Statistical error

In order to approach the sources of errors in Statistical , we will take the example of a survey on a referendum. On the one hand because that concerns all citizens, and in addition the number of possible answers, equal to two, simplify the study largely.

Statistical errors

If the sounder questions only one person, the result of the survey indicates a result of 100% for the choice of single probed. What is aberrant. One cannot interpolate the result of a negligible sample with the whole of population. Only the consultation of the whole of the voters will allow to know the true distribution. Unfortunately in practice one only can to probe a sample of this population. It is then necessary to sully the result with survey by an error known as statistical. This error will be all the more small that the number of probed will tend towards the whole population. Note that for one measure physical the ideal number of measurements is infinite.

A referendum consists in answering by yes or not. That is to say two possibilities. One can thus model the referendum by the binomial distribution. Let us imagine that R = 255 probed on a total of N answer yes = 500 probed people. One then is obtained probability for yes of $p = \ frac {R} {N} = 0,51$ . The variance on R is worth $V (R) = Np (1-p)$ . Thus the variance on p is $V (p) =
\ frac {p (1-p)}{N}$ . One finds from a mathematical point of view it preceding intuitive behavior. If N = 1 the variance is maximum, if N tends towards infinite the variance becomes null. In our case there is a standard deviation of 2,2% for a probability for yes of 51%, that is to say a probability included/understood enters 48,8% and 53,2% for yes, and ranging between 46.8% and 51.2% for not. One can thus draw any valid conclusion on this survey, the number of probed being obviously selected too small.

Systematic errors

We saw that the main difficulty for survey is to choose a sufficient sample. But that is not the only source of error. It is also necessary to take account of skew in systematic matter. In the case of a survey we can enumerate the sources of following errors:

the sample representative of the population
is not probed lies by shame of its choice
probed answers anything to get rid as fast as possible of the sounder

First is interesting, because it interferes with the statistical errors. In effect the statistical errors are due to statistical fluctuations in the sampling of the population. In other words, the statistical errors are the consequence of impossibility of choosing the perfect sample. Another way of studying this phenomenon would consist in calculating the probability of soiling one perfect sample by inverting one, two, three etc probed between yes and not. Imagine a vat of ball containing 51% of red balls and 49% of balls blue. Which would be the configuration of a bag of ball according to its size, filled starting from a negligible part of the vat? This is however an effect of second order. The sounder must take guard not to probe solely one group of individuals directed for yes or not, if not the result would be absolutely skewed. However, that is not so easy in practice.

It is much more difficult to evaluate this type of errors. What brings us to to doubt even more of the preceding result on our survey.

See too

Marge_d' error

Error (metrology)
Interval confidence
other directions of the word “ Error”

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Statistical error