Randomized Complete Block Design Example A researcher studied the effects of 3 diets with varying fat contents on the total lipid (fat) level in plasma. This is a widely used predictor of coronary heart disease. Fifteen male subjects who where within 20 percent of their ideal body weight were grouped into 5 blocks according to age. Within each block, the 3 diets were randomly assigned to the 3 subjects. Data on reduction in lipid level (in g/l) after the subjects were on the died for a fixed period of time are below: Fat content -------------- Age Extremely Low Fairly Low Moderately Low ---- 15-24 .73 .67 .15 25-34 .86 .75 .21 35-44 .94 .81 .26 45-54 1.40 1.32 .75 55-64 1.62 1.41 .78 Does the mean reduction in lipid level differ for the 3 diets? Below is the SAS program to analyze this data, assuming the data is saved in the file diet.dat %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% title 'Randomized Complete Block Design: Diets'; options linesize=79; data wounds; infile 'diet.dat'; input Fat Age Lipids; PROC PRINT; PROC ANOVA; CLASS Fat Age; # Must include our factor (Fat) and our block (Age) MODEL Lipids = Fat Age; #The model MEANS Fat/lsd tukey alpha = 0.1; # Find CI's to compare treatments # Can use all previous methods RUN; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% # NOTE: Can also construct residual plots, just like in the single # factor experiments. Remember that, to obtain the residuals, you need # to use PROC GLM instead of PROC ANOVA. However, how you write the # CLASS and MODEL lines will be exactly the same for PROC GLM and # PROC ANOVA Randomized Complete Block Design: Diets Obs Fat Age Lipids 1 1 1 0.73 2 1 2 0.86 3 1 3 0.94 4 1 4 1.40 5 1 5 1.62 6 2 1 0.67 7 2 2 0.75 8 2 3 0.81 9 2 4 1.32 10 2 5 1.41 11 3 1 0.15 12 3 2 0.21 13 3 3 0.26 14 3 4 0.75 15 3 5 0.78 Randomized Complete Block Design: Diets The ANOVA Procedure Class Level Information Class Levels Values Fat 3 1 2 3 Age 5 1 2 3 4 5 Number of observations 15 Randomized Complete Block Design: Diets The ANOVA Procedure Dependent Variable: Lipids Sum of Source DF Squares Mean Square F Value Pr > F Model 6 2.73924000 0.45654000 189.04 <.0001 Error 8 0.01932000 0.00241500 Corrected Total 14 2.75856000 R-Square Coeff Var Root MSE Lipids Mean 0.992996 5.822589 0.049143 0.844000 Source DF Anova SS Mean Square F Value Pr > F Fat 2 1.32028000 0.66014000 273.35 <.0001 Age 4 1.41896000 0.35474000 146.89 <.0001 Randomized Complete Block Design: Diets The ANOVA Procedure t Tests (LSD) for Lipids NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.1 Error Degrees of Freedom 8 Error Mean Square 0.002415 Critical Value of t 1.85955 Least Significant Difference 0.0578 Means with the same letter are not significantly different. t Grouping Mean N Fat A 1.11000 5 1 B 0.99200 5 2 C 0.43000 5 3 Randomized Complete Block Design: Diets The ANOVA Procedure Tukey's Studentized Range (HSD) Test for Lipids NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ. Alpha 0.1 Error Degrees of Freedom 8 Error Mean Square 0.002415 Critical Value of Studentized Range 3.37394 Minimum Significant Difference 0.0741 Means with the same letter are not significantly different. Tukey Grouping Mean N Fat A 1.11000 5 1 B 0.99200 5 2 C 0.43000 5 3