What is the Standard Error?

What is the Standard Error?

• A. The equivalent of the standard deviation for a normal sampling distribution (rather than individuals, from a distribution of sampling averages)
• B. The probability that the null hypothesis is true
• C. The median of the data set
• D. The variance of individual observations

Answer: (A)

The Standard Error is the typical amount the sample mean would vary from one sample to another if you repeated the study many times. It is the standard deviation of the sampling distribution of the mean. For a normal sampling distribution, this equals the standard deviation of individual observations divided by the square root of the sample size (sigma over sqrt(n), or s over sqrt(n) when sigma is unknown). This tells you how precisely the sample mean estimates the population mean—the smaller the standard error, the more precise the estimate. So it describes the variability of the mean across samples, not the variability of individual data points. The other options describe different ideas: a p-value about the null hypothesis, the median as a central tendency, and the variance of individual observations, none of which capture the variability of the sampling distribution of the mean.

The Standard Error is the typical amount the sample mean would vary from one sample to another if you repeated the study many times. It is the standard deviation of the sampling distribution of the mean. For a normal sampling distribution, this equals the standard deviation of individual observations divided by the square root of the sample size (sigma over sqrt(n), or s over sqrt(n) when sigma is unknown). This tells you how precisely the sample mean estimates the population mean—the smaller the standard error, the more precise the estimate. So it describes the variability of the mean across samples, not the variability of individual data points. The other options describe different ideas: a p-value about the null hypothesis, the median as a central tendency, and the variance of individual observations, none of which capture the variability of the sampling distribution of the mean.