$12-26.$ Grant Thornton LLP is the U$.$S$.$ member firm of Grant Thornton International, one of the six global accounting, tax, and business advisory organizations. It provides firm$-$wide auditing training for its employees in three different auditing methods. Auditors were grouped into four blocks according to the education they had received: $(1)$ high school, $(2)$ bachelor's, $(3)$ master's, and $(4)$ doctorate. Three auditors at each education level were used$-$one assigned to each method. They were given a post training examination consisting of complicated auditing scenarios. The scores for the $12$ auditors were as follows:

$\backslash$table$[[,$Method $1,$Method $2,$Method $3],[$Doctorate$,83,81,82],[$Master$\text{'}$s$,77,75,79],[$Bachelor$\text{'}$s$,74,73,75],[$High School,$72,70,69]]$

a$.$ Indicate why blocking was employed in this design.

b$.$ Determine if blocking was effective for this design by producing the relevant ANOVA.

c$.$ Using a significance level of $0\mathrm{.}05,$ determine if the average post training examination scores among the auditing methods are equal to each other.

d$.$ If you discovered that there were differences among the average post training examination scores among the auditing methods, use the LSD approach to determine which populations have different means.