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Statistical assumptions can be put into two classes, depending upon which approach to inference is used. 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]
The misuse of Statistics can trick the observer who does not understand them into believing something other than what the data shows or what is really 'true'. That is, a misuse of statistics occurs when an argument uses statistics to assert a falsehood. In some cases, the misuse may be accidental.
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The i.i.d. assumption is also used in the central limit theorem, which states that the probability distribution of the sum (or average) of i.i.d. variables with finite variance approaches a normal distribution. [4] The i.i.d. assumption frequently arises in the context of sequences of random variables. Then, "independent and identically ...
Robust statistics are statistics that maintain their properties even if the underlying distributional assumptions are incorrect. Robust statistical methods have been developed for many common problems, such as estimating location , scale , and regression parameters .
Linear errors-in-variables models were studied first, probably because linear models were so widely used and they are easier than non-linear ones. Unlike standard least squares regression (OLS), extending errors in variables regression (EiV) from the simple to the multivariable case is not straightforward, unless one treats all variables in the same way i.e. assume equal reliability.
By comparison, a jingle fallacy is the assumption that two measures which are called by the same name capture the same construct. [4] [5] [6] An example of the jangle fallacy can be found in tests designed to assess emotional intelligence. Some of these tests measure merely personality or regular IQ-tests. [7]
The bootstrap is generally useful for estimating the distribution of a statistic (e.g. mean, variance) without using normality assumptions (as required, e.g., for a z-statistic or a t-statistic). In particular, the bootstrap is useful when there is no analytical form or an asymptotic theory (e.g., an applicable central limit theorem ) to help ...