Enter the responses in C1, named 'y', by treatment groups from A to D.
Enter the treatment groups in C2, named 'brand' by using
*Calc* →
*Make Patterned Data* →
*Text Values* as follows

One-way ANOVA: y versus brandSource DF SS MS F Pbrand 3 15953.47 5317.82 866.12 0.000Error 36 221.03 6.14Total 39 16174.50 S = 2.478 R-Sq = 98.63% R-Sq(adj) = 98.52% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ----+---------+---------+---------+----- A 10 43.140 3.000 (*) B 10 89.440 2.218 (*) C 10 67.950 2.169 (*) D 10 40.470 2.436 (*) ----+---------+---------+---------+----- 45 60 75 90 Pooled StDev = 2.478 Tukey 90% Simultaneous Confidence Intervals All Pairwise Comparisons among Levels of brand Individual confidence level = 97.70% brand = A subtracted from: brand Lower Center Upper -------+---------+---------+---------+-- B 43.667 46.300 48.933 *) C 22.177 24.810 27.443 (*) D -5.303 -2.670 -0.037 (*) -------+---------+---------+---------+-- -30 0 30 60 brand = B subtracted from: brand Lower Center Upper -------+---------+---------+---------+-- C -24.123 -21.490 -18.857 (*) D -51.603 -48.970 -46.337 (*) -------+---------+---------+---------+-- -30 0 30 60 brand = C subtracted from: brand Lower Center Upper -------+---------+---------+---------+-- D -30.113 -27.480 -24.847 (*) -------+---------+---------+---------+-- -30 0 30 60 Fisher 95% Individual Confidence Intervals All Pairwise Comparisons among Levels of brand Simultaneous confidence level = 80.32% brand = A subtracted from: brand Lower Center Upper -------+---------+---------+---------+-- B 44.053 46.300 48.547 *) C 22.563 24.810 27.057 *) D -4.917 -2.670 -0.423 (*) -------+---------+---------+---------+-- -30 0 30 60 brand = B subtracted from: brand Lower Center Upper -------+---------+---------+---------+-- C -23.737 -21.490 -19.243 (*) D -51.217 -48.970 -46.723 (* -------+---------+---------+---------+-- -30 0 30 60 brand = C subtracted from: brand Lower Center Upper -------+---------+---------+---------+-- D -29.727 -27.480 -25.233 (*) -------+---------+---------+---------+-- -30 0 30 60

D A C B 40.47 43.14 67.95 89.44Note that all comparisons are significant (with the comparison between D and A being marginally so) and consequently no underline was drawn. The family error rate was set at 10% resulting in individual confidence level of 97.70% with an error rate of only 2.3%.

D A C B 40.47 43.14 67.95 89.44Again, all comparisons are significant. Notice that, with individual error rate set at 5%, the overall error was 19.68% (since overall confidence level was 80.32%).

Do *Stat* →
*ANOVA* →
*Test for Equal Variances* as follows

95% Bonferroni confidence intervals for standard deviations brand N Lower StDev Upper A 10 1.87765 3.00007 6.63472 B 10 1.38830 2.21821 4.90560 C 10 1.35725 2.16859 4.79587 D 10 1.52481 2.43632 5.38797 Bartlett's Test (normal distribution) Test statistic = 1.20, p-value = 0.753 Levene's Test (any continuous distribution) Test statistic = 0.23, p-value = 0.878

ANOVA: y versus brand Factor Type Levels Values brand fixed 4 A, B, C, D Analysis of Variance for ySource DF SS MS F Pbrand 3 15953.5 5317.8 866.12 0.000Error 36 221.0 6.1Total 39 16174.5 S = 2.47787 R-Sq = 98.63% R-Sq(adj) = 98.52%Expected Mean Square for Each Term (using Variance Error unrestrictedSource component term model)1 brand 2 (2) + Q[1] 2 Error 6.140 (2) Meansbrand N yA 10 43.140 B 10 89.440 C 10 67.950D 10 40.470

To create contrast, say 'amed vs generic', do
*Data* → *Code* → *Text to Numeric*
as follows

From class notes, we have claimed that these contrasts are orthogonal.
This can be verified in MINITAB by copying these contrasts into
a matrix, say M1; obtaining its transpose, say M2; then create a
product matrix (of M2 by M1), say M3. The resulting matrix M3 should be
a diagonal matrix.

To copy columns to matrix, do *Data* → *Copy* →
*Columns to Matrix* as follows

Data Display Matrix M3 10 0 0 0 20 0 0 0 20

To obtain estimates of the contrasts, one can perform computation
in MINITAB by submitting commands (doing
*Edit* → *Command Line Editor*) as follows

Data Display psi1 36.8900 psi2 2.67000 psi3 21.4900

As a matter of fact, it's easier just to run
regression analysis of the response against these three contrast
columns (doing *Stat* → *Regression*
→ *Regression*) as follows

Regression Analysis: y versus named vs generic, A vs D, B vs C The regression equation is y = 60.3 + 36.9 named vs generic + 1.34 A vs D + 10.7 B vs CPredictor Coef SE Coef T PConstant 60.2500 0.3918 153.78 0.000 named vs generic 36.8900 0.7836 47.08 0.000 A vs D 1.3350 0.5541 2.41 0.021 B vs C 10.7450 0.5541 19.39 0.000 S = 2.47787 R-Sq = 98.6% R-Sq(adj) = 98.5% Analysis of VarianceSource DF SS MS F PRegression 3 15953.5 5317.8 866.12 0.000Residual Error 36 221.0 6.1Total 39 16174.5Source DF Seq SSnamed vs generic 1 13608.7CA vs D 1 35.6_{1}CB vs C 1 2309.1_{2}C_{3}

Note that to get the *F* statistics of the contrasts, simply
square their respective *t* statistics.