Lab Session November 20, 2002:

 

With ANOVA we were able to reject the null hypothesis that the following three means are equal:

Industrial (I)      Agricultural (A) Pristine (P)

45.78               70.50                           80.62

n=9                  n=10                            n=8

 

MSE from ANOVA: 634.25

Additionally we calculated q-values for multiple comparisons after Ho was rejected (below) and we want to compare our results using Tukey and S-N-K procedures:

 

We first need to calculate dfe = N-k = 9+10+8-3 = 24

 

Comparison      q                                              Critical q (24 df, alpha=0.05)

P v. I                4.026                                       q(24,3) =3.532 (Tukey crit for all,SNK crit for Pv.I)

A v. I               3.021                                       q(24,2) =2.919 (S-N-K crit for AvI, PvA)

P v. A              1.198

 

Tukey                                      _________________

                         _______________ 

                        I                       A                     P

                        45.78               70.5                 80.62

                        I                       A__                 P

S-N-K

                       

           

With the Tukey procedure we have a contradictory result—we did not find any unique means!  We surmise that we have committed “at least one Type II error”, failing to reject when we should have.

 

With SNK we see that Pristine can be separated from both Agricultural and Industrial, which cannot be separated from each other.