Harmel et al.  compiled a cross-system data set to study the effects of agriculture activities on water quality. The data included in the study were mostly field scale experiments that measured nutrients (P, N) loading leaving a field. The data set (agWQdata.csv) includes the measured TP loading (TPLoad, in kg/ha), land use (LU), tillage method (Tillage), and fertilizer application methods (FAppMethd). You are to determine whether tillage methods affect TP loading.
(a) Estimate the mean TP loading for each tillage method (an easy way to do this in R is to use the function tapply):
(b) Discuss briefly whether logarithm transformation is necessary.
(c) Use statistical test to study whether different tillage methods resulted in different TP loading (state the null and alternative hypothesis, conduct the test, report the result).
(d) Discuss briefly how useful is the test result.