Estimation is an inferential procedure for understanding the “magnitude” of a population parameter of interest (unknown) based on only a sample. It involves not only the reporting of a sample estimate, but it also requires the report of a precision estimate.
To examine the mean change of blood pressure (BP) after taking an anti-hypertensive drug in hypertensive patients, we may recruit a number of patients and measure their BP before and after the administration of the drug. Then, we may use the sample mean BP change from the sample to estimate the "true" mean BP change. The sample mean BP change is a parameter estimate. In addition, we should also report a precision estimate, such as the standard error. Alternatively, we may also report a 95% confidence interval.
A researcher wants to determine the proportion of Hong Kong school children with habitual snoring. A sample of 3047 school children was contacted by phone. Of which, 45 (1.5%) children were found with habitual snoring. The corresponding standard error was 0.0022.
The proportion of Hong Kong school children with habitual snoring is the parameter of interest. The 1.5% obtained from the sample is an estimate of this parameter. The standard error is used to reflect the precision of the sample estimate.