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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]
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 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.
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 .
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 ...
Statistical bias is a systematic tendency in the process of data collection, which results in lopsided, misleading results. This can occur in any of a number of ways, in the way the sample is selected, or in the way data are collected. [ 85 ]
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It is remarkable that the sum of squares of the residuals and the sample mean can be shown to be independent of each other, using, e.g. Basu's theorem.That fact, and the normal and chi-squared distributions given above form the basis of calculations involving the t-statistic: