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# Estimating with samples

BMJ 2002; 325 (Published 01 November 2002) Cite this as: BMJ 2002;325:0211414
1. Wai-Ching Leung, locum general practitioner

In the fifth part of our series on medical statistics, Wai-Ching Leung takes us through sampling

The last article showed that an important use of medical statistics is to draw conclusions from observations.1 We cannot be absolutely certain about our conclusions, however, partly because it is impractical or impossible to collect information from all relevant subjects. For example, we may wish to compare how much money undergraduate students spend at one university compared with another. Although it is theoretically possible to survey all students in both universities, we do not have the time and resources to do so. A common approach is to survey a sample of, say, 500 students from each university and generalise our findings.

## Potential errors in estimating from samples

In generalising our results, we assume that the sample of subjects we collect information on (the study sample) is similar to, or representative of, the group of subjects we want to draw conclusions about (the study population). But this might not be true for two reasons. Firstly, our study sample may be distorted by the way we choose our subjects.2 For example, if we wish to find out how much money undergraduate students spend but decide to survey those students who visit luxurious nightclubs, our findings are likely to show a higher level of expenditure. This is because our sample of students is likely to be more extravagant than the university as a whole (the study population).

Secondly, even if we choose our study subjects properly, our study sample may still differ from our study population by chance. This is more likely to occur the fewer students we decide to sample. Taken to the extreme, if we survey only one student from each university, we would not be too surprised if the monthly expenditure of the student differs considerably from the …

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