Question

Analyze the relationship between standard error and the difference between the means.

A researcher examines the results of two separate studies. In the first study, the difference between group a and group b is two points but the standard error is large and the difference is not significant. in the second study, the difference between group a and group b is also two points but the standard error is small and the difference is significant.

What might be the reason for the difference in standard error across the two studies?

Answer 1

1. The standard error of the mean, or SEM, measures how far the sample mean of the data is likely to be from the true population mean. In other words, it tests the variability of a given set of means around the population mean.

2. The standard error is inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value. Therefore, in the case where the standard error is low, the sample size will be larger and therefore SD differences between the two groups will be significant.