1          OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 NOTE: ODS statements in the SAS Studio environment may disable some output features.
 73         
 74         /* potato.sas */
 75         title 'Rotten Potatoes: Factorial ANOVA several different ways';
 76         
 77         proc format;
 78              value tfmt 1 = '10 Degrees'  2 = '16 Degrees';
 NOTE: Format TFMT is already on the library WORK.FORMATS.
 NOTE: Format TFMT has been output.
 79              value ofmt 1 = '2%' 2 = '6%' 3 = '10%';
 NOTE: Format OFMT is already on the library WORK.FORMATS.
 NOTE: Format OFMT has been output.
 80         
 
 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              239.28k
       OS Memory           31652.00k
       Timestamp           03/16/2024 05:51:58 PM
       Step Count                        66  Switch Count  0
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 81         data fries;
 82              infile '/home/u1407221/441s24/data/potato.data.txt' firstobs=2;
 83                                             /* Skip the header that R uses. */
 84              input id bact temp oxygen rot;
 85              label bact   = 'Bacteria Type'
 86                    temp   = 'Storage Temperature'
 87                    oxygen = 'Oxygen level';
 88              format temp tfmt.; format oxygen ofmt.;
 89         
 
 NOTE: The infile '/home/u1407221/441s24/data/potato.data.txt' is:
       Filename=/home/u1407221/441s24/data/potato.data.txt,
       Owner Name=u1407221,Group Name=oda,
       Access Permission=-rw-r--r--,
       Last Modified=16Mar2024:11:18:53,
       File Size (bytes)=2037
 
 NOTE: 54 records were read from the infile '/home/u1407221/441s24/data/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       0.00 seconds
       system cpu time     0.00 seconds
       memory              762.84k
       OS Memory           32424.00k
       Timestamp           03/16/2024 05:51:58 PM
       Step Count                        67  Switch Count  2
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 90         proc freq data=fries;
 91              tables oxygen*temp*bact / norow nocol nopercent;
 92         
 
 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              3630.06k
       OS Memory           33712.00k
       Timestamp           03/16/2024 05:51:58 PM
       Step Count                        68  Switch Count  4
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 93         proc glm data=fries plots=none;
 94              title2 'Three-way ANOVA with proc glm';
 95              class bact temp oxygen;
 96              model rot=temp|bact|oxygen; /* All main effects and interactions */
 97              means temp|bact; /* Based on the tests */
 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: Means from the MEANS statement are not adjusted for other terms in the model.  For adjusted means, use the LSMEANS statement.
 NOTE: PROCEDURE GLM used (Total process time):
       real time           0.08 seconds
       user cpu time       0.08 seconds
       system cpu time     0.01 seconds
       memory              2378.34k
       OS Memory           34488.00k
       Timestamp           03/16/2024 05:51:58 PM
       Step Count                        69  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              976.75k
       OS Memory           33708.00k
       Timestamp           03/16/2024 05:51:58 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        
 153        /* Drop oxygen. Implicitly we are accepting H0. */
 154        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.12 seconds
       user cpu time       0.13 seconds
       system cpu time     0.00 seconds
       memory              2679.31k
       OS Memory           35008.00k
       Timestamp           03/16/2024 05:51:58 PM
       Step Count                        71  Switch Count  2
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 155        proc tabulate data=mashed;
 156             title2 'Two-way table of means from proc tabulate';
 157             class bact temp;
 158             var rot;
 159             table (temp all), (bact all) * (mean*rot);
 160        
 161        /* Two-way with proc glm, suppressing the lsmeans plots */
 162        ods exclude MeanPlot (persist) DiffPlot (persist);
 
 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       0.02 seconds
       system cpu time     0.01 seconds
       memory              10245.90k
       OS Memory           44756.00k
       Timestamp           03/16/2024 05:51:58 PM
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       Block Output Operations           1640
       
 
 163        proc glm data=mashed;
 164             title2 'Two-way ANOVA, ignoring oxygen level';
 165             class bact temp;
 166             model rot=temp|bact;
 167             lsmeans bact / pdiff tdiff adjust = tukey;
 168             lsmeans bact / pdiff tdiff adjust = bon;
 169             /* ODS output table name = My data table name (Backwards)*/
 170             ods output OverallANOVA = Overall
 171                        ModelANOVA   = TwoWay;
 172        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.
 173        
 
 NOTE: PROCEDURE GLM used (Total process time):
       real time           0.34 seconds
       user cpu time       0.19 seconds
       system cpu time     0.03 seconds
       memory              23199.25k
       OS Memory           54208.00k
       Timestamp           03/16/2024 05:51:58 PM
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       Involuntary Context Switches      0
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 174        proc print data=Overall;
 175             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              731.09k
       OS Memory           52648.00k
       Timestamp           03/16/2024 05:51:58 PM
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 176        proc print data=TwoWay;
 177        
 
 NOTE: There were 6 observations read from the data set WORK.TWOWAY.
 NOTE: PROCEDURE PRINT used (Total process time):
       real time           0.01 seconds
       user cpu time       0.02 seconds
       system cpu time     0.00 seconds
       memory              683.18k
       OS Memory           52648.00k
       Timestamp           03/16/2024 05:51:58 PM
       Step Count                        75  Switch Count  0
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 178        proc iml;
 NOTE: IML Ready
 179             title2 'Proportions of remaining variation';
 180             use overall;
 180      !                    read all into anova1;
 180      !                                          /* "all" means all cases */
 181             use TwoWay;
 181      !                    read all into anova2;
 182             print "Take a look at the matrices";
 183             print anova1;
 183      !                    print anova2;
 184             print "Proportion of remaining variation";
 185             NminusP = anova1[2,1];
 186             s1 = anova2[4,2];
 186      !                        F1 = anova2[4,5];
 186      !                                          /* Main effect for Temperature */
 187             s2 = anova2[5,2];
 187      !                        F2 = anova2[5,5];
 187      !                                          /* Main effect for Bacteria */
 188             s3 = anova2[6,2];
 188      !                        F3 = anova2[6,5];
 188      !                                          /* Interaction */
 189             Temperature  = s1*F1/(s1*F1 + NminusP);
 190             Bacteria     = s2*F2/(s2*F2 + NminusP);
 191             Temp_by_Bact = s3*F3/(s3*F3 + NminusP);
 192             print Temperature Bacteria Temp_by_Bact;
 193        
 194        
 195        /* Regression with cell means coding */
 196        
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.02 seconds
       user cpu time       0.03 seconds
       system cpu time     0.00 seconds
       memory              1104.43k
       OS Memory           52908.00k
       Timestamp           03/16/2024 05:51:58 PM
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 197        data baked;
 198             set mashed;
 199             /* Cell means coding for all 6 treatment combinations
 200                of temperature and bacteria type -- use with proc reg*/
 201             if temp=1 and bact=1 then mu11=1; else mu11=0;
 202             if temp=1 and bact=2 then mu12=1; else mu12=0;
 203             if temp=1 and bact=3 then mu13=1; else mu13=0;
 204             if temp=2 and bact=1 then mu21=1; else mu21=0;
 205             if temp=2 and bact=2 then mu22=1; else mu22=0;
 206             if temp=2 and bact=3 then mu23=1; else mu23=0;
 207             /* Combination variable for temperature and bacteria
 208                type -- use for contrasts with proc glm */
 209             combo = 10*temp+bact; /* 11 12 13 21 22 23 */
 210        
 211        /*
 212                       BACTERIA TYPE
 213        TEMP      1         2        3
 214        Cool    mu11      mu12      mu13
 215        Warm    mu21      mu22      mu23
 216        
 217        The test statement of proc reg uses variable names to stand for the
 218        corresponding regression coefficients. By naming the effect cell mean
 219        coding dummy variables the same as the population cell means, I can
 220        just state the null hypothesis. Isn't this a cute SAS trick? */
 221        
 
 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              1028.15k
       OS Memory           52908.00k
       Timestamp           03/16/2024 05:51:58 PM
       Step Count                        77  Switch Count  2
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       Block Output Operations           272
       
 
 222        proc reg  data = baked plots = none;
 223             title2 'Using the proc reg test statement and cell means coding';
 224             model rot = mu11--mu23 / noint;
 225             Overall:       test mu11=mu12=mu13=mu21=mu22=mu23;
 226             Temperature:   test mu11+mu12+mu13 = mu21+mu22+mu23;
 227             Bacteria:      test mu11+mu21 = mu12+mu22 = mu13+mu23;
 228             Bact_by_Temp1: test mu11-mu21 = mu12-mu22 = mu13-mu23;
 229             Bact_by_Temp2: test mu12-mu11 = mu22-mu21,
 230                                 mu13-mu12 = mu23-mu22;
 231        /* Bact_by_Temp1 checks equality of temperature effects.
 232           Bact_by_Temp2 checks parallel line segments. They are equivalent. */
 233        
 234        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.08 seconds
       user cpu time       0.08 seconds
       system cpu time     0.00 seconds
       memory              2524.87k
       OS Memory           54720.00k
       Timestamp           03/16/2024 05:51:58 PM
       Step Count                        78  Switch Count  2
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       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           104
       
 
 235        proc glm data = baked;
 236             title2 'Proc glm: Using contrasts on the combination variable';
 237             class combo;      /* 11 12 13  21 22 23 */
 238             model rot=combo;
 239             contrast 'Main Effect for Temperature'
 240                combo  1  1  1  -1 -1 -1;
 241             contrast 'Main Effect for Bacteria'
 242                combo  1 -1  0   1 -1  0,
 243                combo  0  1 -1   0  1 -1;
 244             contrast 'Temperature by Bacteria Interaction'
 245                combo  1 -1  0  -1  1  0,
 246                combo  0  1 -1   0 -1  1;
 247        
 248        /* Follow up the interaction and do some more exploration. The regression
 249           with cell means coding is easiest. The final product of several runs
 250           is shown below. For reference, here is the table of population means again.
 251        
 252                       BACTERIA TYPE
 253        TEMP      1         2        3
 254        Cool    mu11      mu12      mu13
 255        Warm    mu21      mu22      mu23                      */
 256        
 
 NOTE: PROCEDURE GLM used (Total process time):
       real time           0.26 seconds
       user cpu time       0.12 seconds
       system cpu time     0.01 seconds
       memory              4841.43k
       OS Memory           55484.00k
       Timestamp           03/16/2024 05:51:59 PM
       Step Count                        79  Switch Count  3
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       Voluntary Context Switches        678
       Involuntary Context Switches      1
       Block Input Operations            0
       Block Output Operations           968
       
 
 257        proc reg plots = none;
 258             title3 'Further exploration using cell means coding';
 259             model rot = mu11--mu23 / noint;
 260             /* Pairwise comparisons of marginal means for Bacteria Type */
 261             Bact1vs2: test mu11+mu21=mu12+mu22;
 262             Bact1vs3: test mu11+mu21=mu13+mu23;
 263             Bact2vs3: test mu12+mu22=mu13+mu23;
 264             /* Effect of temperature for each bacteria type */
 265             Temp_for_Bac1: test mu11=mu21;
 266             Temp_for_Bac2: test mu12=mu22;
 267             Temp_for_Bac3: test mu13=mu23;
 268             /* Effect of bacteria type for each temperature */
 269             Bact_for_CoolTemp: test mu11=mu12=mu13;
 270             Bact_for_WarmTemp: test mu21=mu22=mu23;
 271             /* Pairwise comparisons of bacteria types at warm temperature */
 272             Bact1vs2_for_WarmTemp: test mu21=mu22;
 273             Bact1vs3_for_WarmTemp: test mu21=mu23;
 274             Bact2vs3_for_WarmTemp: test mu22=mu23;
 275             /* Follow up the interaction with pairwise
 276                comparisons of temperature effects. */
 277             TempEffectBact1_vs_2: test mu11-mu21 = mu12-mu22;
 278             TempEffectBact1_vs_3: test mu11-mu21 = mu13-mu23;
 279             TempEffectBact2_vs_3: test mu12-mu22 = mu13-mu23;
 280         run;
 
 281        
 282        /* We have done a lot of tests. Concerned about buildup of Type I
 283        error? We can make ALL the tests into Scheffe follow-ups of the
 284        initial test for equality of the 6 cell means. The Scheffe family
 285        includes all COLLECTIONS of contrasts, not just all contrasts. */
 286        
 
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.18 seconds
       user cpu time       0.18 seconds
       system cpu time     0.00 seconds
       memory              2534.50k
       OS Memory           55232.00k
       Timestamp           03/16/2024 05:51:59 PM
       Step Count                        80  Switch Count  2
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       Page Reclaims                     298
       Page Swaps                        0
       Voluntary Context Switches        23
       Involuntary Context Switches      0
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       Block Output Operations           144
       
 
 287        proc iml;
 NOTE: IML Ready
 288             title3 'Table of critical values for all possible Scheffe tests';
 289             numdf = 5;
 289      !                   /* Numerator degrees of freedom for initial test */
 290             dendf =48;
 290      !                   /* Denominator degrees of freedom for initial test */
 291             alpha = 0.05;
 292             critval = finv(1-alpha,numdf,dendf);
 293             zero = {0 0};
 293      !                    S_table = repeat(zero,numdf,1);
 293      !                                                     /* Make empty matrix */
 294             /* Syntax is repeat(x,nrow,ncol) to get a matrix of repeated x matrices. */
 295             /* Label the columns */
 296             namz = {"Number of Contrasts in followup test"
 297                     "    Scheffe Critical Value"};
 297      !                                             mattrib S_table colname=namz;
 298             do i = 1 to numdf;
 299                s_table[i,1] = i;
 300                s_table[i,2] = numdf/i *  critval;
 301             end;
 302             print "Initial test has"  numdf " and " dendf "degrees of freedom."
 303                   "Using significance level alpha = " alpha;
 304             print s_table;
 305        
 306        
 307        quit;
 NOTE: Exiting IML.
 NOTE: PROCEDURE IML used (Total process time):
       real time           0.01 seconds
       user cpu time       0.02 seconds
       system cpu time     0.00 seconds
       memory              557.18k
       OS Memory           53412.00k
       Timestamp           03/16/2024 05:51:59 PM
       Step Count                        81  Switch Count  1
       Page Faults                       0
       Page Reclaims                     59
       Page Swaps                        0
       Voluntary Context Switches        11
       Involuntary Context Switches      0
       Block Input Operations            0
       Block Output Operations           8
       
 
 308        
 309        /*****************************************************************/
 310        
 311        
 312        
 313        
 314        
 315        
 316        
 317        OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 329