ms-08 mba assignment july dec 2010 Question 4

4. Write a note on “standard error. Distinguish between  Standard error and Sampling error

STANDARD ERROR

For a value that is sampled with an unbiased normally distributed error, the above depicts the proportion of samples that would fall between 0, 1, 2, and 3 standard errors above and below the actual value.

The standard error of a method of measurement or estimation is the standard deviation of the sampling distribution associated with the estimation method. The term may also be used to refer to an estimate of that standard deviation, derived from a particular sample used to compute the estimate.
For example, the sample mean is the usual estimator of a population mean. However, different samples drawn from that same population would in general have different values of the sample mean. The standard error of the mean (i.e., of using the sample mean as a method of estimating the population mean) is the standard deviation of those sample means over all possible samples (of a given size) drawn from the population. Secondly, the standard error of the mean can refer to an estimate of that standard deviation, computed from the sample of data being analysed at the time.
A mnemonic for remembering the term standard error is that, as long as the estimator is unbiased, the standard deviation of the error (the difference between the estimate and the true value) is the same as the standard deviation of the estimates themselves; this is true since the standard deviation of the difference between the random variable and its expected value is equal to the standard deviation of a random variable itself.
In many practical applications, the true value of the standard deviation is usually unknown. As a result, the term standard error is often used to refer to an estimate of this unknown quantity. In such cases it is important to be clear about what has been done and to attempt to take proper account of the fact that the standard error is only an estimate. Unfortunately, this is not often possible and it may then be better to use an approach that avoids using a standard error, for example by using maximum likelihood or a more formal approach to deriving confidence intervals. One well-known case where a proper allowance can be made arises where the Student's t-distribution is used to provide a confidence interval for an estimated mean or difference of means. In other cases, the standard error may usefully be used to provide an indication of the size of the uncertainty, but its formal or semi-formal use to provide confidence intervals or tests should be avoided unless the sample size is at least moderately large. Here "large enough" would depend on the particular quantities being analysed.
SAMPLING ERROR
In statistics, sampling error or estimation error is the error caused by observing a sample instead of the whole population. The sampling error can be found by subtracting the value of a parameter from the value of a statistic. In nursing research, a sampling error is the difference between a sample statistic used to estimate a population parameter and the actual but unknown value of the parameter . An estimate of a quantity of interest, such as an average or percentage, will generally be subject to sample-to-sample variation. These variations in the possible sample values of a statistic can theoretically be expressed as sampling errors, although in practice the exact sampling error is typically unknown. Sampling error also refers more broadly to this phenomenon of random sampling variation.
The likely size of the sampling error can generally be controlled by taking a large enough random sample from the population,although the cost of doing this may be prohibitive; see sample size and statistical power for more detail. If the observations are collected from a random sample, statistical theory provides probabilistic estimates of the likely size of the sampling error for a particular statistic or estimator. These are often expressed in terms of its standard error.
Sampling bias is a possible source of sampling errors. It leads to sampling errors which either have a prevalence to be positive or negative. Such errors can be considered to be systematic errors.
Sampling error can be contrasted with non-sampling error. Non-sampling error is a catch-all term for the deviations from the true value that are not a function of the sample chosen, including various systematic errors and any random errors that are not due to sampling. Non-sampling errors are much harder to quantify than sampling error.