When we look at the differences between scores for two groups, we must judge the difference between their means relative to the spread or variability of their scores. The t-test does this. Let's say, for example, that Protestants have a mean of 13.6 years of education and Catholics have a mean of 12.4 years. We find that the observed difference is statistically significant. There is no simple way to answer this question.
Substantive differences are different from statistically significant differences.
The formula for the t-test is a ratio. The top part of the equation is the difference between the two means. The bottom part is a measure of the variability or dispersion of the scores. The bottom part of the formula is called the standard error of the difference . We add these two values, then take their square root.