Payscale does provide the data by major as well. The problem is that with smaller schools, there may not be enough data to provide a statistically significant sample in a given year. In general, California/west coast pays more than Boston/east coast which pays more than St. Louis/midwest.
For apples to apples engineering you need to use 2014 data because the sample size in 2015 is not big enough for Tufts Engineering or HMudd Engineering.
http://www.payscale.com/college-salary-report-2014/best-schools-by-major/engineering
Wash U has an undergrad business school that skews the starting salary data upward. Tufts has a higher percentage of fine arts majors that skews the data lower.