calculating difference categories not reference

Calculating estimated differences between two categories that aren't the reference category

If Engineering majors are rated 2.25 points lower than Business Majors, and Humanities Majors are rated 1.56 points higher, then those whose major was in the business school are rated 3.81 points lower than those who majored in the humanities (2.25+1.56). 

However, note that we don't have a significance test for this relationship. This is one reason among many to think carefully about the reference category! 

Hint: Draw it!