Editing Data dredging (section)

=== Multiple modelling ===
Another aspect of the conditioning of [[statistical test]]s by knowledge of the data can be seen while using the {{clarify span|system or machine analysis and [[linear regression]] to observe the frequency of data.|date=October 2019}} A crucial step in the process is to decide which [[covariate]]s to include in a relationship explaining one or more other variables. There are both statistical (see [[stepwise regression]]) and substantive considerations that lead the authors to favor some of their models over others, and there is a liberal use of statistical tests. However, to discard one or more variables from an explanatory relation on the basis of the data means one cannot validly apply standard statistical procedures to the retained variables in the relation as though nothing had happened. In the nature of the case, the retained variables have had to pass some kind of preliminary test (possibly an imprecise intuitive one) that the discarded variables failed. In 1966, Selvin and Stuart compared variables retained in the model to the fish that don't fall through the net—in the sense that their effects are bound to be bigger than those that do fall through the net. Not only does this alter the performance of all subsequent tests on the retained explanatory model, but it may also introduce bias and alter [[mean square error]] in estimation.<ref name="Selvin">
{{Cite journal
|author1=Selvin, H.&nbsp;C.
|author2=Stuart, A.
|title = Data-Dredging Procedures in Survey Analysis
|journal = The American Statistician
|volume = 20
|issue = 3
|pages = 20–23
|year = 1966
|doi=10.1080/00031305.1966.10480401
|jstor=2681493}}
</ref><ref name="BerkBrownZhao">
{{Cite journal
|author1=Berk, R. |author2=Brown, L. |author3=Zhao, L.
|title = Statistical Inference After Model Selection
|journal = J Quant Criminol
|doi = 10.1007/s10940-009-9077-7
|year = 2009 |volume=26 |issue=2 |pages=217–236 |s2cid=10350955 |url=https://repository.upenn.edu/statistics_papers/540 }}
</ref>