Section 3 explains current approaches for corrected learning on biased samples
, and we propose two new methods based on drawing observations from theoretical distributions assumed for the given data.
In an earlier paragraph, we describer the tendency of our RDD to produce a biased sample
that included only internet users.
The Publish or Perish Fallacy is: When you need a paper, and academics always need papers, do a survey, call the questionnaire an "instrument," then apply an unnecessarily complicated, opaque, sui generis, unreplicable statistical procedure to a trivially small, biased sample
, but be sure the "findings" accord with received wisdom.
Claims in the Spanish data set are randomly selected from each class to create a biased sample
of 1,000 claims with a target sample fraud rate of 25 percent (versus 49.97 percent in the original Spanish data set).
Unfortunately, such methods still do not correct for missing-data bias in general, because these missing-data imputations themselves may be based on a biased sample
. There are, however, special cases where such methods can lead to valid point estimators: when one can assume data are missing at random (MAR)  the mean or regression imputation process for linear estimators can use the MAR property (e.g., the mean imputation can be performed separately for the two gender groups or the regression imputation can use gender as a covariate).
If sample is collected in such a way that some members of the study population have less chance of being included than others, then the resulting sample is a biased sample
, and the results obtained from such a sample will not be valid or generalizable to the entire study population.
Any particular capture method may, however, give a biased sample
due to differences in capture probability among size, age or sex classes, and may be influenced by body condition, suggesting that a sampling protocol should combine different sampling methods (Conroy & Nichols 1996, Greenwood 1996, Laves & Loeb 2006).
A re-analysis of results addressed the fact that the researchers had selected a biased sample
of supernovae, favouring intrinsically brighter objects.
Unfortunately 127 participants were excluded and, therefore, results were based on a potentially biased sample
. This partly relates to the retrospective nature of the data analysis, with a meaning being ascribed to data that were not collected for this purpose.
Their concern about a biased sample
selection is equally unfounded.