In some circumstances the sample may consist of all the members of a specifically defined population. For practical reasons, this is only likely to be the case if the population of interest is not too large. Clearly complete sampling of a large population will be very expensive and time-consuming.
Example - complete sample - reinfection with Lyme borreliosis
Bennet and Berglund (2002) studied all patients diagnosed with erythema migrans (EM) following vector-borne infection by Lyme borreliosis (LB) some 10 years earlier. They contacted all these patients and asked if they had had any new tick bites over the period May 1993 to May 1998. From the 976 infected and eligible for the study, 708 participants replied and from these a reinfection rate of 4% was computed.
In this case, since the study purpose was to investigate the long-term consequences of an infection, the choice of the population was very specifically confined to those who had been diagnosed with EM. Despite seeking a complete sample, only a proportion (but not a random sample) of this population provided the information requested. There is therefore a real possibility of bias in the estimate of the reinfection rate so obtained. However, the sample comprised a large proportion (73%) of the total and the authors checked that there were no major differences in terms of age and gender between those who participated and those who did not.
In contrast, if all members of the population can be assessed, there is no bias as the 'estimate' is the value of the population parameter itself. In this idealised situation we know all about the population as we have examined all its members. This will rarely be the case.
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