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Standard Error (SE): This term is often used interchangeably with “standard error of the mean,“ but it can more broadly refer to the standard deviation of any kind of statistical estimate. It's a measure of the variability or dispersion of a sample statistic (like the mean, median, proportion) from a sample. The standard error can be calculated for various statistics, and it reflects how much that estimate varies when different samples are taken from the same population. Standard Error of the Mean (SEM): This is a specific type of standard error that specifically measures the dispersion of sample means around the population mean. It's calculated by dividing the standard deviation of the sample by the square root of the sample size. SEM gives an idea of how precise our estimate of the population mean is based on our sample. A smaller SEM indicates a more precise estimate. In summary, while the standard error of the mean is a specific type of standard error, the term standard error can be applied more broadly to other types of statistical estimates. Problem: Suppose we compared 2 random samples taken from the California all-discharge database described above. Sample A is a random sample with 100 discharges. Sample B is a random sample with 2,000 discharges. What can be said about the relationship between the sample standard error in Sample A (SEA) relative to the sample standard error of length-of- stay value in Sample B (SEB)? A) SEA less than SEB B) SEA bigger than SEB * C) SEA is exactly equal to SEB D) Not enough information given to determine the relationship between the two standard errors.
