Which statement correctly distinguishes the standard error of differences from the standard error of the mean?

Which statement correctly distinguishes the standard error of differences from the standard error of the mean?

• A. Standard error of differences refers to variability among individual scores.
• B. Standard error of differences is the standard deviation of the sampling distribution of the difference between two means.
• C. Standard error of the mean describes variability of differences between samples.
• D. They are the same concept.

Answer: (B)

The concept being tested is how variability is characterized for a single mean versus a difference between two means. The standard error of the mean describes how much a single sample mean would vary across repeated samples from the same population; it’s the standard deviation of the sampling distribution of the mean and depends on the data’s spread and the sample size (roughly the population standard deviation divided by the square root of n). The standard error of the differences, by contrast, describes how much the difference between two sample means would vary across repeated studies; it is the standard deviation of the sampling distribution of that difference and combines the variability from both samples (for independent samples, often written as a function of the two sample variances and sizes). This distinction makes the statement that the standard error of differences is the standard deviation of the sampling distribution of the difference between two means correct. The standard error of the mean does not describe variability of differences between samples, and they are not the same concept.

The concept being tested is how variability is characterized for a single mean versus a difference between two means. The standard error of the mean describes how much a single sample mean would vary across repeated samples from the same population; it’s the standard deviation of the sampling distribution of the mean and depends on the data’s spread and the sample size (roughly the population standard deviation divided by the square root of n). The standard error of the differences, by contrast, describes how much the difference between two sample means would vary across repeated studies; it is the standard deviation of the sampling distribution of that difference and combines the variability from both samples (for independent samples, often written as a function of the two sample variances and sizes). This distinction makes the statement that the standard error of differences is the standard deviation of the sampling distribution of the difference between two means correct. The standard error of the mean does not describe variability of differences between samples, and they are not the same concept.