Bias is the error in estimates due to systematic mistakes that lead to consistently high or low results as compared to the actual values. The individual bias of an estimate known to be biased is the difference between the estimated and actual values. If the estimate is not known to be biased, the difference could also be due to random error or other inaccuracies. Contrary to bias, which always acts in one direction, these errors can be positive or negative.
To calculate the bias of a method used for many estimates, find the errors by subtracting each estimate from the actual or observed value. Add up all the errors and divide by the number of estimates to get the bias. If the errors add up to zero, the estimates were unbiased, and the method delivers unbiased results. If the estimates are biased, it may be possible to find the source of the bias, and eliminate it to improve the method.
TL;DR (Too Long; Didn't Read)
Calculate bias by finding the difference between an estimate and the actual value. To find the bias of a method, perform many estimates, and add up the errors in each estimate compared to the real value. Dividing by the number of estimates gives the bias of the method. In statistics, there may be many estimates to find a single value. Bias is the difference between the mean of these estimates and the actual value.
How Bias Works
When estimates are biased they are consistently wrong in one direction due to mistakes in the system used for the estimates. For example, a weather forecast may consistently predict temperatures that are higher than those actually observed. The forecast is biased, and somewhere in the system there is a mistake that gives too high an estimate. If the forecast method is unbiased, it may still predict temperatures that are not correct, but the incorrect temperatures will sometimes be higher and sometimes lower than the temperatures observed.
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Statistical bias works the same way but is usually based on a large number of estimates, surveys or forecasts. These results can be graphically represented in a distribution curve and the bias is the difference between the mean of the distribution and the actual value. If there is bias, there will always be a difference even though some individual estimates may fall either side of the actual value.
Bias in Surveys
An example of bias is a survey company that runs polls during election campaigns, but their polling results consistently overestimate the results for one political party compared to the actual election results. The bias can be calculated for each election by subtracting the actual result from the poll prediction. The average bias of the polling method used can be calculated by finding the average of the individual errors. If the bias is large and consistent, the polling company can try to find out why their method is biased.
Bias can come from two main sources. Either the selection of participants for the poll is biased, or the bias results from the interpretation of the information received from the participants. For example, internet polls are inherently biased because the poll participants who fill out the internet forms are not representative of the whole population. This is a selection bias.
Polling companies are aware of this selection bias and compensate by adjusting the numbers. If the results are still biased, it is an information bias because the companies did not interpret the information correctly. In all these cases, a bias calculation shows to what extent the estimated values are useful and when the methods need adjustment.