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Colloquially, a statistic may be described as “biased” if it misrepresents whatever it’s intended to represent, whether or not it was more likely a priori to err in one direction or another. (This type of “bias” is often larger for estimates made from small samples.) explain how this usage of “bias” differs from statisticians’ use of the same term. Make the explanation suitable for a friend or relative who’s never taken a statistics class, and include one or two made-up examples to illustrate the difference."

For my understanding I think the common sense bias is a general notion while the statistical bias is a quantity (i.e. estimator). Is it right? However, I am not sure if it is the case for all kinds of statistical bias.

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closed as off-topic by Nick Cox, Michael Chernick, Mark White, SmallChess, mdewey Jan 6 '18 at 13:27

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I don't agree that that is a colloquial definition of bias.

Suppose you have a scale and, on multiple weighings you get weights of 90kg, 80kg, 70kg when your true weight is 80kg. I don't think people would call this scale biased, just inaccurate. On the other hand, if you got weights of 82kg, 81kg and 81.5 kg then I think people would say it was biased, but more accurate.

Statistics lets us make these notions precise, but I think it generally agrees with common usage.

Where common usage is markedly different from statisticians' use of bias is in things like asking whether a test like the SAT is biased. But that's a different issue.

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Colloquially, a statistic may be described as “biased” if it misrepresents whatever it’s intended to represent ...

Such definition is too broad. Statistic is a function of a random variable, so it will never represent anything perfectly. Saying it differently, statistic is calculated on a sample from the population and it is ought to represent some property of the population, so it is based on partial data and would never be accurate. Moreover, statistic is always an approximation. “All models are wrong.”

In statistics bias is the amount of how much “on average” does the estimate differ from what it estimated.

Colloquially, if people say that something is “biased”, they often mean many different things, e.g. “inaccurate”, or simply “wrong”. It is hard to compare precise definition with ambiguities of the colloquial language.

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