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Spectrum bias arises from evaluating diagnostic tests on biased patient samples, leading to an overestimate of the sensitivity and specificity of the test. For example, a high prevalence of disease in a study population increases positive predictive values, which will cause a bias between the prediction values and the real ones. [4]
For instance, a mixed distribution consisting of very thin Gaussians centred at −99, 0.5, and 2 with weights 0.01, 0.66, and 0.33 has a skewness of about −9.77, but in a sample of 3 has an expected value of about 0.32, since usually all three samples are in the positive-valued part of the distribution, which is skewed the other way.
In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample [ 1 ] of a population (or non-human factors) in which all individuals, or instances, were not equally likely to have been selected ...
For example, the square root of the unbiased estimator of the population variance is not a mean-unbiased estimator of the population standard deviation: the square root of the unbiased sample variance, the corrected sample standard deviation, is biased. The bias depends both on the sampling distribution of the estimator and on the transform ...
Heteroscedasticity does not cause ordinary least squares coefficient estimates to be biased, although it can cause ordinary least squares estimates of the variance (and, thus, standard errors) of the coefficients to be biased, possibly above or below the true of population variance. Thus, regression analysis using heteroscedastic data will ...
Given an r-sample statistic, one can create an n-sample statistic by something similar to bootstrapping (taking the average of the statistic over all subsamples of size r). This procedure is known to have certain good properties and the result is a U-statistic. The sample mean and sample variance are of this form, for r = 1 and r = 2.
Statistics, when used in a misleading fashion, can trick the casual observer into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the perpetrator.
However, if the distribution has skew, trimmed estimators will generally be biased and require adjustment. For example, in a skewed distribution, the nonparametric skew (and Pearson's skewness coefficients) measure the bias of the median as an estimator of the mean.