what is meant by the standard error of a statistic? what is it an index of? what is meant by the standard error of the mean? what it is an index of?
The standard error of a statistic measures the variability or precision of that statistic. It tells us how much the statistic tends to vary from its average value.
To calculate the standard error of a statistic, such as the mean, you typically need to know the sample size, the variability of the data, and the distribution underlying the data. For a given sample size, larger variability or a more spread-out distribution will result in a larger standard error.
The standard error is an index of the precision of an estimated statistic. It provides valuable information about the likely range of values within which the true population parameter is expected to lie.
Specifically, the standard error of the mean (SEM) is the standard deviation of the sample mean. It measures how much the sample means are expected to vary from the true population mean. The SEM is often used to estimate the uncertainty or margin of error associated with the sample mean.
To calculate the standard error of the mean, you divide the standard deviation of the sample by the square root of the sample size. This means that as the sample size increases, the standard error of the mean decreases, indicating greater precision in estimating the population mean.
In summary, the standard error of a statistic, such as the mean, is an index of the variability or precision of that statistic. The standard error of the mean specifically represents the expected variation of sample means from the true population mean.