Ex 7-49 in page 429

OPTIONS NOOVP NODATE NONUMBER LS=80;proc format; value tm 1='20min' 2='25min' 3='30min';DATA ex749;INPUT paint time finish @@; format time tm.;cards;1 1 74 1 1 64 1 1 502 1 92 2 1 86 2 1 681 2 73 1 2 61 1 2 442 2 98 2 2 73 2 2 881 3 78 1 3 85 1 3 922 3 66 2 3 45 2 3 85PROC GLM DATA=ex749; CLASS paint time; MODEL finish= paint time paint*time; MEANS paint time paint*time/snk; contrast 'AB11-AB12' paint*time 1 -1 0 -1 1 0; contrast 'AB11-AB13' paint*time 1 0 -1 -1 0 1;TITLE 'Two-way ANOVA';run; QUIT;

7-7 Factorial Experiments with More than Two Levels

Two-way ANOVA

The GLM ProcedureDependent Variable: finish Sum of Source DF Squares Mean Square F Value Pr > F

Model 5 2261.777778 452.355556 2.42 0.0973 Error 12 2242.666667 186.888889 Corrected Total 17 4504.444444

R-Square Coeff Var Root MSE finish Mean 0.502121 18.61370 13.67073 73.44444

Source DF Type I SS Mean Square F Value Pr > F paint 1 355.555556 355.555556 1.90 0.1930 time 2 27.444444 13.722222 0.07 0.9296 paint*time 2 1878.777778 939.388889 5.03 0.0260

Source DF Type III SS Mean Square F Value Pr > F paint 1 355.555556 355.555556 1.90 0.1930 time 2 27.444444 13.722222 0.07 0.9296 paint*time 2 1878.777778 939.388889 5.03 0.0260

7-7 Factorial Experiments with More than Two Levels

The GLM Procedure Student-Newman-Keuls Test for finish

NOTE: This test controls the Type I experimentwise error rate under the complete null hypothesis but not under partial null hypotheses.

Alpha 0.05 Error Degrees of Freedom 12 Error Mean Square 186.8889

Number of Means 2 Critical Range 14.040684

Means with the same letter are not significantly different.

SNK Grouping Mean N paint

A 77.889 9 2 A 69.000 9 1

7-7 Factorial Experiments with More than Two Levels

The GLM Procedure Student-Newman-Keuls Test for finish

NOTE: This test controls the Type I experimentwise error rate under the complete null hypothesis but not under partial null hypotheses.

Alpha 0.05 Error Degrees of Freedom 12 Error Mean Square 186.8889

Number of Means 2 3 Critical Range 17.196255 21.056672

Means with the same letter are not significantly different.

SNK Grouping Mean N time

A 75.167 6 30min A 72.833 6 25min A 72.333 6 20min

The GLM Procedure

Level of Level of ------------finish----------- paint time N Mean Std Dev

1 20 min 3 62.6666667 12.0554275 1 25min 3 59.3333333 14.5716620 1 30min 3 85.0000000 7.0000000 2 20 min 3 82.0000000 12.4899960 2 25min 3 86.3333333 12.5830574 2 30min 3 65.3333333 20.0083316

7-7 Factorial Experiments with More than Two Levels

Two-way ANOVA

The GLM ProcedureDependent Variable: finish

Contrast DF Contrast SS Mean Square F Value Pr > F

AB11-AB12 1 44.083333 44.083333 0.24 0.6359 AB11-AB13 1 1140.750000 1140.750000 6.10 0.0295

Coefficients for contrasts m11 = m12 is 1 -1 0 -1 1 0

B

1 2 3

1 -1 0

A 1 1 1 -1 0

2 -1 -1 1 0