Colloquially, a statistic may be described as \"biased\" if it misrepresents wha
ID: 3200291 • Letter: C
Question
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. Name a technical distinction that statisticians draw in order to distinguish errors of estimation that trend in a particular direction from other errors that do not. Use it to explain how bias in the statistical sense can vanish even with samples small enough that estimates based on them are likely to be "biased" in the colloquial sense.Explanation / Answer
Bias is a very large source of errors in Statistics. When sample drawn is biased, the estimates done on them becomes erroneous and this leads to various errors of estimation. This errors of estimation based on bias is mainly highly effective in case of small samples.
This is due to the fact that in case of small samples, there is no enough scope of randomness and this leads to bias. Sample is nothing but a representative of the whole population. But if a sample is biased, it is highly likely that the sample will not be able to capture all sorts of variations in the population.
Hence it may happen that some classes/features of the population remains absent in the population. This leads to estimation errors.
In order to reduce estimation errors, randomness is done. And while doing random sampling, it is taken care of that the estimates do converge in the long run. This is the technical distintion that statisticians mainly use in order to distinguish erros of estimation that trend in a particular direction from other errors that do not.
Convergence is very important while estimating something. And care should be taken to make sure that the estimators do converge in the long run. Because if they converge then this means that statistical errors will reduce in the long run.
However this is not true in case of divergent estimators. Hence for convergent estimators bias vanishes in long run while in divergent cases biases does not get eliminated completely