example, a realist perspective considering the observed phenomena as an external and independent reality is often associated with an emphasis on empirical data ...
Independence of observations – this is an assumption of the model that simplifies the statistical analysis. Normality – the distributions of the residuals are normal . Equality (or "homogeneity") of variances, called homoscedasticity —the variance of data in groups should be the same.
The assumptions underlying a t-test in the simplest form above are that: X follows a normal distribution with mean μ and variance σ 2 /n. s 2 (n − 1)/σ 2 follows a χ 2 distribution with n − 1 degrees of freedom. This assumption is met when the observations used for estimating s 2 come from a normal distribution (and i.i.d. for each group).
A causal relationship between the observations and hypothesis does not exist to cause the observation to be taken as evidence, [3] but rather the causal relationship is provided by the person seeking to establish observations as evidence. A more formal method to characterize the effect of background beliefs is Bayesian inference. [5]
Observation in the natural sciences [1] is an act or instance of noticing or perceiving [2] and the acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the perception and recording of data via the use of scientific instruments. The term may also refer to ...
Consider an experiment to study the effect of three different levels of a factor on a response (e.g. three levels of a fertilizer on plant growth). If we had 6 observations for each level, we could write the outcome of the experiment in a table like this, where a 1, a 2, and a 3 are the three levels of the factor being studied.