# Kuehl+-+Chapter+3+Notes+-+Overheads+(06) - Treatment...

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Chapter 3 Treatment Comparisons 1 Treatment Comparisons Answer Research Questions Section 3.1 pp 73-74 There are implicit questions in most experiments. For the meat example we might have. .. Is the creation of an artificial atmosphere more effective in reducing bacterial growth than ambient air with commercial wrap? Are the gases more effective in reducing bacterial growth than a complete vacuum? 22 Is pure CO more effective than a mixture of CO, O , and N in reducing bacterial growth? Planning Comparisons Among Treatments Section 3.2 pp 74-83 Display 3.1 page 74 2 Commercial Vacuum Mixed Gas Pure CO 7.48 5.50 7.26 3.36 i t=4, r =3, s =MSE=0.116 with 8 df 2 Contrasts are special forms of linear functions.

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Chapter 3 Treatment Comparisons 2 commercial wrap vs mean of other three vacuum vs gases 2 mixed gases versus pure CO
Chapter 3 Treatment Comparisons 3 commercial vs other three (again). Note that our answer for this question of differences will be the same as we just showed. That changes if we change the question we are asking. cell means model treatment means model combine terms

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Chapter 3 Treatment Comparisons 4 Estimates are similar to Contrasts An estimate of the mean of the other treatments (i.e. vacuum; 2 mixed or pure CO ) cell means model treatment means model combine terms 41 Note that c contains : while c did not. That requires different coding in SAS.
Chapter 3 Treatment Comparisons 5 proc glm data=a Order=Data; class packcond; model logcnt = packcond; means packcond / lsd; *these first two are both contrast 1 (i.e. c1).; contrast "c1 way 1" packcond 1 -.33333 -.33333 -.33333; contrast "c1 way 2" packcond 3 -1 -1 -1; *these three are estimates of the mean diff of contrast 1 (i.e. c1); estimate "c1 way 1" packcond 1 -.33333 -.33333 -.33333; estimate "c1 way 2" packcond 3 -1 -1 -1; estimate "c1 way 3" packcond 3 -1 -1 -1 / divisor=3; *these are the estimates for mean diff of contrast 2 (i.e. c2); estimate "c2 way 1" packcond 0 1 -.5 -.5; estimate "c2 way 2" packcond 0 2 -1 -1 / divisor=2; *this the estimate for mean diff of contrast 3 (i.e. c3); estimate "c3" packcond 0 0 1 -1; * these are estimates of the mean of contrast 4 (i.e. c4); estimate "c4 way 1" intercept 1 packcond 0 .33333 .33333 .33333; estimate "c4 way 2" intercept 3 packcond 0 1 1 1; estimate "c4 way 2" intercept 3 packcond 0 1 1 1/divisor=3; run;

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Chapter 3 Treatment Comparisons 6 Dependent Variable: logcnt Sum of Source DF Squares Mean Square F Value Pr > F Model 3 32.87280000 10.95760000 94.58 <.0001 Error 8 0.92680000 0.11585000 Cor Total 11 33.79960000 R-Square Coeff Var Root MSE logcnt Mean 0.972580 5.768940 0.340367 5.900000 Type I SS packcond Type III SS Tests (LSD) for logcnt NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 8 Error Mean Square 0.11585 Critical Value of t 2.30600 Least Significant Difference 0.6409
Chapter 3 Treatment Comparisons 7 Mean N packcond A 7.4800 3 Commerical 7.2600 Mixed Gas B 5.5000 Vacuum C 3.3600 PureCO2 Dependent Variable: logcnt Contrast DF Contrast SS Mean Square F Value Pr > F c1 way 1 1 9.98579086 86.20 <.0001 c1 way 2 9.98560000 86.19 Standard Parameter Estimate Error t Value Pr > |t| 2.1066868 0.22691163 9.28 6.3200000 0.68073490 c1 way 3 2.1066667 c2 way 1 0.1900000 0.24067613 0.79 0.4526 c2 way 2 c3 3.9000000 0.27790886 14.03 c4 way 1 5.3733132 0.11345582 47.36 c4 way 2 16.1200000 0.34036745 5.3733333

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Chapter 3 Treatment Comparisons 8 variance and standard error of a contrast Note rounding differences between this and the book.
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