Standard error of differences is the standard deviation of the sampling distribution of what?

Standard error of differences is the standard deviation of the sampling distribution of what?

• A. Differences within a single sample.
• B. Means of a single sample.
• C. Individual scores.
• D. Differences between sample means.

Answer: (D)

Think of what a standard error represents: how much a statistic would vary if you took many samples. Here, the statistic of interest is the difference between two sample means, so you’re looking at the spread of the sampling distribution of that difference. The standard error of differences is the standard deviation of that distribution, i.e., how much the difference between sample means tends to vary across repeated samples. The other options don’t fit: differences within a single sample aren’t describing a sampling distribution of a statistic; the standard error of a single sample mean refers to the mean itself, not the difference between means; and the standard deviation of individual scores is about raw data variation, not the variability of a sampling statistic.

Think of what a standard error represents: how much a statistic would vary if you took many samples. Here, the statistic of interest is the difference between two sample means, so you’re looking at the spread of the sampling distribution of that difference. The standard error of differences is the standard deviation of that distribution, i.e., how much the difference between sample means tends to vary across repeated samples. The other options don’t fit: differences within a single sample aren’t describing a sampling distribution of a statistic; the standard error of a single sample mean refers to the mean itself, not the difference between means; and the standard deviation of individual scores is about raw data variation, not the variability of a sampling statistic.