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The primary role of statistics in epidemiology is to make conclusions about a population of interest when data is only available from a sample. Statistics accounts for the uncertainty.
In epidemiological datasets there are usually measured observations of an occurance of a disease as well as measured indicators of exposure. An epidemiologist may for example be interested in whether exposure (e.g. smoking) increases the risk of disease (e.g. cancer). Information on smoking however may not be available for all people in the population of interest because of limited resources, so an epidemiologist would have to consider taking a sample. An epidemiologist would use a random sample in order to use statistics to to make inference about the association between smoking and cancer in the population. The role of statistics is to determine whether any association that is observed in the random sample is actually a real one. In most cases there will be some association even if it is very small. The role of the statistician is to determine if the association is different than what would occur by chance.
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