SAS Program Part 1: proc import datafile="y:\iowa_classes\stat_5201_design\examples\2-23_drillspeed_feed\mont_5-7.csv" out=ds dbms=csv replace; run;
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1 STAT:5201 Applied Statistic II (two-way ANOVA with contrasts Two-Factor experiment Drill Speed: 125 and 200 Feed Rate: 0.02, 0.03, 0.05, 0.06 Response: Force All 16 runs were done in random order. This is a completely randomized design (CRD. SAS Program Part 1: proc import datafile="y:\iowa_classes\stat_5201_design\examples\2-23_drillspeed_feed\mont_5-7.csv" out=ds dbms=csv replace; symbol1 value=circle color=black height=3; symbol2 value=plus color=blue height=3; proc gplot data=ds; plot Force*Feed_Rate=Drill_Speed/haxis=0 to 0.08 by.01; Fit a 2way ANOVA (nonadditive model, with interaction: proc glm data=ds; class Feed_Rate Drill_Speed; model Force=Feed_Rate Drill_Speed; estimate drill: 125 vs. 200 Drill_Speed 1-1; estimate feed: 0.02 vs Feed_Rate ; estimate 125 vs 200 within Feed=0.02 Drill_Speed 1-1 Feed_Rate*Drill_Speed ; estimate 125 at 0.02 vs 200 at 0.06 Drill_Speed 1-1 Feed_Rate Drill_Speed*Feed_Rate ; lsmeans Drill_Speed; lumens Feed_Rate; lsmeans Drill_Speed*Feed_Rate; 1
2 Profile plot provided from PROC GPLOT (when Feed Rate is first class variable listed in class statement. The GLM Procedure Class Level Information Class Levels Values Feed_Rate Drill_Speed The GLM Procedure Dependent Variable: Force Sum of Source DF Squares Mean Square F Value Pr > F Model Error Corrected Total Source DF Type I SS Mean Square F Value Pr > F Drill_Speed <.0001 Feed_Rate Drill_Spee*Feed_Rate Source DF Type III SS Mean Square F Value Pr > F Drill_Speed <.0001 Feed_Rate Drill_Spee*Feed_Rate
3 Standard Parameter Estimate Error t Value Pr > t drill: 125 vs <.0001 feed: 0.02 vs vs 200 within Feed= at 0.02 vs 200 at Let s pick-apart the SAS coding on one of these contrasts. The effects model for the data can be written as Y ijk = µ + α i + β j + (αβ ij + ɛ ijk for i = 1, 2 j = 1, 2, 3, 4 k = 1, 2 and ɛ ijk iid N(0, σ 2. estimate 125 vs 200 within Feed=0.02 Drill_Speed 1-1 Feed_Rate*Drill_Speed ; [µ + α 1 + β 1 + (αβ 11 ] [µ + α 2 + β 1 + (αβ 21 ] = α 1 α 2 + (αβ 11 (αβ 21 estimate 125 at 0.02 vs 200 at 0.06 Drill_Speed 1-1 Feed_Rate Drill_Speed*Feed_Rate ; [µ + α 1 + β 1 + (αβ 11 ] [µ + α 2 + β 4 + (αβ 24 ] = α 1 α 2 + β 1 β 4 + (αβ 11 (αβ 24 The GLM Procedure Least Squares Means Drill_ Speed Force LSMEAN Feed_Rate Force LSMEAN Drill_ Speed Feed_Rate Force LSMEAN
4 Contrasts in R using the Contrast package: ## Coerce numerically coded factors to type factor : > dt$drill.speed<-factor(dt$drill.speed > dt$feed.rate<-factor(dt$feed.rate ## Check default dummy variable coding for factors (shows reference group: > contrasts(drill.speed > contrasts(feed.rate > library(contrast > attach(dt ## Fit full model with interaction: > lmout<-lm(force~drill.speed + Feed.Rate + Drill.Speed:Feed.Rate ## NOTE: Same as lmout<-lm(force~(drill.speed + Feed.Rate^2 1 Drill: 125 vs. 200 (main effect comparison: cont125v200<-contrast(lmout, list(drill.speed="125",feed.rate=levels(feed.rate, list(drill.speed="200",feed.rate=levels(feed.rate, > print(cont125v e-04 ## Another option is to consider the 8 group superfactor : > trt<-drill.speed:feed.rate > lmout2<-lm(force~trt > contrast(lmout2,a=list(trt=c("125:0.02","125:0.03","125:0.05","125:0.06", b=list(trt=c("200:0.02","200:0.03","200:0.05","200:0.06", 4
5 e-04 2 Feed: 0.02 vs (main effect comparison > cont0.02v0.03<-contrast(lmout, list(drill.speed=levels(drill.speed,feed.rate="0.02", list(drill.speed=levels(drill.speed,feed.rate="0.03", > print(cont0.02v vs 200 within Feed 0.02: > cont125v200in0.02<-contrast(lmout, list(drill.speed="125",feed.rate="0.02", list(drill.speed="200",feed.rate="0.02", > print(cont125v200in at 0.02 vs 200 at 0.06: > contlast<-contrast(lmout, list(drill.speed="125",feed.rate="0.02", list(drill.speed="200",feed.rate="0.06", > print(contlast
6 All pairwise comparisons of eight means in SAS (no multiple comparison adjustment: proc glm data=ds plot=diagnostics; class Drill_Speed Feed_Rate; model Force=Drill_Speed Feed_Rate; lsmeans Feed_Rate*Drill_Speed/adjust=T; Drill_ LSMEAN Speed Feed_Rate Force LSMEAN Number Least Squares Means for effect Drill_Spee*Feed_Rate Pr > t for H0: LSMean(i=LSMean(j Dependent Variable: Force i/j < <.0001 < < < < NOTE: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used. 6
7 All pairwise comparisons of eight means in R (no multiple comparison adjustment: > pairwise.t.test(force,drill.speed:feed.rate,p.adjust.method="none" Pairwise comparisons using t tests with pooled SD data: Force and Drill.Speed:Feed.Rate 125: : : : : : : : : : : e : : e : e P value adjustment method: none 7
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