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An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an objective property of an estimator. Bias is a distinct concept from consistency: consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased (see bias versus consistency for more).
Detection bias occurs when a phenomenon is more likely to be observed for a particular set of study subjects. For instance, the syndemic involving obesity and diabetes may mean doctors are more likely to look for diabetes in obese patients than in thinner patients, leading to an inflation in diabetes among obese patients because of skewed detection efforts.
When interpreting the floating-point number, the bias is subtracted to retrieve the actual exponent. For a half-precision number, the exponent is stored in the range 1 .. 30 (0 and 31 have special meanings), and is interpreted by subtracting the bias for an 5-bit exponent (15) to get an exponent value in the range −14 .. +15.
Under simple random sampling the bias is of the order O( n −1). An upper bound on the relative bias of the estimate is provided by the coefficient of variation (the ratio of the standard deviation to the mean). [2] Under simple random sampling the relative bias is O( n −1/2).
Correction factor versus sample size n.. When the random variable is normally distributed, a minor correction exists to eliminate the bias.To derive the correction, note that for normally distributed X, Cochran's theorem implies that () / has a chi square distribution with degrees of freedom and thus its square root, / has a chi distribution with degrees of freedom.
The bias is a trivial calculation, but the variance of ¯ is more involved since the jackknife replicates are not independent. For the special case of the mean, one can show explicitly that the jackknife estimate equals the usual estimate:
Because actual rather than absolute values of the forecast errors are used in the formula, positive and negative forecast errors can offset each other; as a result, the formula can be used as a measure of the bias in the forecasts. A disadvantage of this measure is that it is undefined whenever a single actual value is zero.
A typical measure of bias of forecasting procedure is the arithmetic mean or expected value of the forecast errors, but other measures of bias are possible. For example, a median-unbiased forecast would be one where half of the forecasts are too low and half too high: see Bias of an estimator .