7 2 Factorial Experiments 7 2 Factorial Experiments

7 -2 Factorial Experiments

7 -2 Factorial Experiments A significant interaction mask the significance of main effects. Consequently, when interaction is present, the main effects of the factors involved in the interaction may not have much meaning.

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels Sum of Squares partition: Degrees of freedom partition:

7 -7 Factorial Experiments with More than Two Levels Mean Squares:

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels Model Adequacy

7 -7 Factorial Experiments with More than Two Levels Model Adequacy

7 -7 Factorial Experiments with More than Two Levels Model Adequacy

7 -7 Factorial Experiments with More than Two Levels Computer Output

7 -7 Factorial Experiments with More than Two Levels Example 7 -11 OPTIONS NOOVP NODATE NONUMBER LS=80; DATA ex 711; DO obs= 1 to 3; DO type=1 to 3; DO method='Dipping', 'Spraying'; INPUT force @@; OUTPUT; END; CARDS; 4 5. 6 5. 8 3. 8 5. 5 4. 9 6. 1 3. 7 5 4. 3 5. 6 5. 4 6. 3 4 5 ods graphics on; PROC GLM DATA=ex 711 plots=all; CLASS type method; MODEL force= type method type*method; MEANS type method type*method/snk; output out=new r=resid; TITLE 'Two-way ANOVA'; PROC PLOT DATA=NEW; PLOT RESID*TYPE; PLOT RESID*METHOD; run; QUIT;

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels Residual Plot resid*type 도표. 범례: A = 1 관측치, B = 2 관측치, 등. resid | 0. 35 + | A 0. 30 +A A | 0. 25 + |A A 0. 20 + | A 0. 15 + | 0. 10 +A A | 0. 05 + |A A 0. 00 + | A -0. 05 + | -0. 10 + | A -0. 15 + | B -0. 20 + | -0. 25 + |A A -0. 30 + | -0. 35 + | -0. 40 +A A | -+-----------------------------------+ 1 2 3 type Residual Plot resid*method 도표. 범례: A = 1 관측치, B = 2 관측치, 등. resid | 0. 35 + | A 0. 30 + A A | 0. 25 + | A A 0. 20 + | A 0. 15 + | 0. 10 + A A | 0. 05 + | A A 0. 00 + | A -0. 05 + | -0. 10 + | A -0. 15 + | B -0. 20 + | -0. 25 + | A A -0. 30 + | -0. 35 + | -0. 40 + A A | ---+------------------------+-Dipping Sprayin method

7 -7 Factorial Experiments with More than Two Levels Exercise 7 -49 OPTIONS NOOVP NODATE NONUMBER LS=80; proc format; value tm 1='20 min' 2='25 min' 3='30 min'; DATA ex 749; INPUT paint time finish @@; format time tm. ; cards; 1 1 74 1 1 64 1 1 50 2 1 92 2 1 86 2 1 68 1 2 73 1 2 61 1 2 44 2 2 98 2 2 73 2 2 88 1 3 78 1 3 85 1 3 92 2 3 66 2 3 45 2 3 85 ods graphics on; PROC GLM DATA=ex 749 plots=(diagnostics); CLASS paint time; MODEL finish= paint time paint*time; MEANS paint time paint*time/snk; OUTPUT out=new p=phat r=resid; TITLE 'Two-way ANOVA'; PROC PLOT data=new; PLOT resid*(paint time); /* Residual plots */ TITLE 1 'Residual Plot'; run; ods graphics off; QUIT;

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

7 -7 Factorial Experiments with More than Two Levels

The Latin Square Design The Latin square design is used to eliminate two nuisance sources of variability; that is, it systemically allows blocking two dimensions. Thus, the rows and columns actually represent two restrictions on randomization. In a Latin square design, there are p treatments and p levels of each of the two blocking variables. Each treatment level appears in each row and column once. The arrangement should be randomly selected from all possible arrangement. For instance, there is only 1 3 x 3, 4 4 x 4, 56 5 x 5, and 9408 6 x 6 Latin squares.

The Latin Square Design

The Latin Square Design Example 5 -4

The Latin Square Design OPTIONS NOOVP NODATE NONUMBER LS=80; DATA latin; INPUT operator batch treat$ force @@; CARDS; 1 1 A -1 1 2 B -8 1 3 C -7 1 4 D 1 1 5 E -3 2 1 B -5 2 2 C -1 2 3 D 13 2 4 E 6 2 5 A 5 3 1 C -6 3 2 D 5 3 3 E 1 3 4 A 1 3 5 B -5 4 1 D -1 4 2 E 2 4 3 A 2 4 4 B -2 4 5 C 4 5 1 E -1 5 2 A 11 5 3 B -4 5 4 C -3 5 5 D 6 ods graphics on; PROC GLM data=latin plots=(diagnostics); CLASS operator batch treat; MODEL force = operator batch treat; MEANS operator batch treat/snk; output out=new p=phat r=resid; TITLE 'Latin Square Design'; proc plot data=new; plot resid*(operator batch treat)/vaxis= -3. 5 to 5. 0 by 0. 5; Title 'Residual plot'; RUN; QUIT;

The Latin Square Design

The Latin Square Design

The Latin Square Design

The Latin Square Design

The Latin Square Design

The Latin Square Design

The Latin Square Design

The Latin Square Design

The Latin Square Design