The following is part of the printout from an SPSS analysis of data on paired samples. Use it to answer the next several questions.

The standard error of the mean of difference scores could be calculated by
A) taking the standard deviation of the differences.
B) repeating the study many times and looking at the distribution of means.
C) dividing the standard deviation of difference scores by the square root of the sample size.
D) looking at the standard deviation of the posttest scores.

Question

The following is part of the printout from an SPSS analysis of data on paired samples.  Use it to answer the next several questions.

The standard error of the mean of difference scores could be calculated by
A) taking the standard deviation of the differences. 
B) repeating the study many times and looking at the distribution of means. 
C) dividing the standard deviation of difference scores by the square root of the sample size. 
D) looking at the standard deviation of the posttest scores.

Quizplus · Accepted Answer

The standard error of the mean of difference scores is calculated by dividing the standard deviation of the difference scores by the square root of the sample size. This is because the standard error is a measure of how much the mean of the difference scores in the sample deviates from the population mean of difference scores. The larger the sample size, the smaller the standard error, which means that the sample mean is a better estimate of the population mean. Option A is incorrect because taking the standard deviation of the differences gives us a measure of the variability of the differences, not their standard error. Option B is incorrect because repeating the study many times and looking at the distribution of means would give us information about the sampling distribution of means, not the standard error of the mean of difference scores. Option D is also incorrect because the standard deviation of the posttest scores does not provide information about the standard error of the mean of difference scores.

The Following Is Part of the Printout from an SPSS