1          OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 NOTE: ODS statements in the SAS Studio environment may disable some output features.
 71         
 72         /* potato2020.sas */
 73         title 'Rotten Potatoes: Factorial ANOVA several different ways';
 74         
 75         proc format;
 76              value tfmt 1 = '10 Degrees'  2 = '16 Degrees';
 NOTE: Format TFMT has been output.
 77              value ofmt 1 = '2%' 2 = '6%' 3 = '10%';
 NOTE: Format OFMT has been output.
 78         
 
 NOTE: PROCEDURE FORMAT used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              247.37k
       OS Memory           29092.00k
       Timestamp           02/18/2020 09:37:20 PM
       Step Count                        72  Switch Count  0
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       Block Output Operations           40
       
 
 79         data fries;
 80              infile '/home/brunner0/441s20/potato.data.txt' firstobs=2;
 81                                             /* Skip the header that R uses. */
 82              input id bact temp oxygen rot;
 83              label bact   = 'Bacteria Type'
 84                    temp   = 'Storage Temperature'
 85                    oxygen = 'Oxygen level';
 86              format temp tfmt.; format oxygen ofmt.;
 87         
 
 NOTE: The infile '/home/brunner0/441s20/potato.data.txt' is:
       Filename=/home/brunner0/441s20/potato.data.txt,
       Owner Name=brunner0,Group Name=oda,
       Access Permission=-rw-r--r--,
       Last Modified=18Feb2020:16:35:13,
       File Size (bytes)=2037
 
 NOTE: 54 records were read from the infile '/home/brunner0/441s20/potato.data.txt'.
       The minimum record length was 35.
       The maximum record length was 35.
 NOTE: The data set WORK.FRIES has 54 observations and 5 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.00 seconds
       user cpu time       0.01 seconds
       system cpu time     0.00 seconds
       memory              763.75k
       OS Memory           29608.00k
       Timestamp           02/18/2020 09:37:20 PM
       Step Count                        73  Switch Count  2
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       Block Output Operations           264
       
 
 88         proc freq data=fries;
 89              tables oxygen*temp*bact / norow nocol nopercent;
 90              run;
 
 NOTE: There were 54 observations read from the data set WORK.FRIES.
 NOTE: PROCEDURE FREQ used (Total process time):
       real time           0.06 seconds
       user cpu time       0.05 seconds
       system cpu time     0.00 seconds
       memory              3252.12k
       OS Memory           31152.00k
       Timestamp           02/18/2020 09:37:20 PM
       Step Count                        74  Switch Count  4
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       Block Output Operations           536
       
 
 91         
 92         proc glm data=fries;
 93              title2 'Three-way ANOVA with proc glm';
 94              class bact temp oxygen;
 95              model rot=temp|bact|oxygen; /* All main effects and interactions */
 96              means temp|bact; /* Based on the tests */
 97         run;
 
 NOTE: Means from the MEANS statement are not adjusted for other terms in the model.  For adjusted means, use the LSMEANS statement.
 98         
 99         /* Want to test everything involving oxygen, all at once.
 100           Null hypothesis is that oxygen level has no effect within ANY
 101           combination of temperature and bacteria type. This is
 102           sometimes called "conditional independence." Do it with
 103           effect coding and proc reg. */
 104        
 
 NOTE: PROCEDURE GLM used (Total process time):
       real time           2.78 seconds
       user cpu time       0.30 seconds
       system cpu time     0.02 seconds
       memory              17084.84k
       OS Memory           47424.00k
       Timestamp           02/18/2020 09:37:23 PM
       Step Count                        75  Switch Count  3
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 105        data mashed;
 106             set fries;
 107             /* Effect coding, with interactions */
 108                if bact = 1 then b1 =  1;
 109                   else if bact = 2 then b1 =  0;
 110                   else if bact = 3 then b1 = -1;
 111                if bact = 1 then b2 =  0;
 112                   else if bact = 2 then b2 =  1;
 113                   else if bact = 3 then b2 = -1;
 114        
 115                if temp = 1 then t =  1;
 116                   else if temp = 2 then t = -1;
 117        
 118                if oxygen = 1 then ox1 =  1;
 119                   else if oxygen = 2 then ox1 =  0;
 120                   else if oxygen = 3 then ox1 = -1;
 121                if oxygen = 1 then ox2 =  0;
 122                   else if oxygen = 2 then ox2 =  1;
 123                   else if oxygen = 3 then ox2 = -1;
 124        
 125             /******* Interaction terms *******/
 126                /**** temp by bact ****/
 127                tb1 = t*b1; tb2 = t*b2;
 128                /**** temp by oxygen ****/
 129                tox1 = t*ox1; tox2 = t*ox2;
 130                /**** bact by oxygen ****/
 131                b1ox1 = b1*ox1; b1ox2 = b1*ox2;
 132                b2ox1 = b2*ox1; b2ox2 = b2*ox2;
 133                /**** temp by bact by oxygen ****/
 134                tb1ox1 = t*b1ox1; tb1ox2 = t*b1ox2;
 135                tb2ox1 = t*b2ox1; tb2ox2 = t*b2ox2;
 136        
 
 NOTE: There were 54 observations read from the data set WORK.FRIES.
 NOTE: The data set WORK.MASHED has 54 observations and 22 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              972.96k
       OS Memory           45996.00k
       Timestamp           02/18/2020 09:37:23 PM
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 137        proc reg data=mashed plots=none;
 138             title2 'Three-way ANOVA with proc reg and effect coding';
 139             model rot = b1 -- tb2ox2;
 140             /* Test main effects and interactions in the same order
 141                as proc glm */
 142             Temperature:            test t=0;
 143             Bacteria:               test b1=b2=0;
 144             Bact_by_Temp:           test tb1=tb2=0;
 145             Oxygen:                 test ox1=ox2=0;
 146             Temp_by_Oxygen:         test tox1=tox2=0;
 147             Bact_by_Oxygen:         test b1ox1=b1ox2=b2ox1=b2ox2=0;
 148             Bact_by_Temp_by_Oxygen: test tb1ox1=tb1ox2=tb2ox1=tb2ox2=0;
 149             Conditional_Indep:      test ox1=ox2 = tox1=tox2 =
 150                                          b1ox1=b1ox2=b2ox1=b2ox2 =
 151                                          tb1ox1=tb1ox2=tb2ox1=tb2ox2 = 0;
 152        run;
 
 153        
 154        /* Drop oxygen. Implicitly we are accepting H0. */
 155        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.15 seconds
       user cpu time       0.16 seconds
       system cpu time     0.00 seconds
       memory              2776.62k
       OS Memory           47552.00k
       Timestamp           02/18/2020 09:37:23 PM
       Step Count                        77  Switch Count  2
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       Block Output Operations           120
       
 
 156        proc tabulate data=mashed;
 157             title2 'Two-way table of means from proc tabulate';
 158             class bact temp;
 159             var rot;
 160             table (temp all), (bact all) * (mean*rot);
 161        run;
 
 NOTE: There were 54 observations read from the data set WORK.MASHED.
 NOTE: PROCEDURE TABULATE used (Total process time):
       real time           0.03 seconds
       user cpu time       0.03 seconds
       system cpu time     0.01 seconds
       memory              9707.75k
       OS Memory           56012.00k
       Timestamp           02/18/2020 09:37:23 PM
       Step Count                        78  Switch Count  10
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       Block Output Operations           1104
       
 
 162        
 163        /* Suppressing the lsmeans plots */
 164        ods exclude MeanPlot (persist) DiffPlot (persist);
 165        proc glm data=mashed;
 166             title2 'Two-way ANOVA, ignoring oxygen level';
 167             class bact temp;
 168             model rot=temp|bact;
 169             lsmeans bact / pdiff tdiff adjust = tukey;
 170             lsmeans bact / pdiff tdiff adjust = bon;
 171             /* ODS output table name = My data table name (Backwards)*/
 172             ods output OverallANOVA = Overall
 173                        ModelANOVA   = TwoWay;
 174        run;
 
 NOTE: The data set WORK.TWOWAY has 6 observations and 8 variables.
 NOTE: The data set WORK.OVERALL has 3 observations and 7 variables.
 175        
 
 NOTE: PROCEDURE GLM used (Total process time):
       real time           0.38 seconds
       user cpu time       0.18 seconds
       system cpu time     0.01 seconds
       memory              4999.23k
       OS Memory           48968.00k
       Timestamp           02/18/2020 09:37:23 PM
       Step Count                        79  Switch Count  8
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       Involuntary Context Switches      0
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       Block Output Operations           1280
       
 
 176        proc print data=Overall;
 177             title2 'Look at the ODS output tables';
 
 NOTE: There were 3 observations read from the data set WORK.OVERALL.
 NOTE: PROCEDURE PRINT used (Total process time):
       real time           0.01 seconds
       user cpu time       0.01 seconds
       system cpu time     0.00 seconds
       memory              668.18k
       OS Memory           46760.00k
       Timestamp           02/18/2020 09:37:23 PM
       Step Count                        80  Switch Count  1
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 178        proc print data=TwoWay;
 179        
 
 NOTE: There were 6 observations read from the data set WORK.TWOWAY.
 NOTE: PROCEDURE PRINT used (Total process time):
       real time           0.02 seconds
       user cpu time       0.03 seconds
       system cpu time     0.00 seconds
       memory              675.40k
       OS Memory           46760.00k
       Timestamp           02/18/2020 09:37:23 PM
       Step Count                        81  Switch Count  0
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 180        proc iml;
 NOTE: IML Ready
 181             title2 'Proportions of remaining variation';
 182             use overall;
 182      !                    read all into anova1;
 182      !                                          /* "all" means all cases */
 183             use TwoWay;
 183      !                    read all into anova2;
 184             print "Take a look at the matrices";
 185             print anova1;
 185      !                    print anova2;
 186             print "Proportion of remaining variation";
 187             NminusP = anova1[2,1];
 188             s1 = anova2[4,2];
 188      !                        F1 = anova2[4,5];
 188      !                                          /* Main effect for Temperature */
 189             s2 = anova2[5,2];
 189      !                        F2 = anova2[5,5];
 189      !                                          /* Main effect for Bacteria */
 190             s3 = anova2[6,2];
 190      !                        F3 = anova2[6,5];
 190      !                                          /* Interaction */
 191             Temperature  = s1*F1/(s1*F1 + NminusP);
 192             Bacteria     = s2*F2/(s2*F2 + NminusP);
 193             Temp_by_Bact = s3*F3/(s3*F3 + NminusP);
 194             print Temperature Bacteria Temp_by_Bact;
 195        
 196        
 197        /* Regression with cell means coding */
 198        
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.03 seconds
       user cpu time       0.03 seconds
       system cpu time     0.00 seconds
       memory              1078.75k
       OS Memory           47020.00k
       Timestamp           02/18/2020 09:37:23 PM
       Step Count                        82  Switch Count  1
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 199        data baked;
 200             set mashed;
 201             /* Cell means coding for all 6 treatment combinations
 202                of temperature and bacteria type -- use with proc reg*/
 203             if temp=1 and bact=1 then mu11=1; else mu11=0;
 204             if temp=1 and bact=2 then mu12=1; else mu12=0;
 205             if temp=1 and bact=3 then mu13=1; else mu13=0;
 206             if temp=2 and bact=1 then mu21=1; else mu21=0;
 207             if temp=2 and bact=2 then mu22=1; else mu22=0;
 208             if temp=2 and bact=3 then mu23=1; else mu23=0;
 209             /* Combination variable for temperature and bacteria
 210                type -- use for contrasts with proc glm */
 211             combo = 10*temp+bact; /* 11 12 13 21 22 23 */
 212        
 213        /*
 214                       BACTERIA TYPE
 215        TEMP      1         2        3
 216        Cool    mu11      mu12      mu13
 217        Warm    mu21      mu22      mu23
 218        
 219        The test statement of proc reg uses variable names to stand for the
 220        corresponding regression coefficients. By naming the effect cell mean
 221        coding dummy variables the same as the population cell means, I can
 222        just state the null hypothesis. Isn't this a cute SAS trick? */
 223        
 
 NOTE: There were 54 observations read from the data set WORK.MASHED.
 NOTE: The data set WORK.BAKED has 54 observations and 29 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.00 seconds
       user cpu time       0.00 seconds
       system cpu time     0.00 seconds
       memory              1014.43k
       OS Memory           47276.00k
       Timestamp           02/18/2020 09:37:23 PM
       Step Count                        83  Switch Count  2
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 224        proc reg  data = baked plots = none;
 225             title2 'Using the proc reg test statement and cell means coding';
 226             model rot = mu11--mu23 / noint;
 227             Overall:       test mu11=mu12=mu13=mu21=mu22=mu23;
 228             Temperature:   test mu11+mu12+mu13 = mu21+mu22+mu23;
 229             Bacteria:      test mu11+mu21 = mu12+mu22 = mu13+mu23;
 230             Bact_by_Temp1: test mu11-mu21 = mu12-mu22 = mu13-mu23;
 231             Bact_by_Temp2: test mu12-mu11 = mu22-mu21,
 232                                 mu13-mu12 = mu23-mu22;
 233        /* Bact_by_Temp1 checks equality of temperature effects.
 234           Bact_by_Temp2 checks parallel line segments. They are equivalent. */
 235        run;
 
 236        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.10 seconds
       user cpu time       0.11 seconds
       system cpu time     0.00 seconds
       memory              2468.00k
       OS Memory           48832.00k
       Timestamp           02/18/2020 09:37:24 PM
       Step Count                        84  Switch Count  2
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       Voluntary Context Switches        19
       Involuntary Context Switches      3
       Block Input Operations            0
       Block Output Operations           104
       
 
 237        proc glm data = baked;
 238             title2 'Proc glm: Using contrasts on the combination variable';
 239             class combo;      /* 11 12 13  21 22 23 */
 240             model rot=combo;
 241             contrast 'Main Effect for Temperature'
 242                combo  1  1  1  -1 -1 -1;
 243             contrast 'Main Effect for Bacteria'
 244                combo  1 -1  0   1 -1  0,
 245                combo  0  1 -1   0  1 -1;
 246             contrast 'Temperature by Bacteria Interaction'
 247                combo  1 -1  0  -1  1  0,
 248                combo  0  1 -1   0 -1  1;
 249        run;
 
 250        
 251        
 252        /* Follow up the interaction and do some more exploration. The regression
 253           with cell means coding is easiest. The final product of several runs
 254           is shown below. For reference, here is the table of population means again.
 255        
 256                       BACTERIA TYPE
 257        TEMP      1         2        3
 258        Cool    mu11      mu12      mu13
 259        Warm    mu21      mu22      mu23                      */
 260        
 
 NOTE: PROCEDURE GLM used (Total process time):
       real time           0.35 seconds
       user cpu time       0.11 seconds
       system cpu time     0.01 seconds
       memory              3987.90k
       OS Memory           49216.00k
       Timestamp           02/18/2020 09:37:24 PM
       Step Count                        85  Switch Count  3
       Page Faults                       0
       Page Reclaims                     494
       Page Swaps                        0
       Voluntary Context Switches        620
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           728
       
 
 261        proc reg plots = none;
 262             title3 'Further exploration using cell means coding';
 263             model rot = mu11--mu23 / noint;
 264             /* Pairwise comparisons of marginal means for Bacteria Type */
 265             Bact1vs2: test mu11+mu21=mu12+mu22;
 266             Bact1vs3: test mu11+mu21=mu13+mu23;
 267             Bact2vs3: test mu12+mu22=mu13+mu23;
 268             /* Effect of temperature for each bacteria type */
 269             Temp_for_Bac1: test mu11=mu21;
 270             Temp_for_Bac2: test mu12=mu22;
 271             Temp_for_Bac3: test mu13=mu23;
 272             /* Effect of bacteria type for each temperature */
 273             Bact_for_CoolTemp: test mu11=mu12=mu13;
 274             Bact_for_WarmTemp: test mu21=mu22=mu23;
 275             /* Pairwise comparisons of bacteria types at warm temperature */
 276             Bact1vs2_for_WarmTemp: test mu21=mu22;
 277             Bact1vs3_for_WarmTemp: test mu21=mu23;
 278             Bact2vs3_for_WarmTemp: test mu22=mu23;
 279             /* Follow up the interaction with pairwise
 280                comparisons of temperature effects. */
 281             TempEffectBact1_vs_2: test mu11-mu21 = mu12-mu22;
 282             TempEffectBact1_vs_3: test mu11-mu21 = mu13-mu23;
 283             TempEffectBact2_vs_3: test mu12-mu22 = mu13-mu23;
 284        
 285        /* We have done a lot of tests. Concerned about buildup of Type I
 286        error? We can make ALL the tests into Scheffe follow-ups of the
 287        initial test for equality of the 6 cell means. The Scheffe family
 288        includes all COLLECTIONS of contrasts, not just all contrasts. */
 289        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.22 seconds
       user cpu time       0.23 seconds
       system cpu time     0.00 seconds
       memory              2537.90k
       OS Memory           48832.00k
       Timestamp           02/18/2020 09:37:24 PM
       Step Count                        86  Switch Count  2
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       Page Reclaims                     257
       Page Swaps                        0
       Voluntary Context Switches        18
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           144
       
 
 290        proc iml;
 NOTE: IML Ready
 291             title3 'Table of critical values for all possible Scheffe tests';
 292             numdf = 5;
 292      !                   /* Numerator degrees of freedom for initial test */
 293             dendf =48;
 293      !                   /* Denominator degrees of freedom for initial test */
 294             alpha = 0.05;
 295             critval = finv(1-alpha,numdf,dendf);
 296             zero = {0 0};
 296      !                    S_table = repeat(zero,numdf,1);
 296      !                                                     /* Make empty matrix */
 297             /* Label the columns */
 298             namz = {"Number of Contrasts in followup test"
 299                     "    Scheffe Critical Value"};
 299      !                                             mattrib S_table colname=namz;
 300             do i = 1 to numdf;
 301                s_table(|i,1|) = i;
 302                s_table(|i,2|) = numdf/i *  critval;
 303             end;
 304             reset noname;
 304      !                    /* Makes output look nicer in this case */
 305             print "Initial test has"  numdf " and " dendf "degrees of freedom."
 306                   "Using significance level alpha = " alpha;
 307             print s_table;
 308        
 309        
 310        /*****************************************************************/
 311        
 312        
 313        
 314        
 315        
 316        
 317        
 318        OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 329