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In addition, occasionally, robustness and powerfulness of a test are questioned together. And intuitively, I couldn"t differentiate between the 2 principles. What is an effective test? How is it various from a durable statistical test?
Robustness has various interpretations in statistics, but all suggest some resilience to alters in the form of data provided. This might sound a little ambiguous, but that is because robustness have the right to refer to different kinds of insensitivities to transforms. For example: Robustness to outliersRobustness to non-normalityRobustness to non-consistent variance (or heteroscedasticity)
In the case of tests, robustness typically describes the test still being valid offered such a adjust. In various other words, whether the outcome is substantial or not is just coherent if the assumptions of the test are met. When such presumptions are serene (i.e. not as important), the test is said to be robust.
The power of a test is its capacity to detect a significant distinction if tright here is a true distinction. The factor certain tests and also models are provided via miscellaneous assumptions is that these assumptions simplify the problem (e.g. call for much less parameters to be estimated). The even more presumptions a test makes, the less durable it is, because all these assumptions have to be met for the test to be valid.
On the other hand also, a test via fewer assumptions is more robust. However, robustness mainly comes at the expense of power, bereason either less indevelopment from the input is used, or even more parameters should be estimated.
RobustA $t$-test can be shelp to be robust, bereason while it assumes commonly spread teams, it is still a valid test for comparing approximately normally spread teams.
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A Wilcoxon test is much less effective as soon as the presumptions of the $t$-test are met, but it is even more robust, because it does not assume an underlying circulation and is therefore valid for non-normal information. Its power is generally lower because it provides the ranks of the information, quite than the original numbers and for this reason fundamentally discards some indevelopment.
Not RobustAn $F$-test is a compariboy of variances, but it is incredibly sensitive to non-normality and also therefore invalid for approximate normality. In other words, the $F$-test is not durable.