Hello colleagues,
In a cross-sectional study
When using the sampling formula for a population rate, in which cases do we use absolute error? , and in which case do we use relative error?
Thank you so much!
In a cross-sectional study, the choice between using absolute error and relative error in the sampling formula for a population rate depends on the specific context and the desired precision of the estimate.
Absolute error is the difference between the estimated population rate and the true population rate, expressed in absolute units (e.g., number of cases). It is appropriate to use absolute error when the focus is on the magnitude of the difference between the estimated and true rates, regardless of the overall size of the population. For instance, if you are estimating the prevalence of a rare disease, absolute error would be more relevant than relative error, as even a small absolute difference in the estimated rate could have significant implications for public health.
Relative error, on the other hand, is the difference between the estimated population rate and the true population rate, expressed as a percentage of the true rate. It is appropriate to use relative error when the focus is on the proportional difference between the estimated and true rates, relative to the overall size of the population. For example, if you are estimating the prevalence of a common condition, relative error would be more relevant than absolute error, as a small absolute difference in the estimated rate might not be as concerning when compared to the large overall size of the population.
In general, absolute error is more appropriate for situations where the focus is on the magnitude of the difference between the estimated and true rates, regardless of the population size, while relative error is more appropriate for situations where the focus is on the proportional difference between the estimated and true rates, relative to the population size.
depending on the linear regression: when theres a relation Y~a+bX the absolute error is used, on logaritm relations Y~a+b*log(X) is used the error estimation dx/X which is the corresponding estimation.
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