Analysis Using SAS 

For ease of understanding, recode the treatments  as follows:

Data Input:
For performing analysis, input the data in the following format. 

{Here we call the replications as blk, Treatment as: trt and yield as yld. It may, however, be noted that one can retain the same name or can code in any other fashion}.

 Prepare a SAS data file using

/*Creating the SAS Data set based on the data from a block design*/

data test;

input blk trt yld;

cards;

1      1      8.9

1      2      10.65

1      3      10.6

1      4      9.15

1      5      13.0

1      6      9.8

2      1      9.3

2      2      10.5

2      3      11.25

2      4      8.9

2      5      9.91

2      6      9.95

3      1      9.2

3      2      10.1

3      3      10.25

3      4      9.3

3      5     10.14

3      6      9.95

4      1      9.1

4      2      11.05

4      3      11.50

4      4      10.3

4      5      8.85

4      6      10.2

;

options mprint mlogic;

/***********************************************************************************/

/*From here, the testing Assumptions and analysis is started/

/************************************************************************************/

options nodate nonumber mprint mlogic; *option for deactivate the print date and page number;

/****************************************************************************/

/* Macro start is here, The Macros are called whenever needed */

%macro start;

%global loop deg var opt brln test1; /* Making global variable */

%let loop = 1;

%start1(test);/* Calling start1 macro with parameter SAS data set Name i.e. the nae given the Data section*/

%let loop = 2;

%anal(test); /*Calling anal macro for anlysis of data set*/

proc iml;

mm = &norm;

print mm;

run;

%if &norm = NNR or &test1 < 0.05 %then %do; %box(test);%start1(data1); /* calling Box macro for transformation*/

%if &norm = NNR or &test1 < 0.05 %then %skilling;%else %anal(data1);%end;

%mend start;

/*End of Macro start*/

/*************************************************************************************/

/*************************************************************************/

/* Macro Start1 is started. in this macro we perform the testing assumption and

Accordingly go for appropriate analysis */

%macro start1(par);

proc iml; use test; read all into temp;nc = ncol(temp);nc = char(nc);print nc;

call symput('deg',nc); /* puting no. of variable of data set in deg variable*/

%if &deg = 2 %then %let var = trt; %else %let var = blk trt; /*making the class variable for GLM*/

%t1(&par); /* calling the macro t1 with parameter par*/

proc iml; use nor; read all into pn; /*performing normality test*/

title "Shapiro Wilk's Test for Normality of Data";

Probability = pn;

if probability >= 0.05 then Interpretation = "Data is Normal at 5% level of Significance";

else Interpretation = "Data is Non-Normal at 5% level of Significance";

print probability,Interpretation;/* printing the value of normality test*/

title ' ' ;

%if &norm = NR %then %bart;

%else %levene;

%mend start1;

/* End of macro start1 */

/**************************************************************************/

/***********************************************************************************/

/*Macro t1 is written for the testing the normality of data. */

%macro t1(ts);

%global norm;    *Declaring a global variable norm which store normality status of data;

proc glm data = &ts  noprint;       /* Here, we call PROC glm to get the residuals of data

class &var;                                                based on the design             */

model yld = &var;                                

output out = err r = ss;        

run;                                             

proc means data = err noprint;

/*Calling PROC means to compute variance of residuals    */

class trt;

output out = mn  var(ss)= var;

run;

proc univariate data = err normal noprint;/*Performing test for normality of residuals*/

var ss;output out=nor probn=pnor;run;

proc iml;use nor; read all into pn; /* Using the global variable norm to store normality */

if pn > 0.05 then call symput('norm','NR');/*status of data -- NR for Normal and NNR for */

else call symput('norm','NNR');

mm = &nnr;

print mm;/*Non-normal                                           */

%mend t1;

/* End of macro t1 */

/**************************************************************************************/

/*************************************************************************************/

/* Macro Bart is written for the testing the homogeneity of variances */

%macro Bart;

/*%global evar;*/

title "Bartlett's Test for Homogeneity of Variances";

proc iml;use mn; read all into m1; /* use variances of residual variance putting it in m1 variable*/

a =m1[2:nrow(m1),ncol(m1)-1:ncol(m1)];/*from m1 we extracting variances and number of observations */

v =0;ct = 0;nchi = 0;St = 0;

do i = 1 to nrow(a);           /* computing pooled variance */

            St = St + (a[i,1]-1)*a[i,2];

            v = v + (a[i,1]-1);

            ct = ct + 1/(a[i,1]-1);

end;S = St/v;

dchi = (1 + (1/(3*(nrow(a)-1)))*(ct-(1/v))); /*computing denominator of Bartlett's chi-square statistic*/

do i = 1 to nrow(a);nchi = nchi + (a[i,1]-1)*(log(S/a[i,2])); end;

chi = nchi/dchi;

if chi < 0 then chi = 0;

probability = 1 - probchi(chi,(nrow(a)-1));/*computinf chi value and prob.*/

df = (nrow(a)-1);print probability chi df S; /* printing chi value, prob and degee of freedom*/

if probability >= 0.05 then Interpretation = "Data is Homogeneous at 5% level of Significance";

else Interpretation = "Data is Heterogeneous at 5% level of Significance";

print Interpretation; /* testing and printing interpretation/

pb = char(probability);

call symput('test1',pb); /*putting probability to a variable test1 for further use*/

title ' ';

%mend bart;

/* End of macro Bart */

/***********************************************************************************/

/*****************************************************************************/

/* Macro Levene for testing the homogeneity of variances when data is non normal*/

%macro levene;

title ' Levene Test for Homogeneity of variances';

proc means data = err noprint; /* computing median of the residuals*/

output out = media mean = mn;

class trt;var ss;run;

proc sort data = err; /* Sorting the residual by treatment*/

by trt;run;

proc iml; use media; read all into lev; /* Reading the residuals in a matrix*/

md = lev[2:nrow(lev),];

use err;read all into error;

s = 1;

do i = 1 to nrow(error);

            if error[i,2] = s then di = di//(error[i,ncol(error)]-md[s,ncol(md)]);

            else do; s = s + 1; i = i-1;end;

end;

if "&opt" = "mean" then trt = error[,2]||di##2;

else trt = error[,2]||abs(di);

create  res from trt[colname = {trt di}];append from trt;

quit;

proc glm data = res outstat = problev noprint;

class trt;

model di = trt;

run;

proc iml;use problev; read all into pl;

Probability = pl[2,ncol(pl)];

if probability >= 0.05 then Interpretation = "Data is Homogeneous at 5% level of Significance";

else Interpretation = "Data is Heterogeneous at 5% level of Significance";

print probability, Interpretation;

pb = char(probability);

call symput('test1',pb);

title ' ';

%mend levene;

/* End of macro Levene */

/************************************************************************/

/**********************************************************************************/

/* Macro Box for transformation of observations*/

%macro Box(gh);

proc iml;

use &gh; read all into box; /*using the SAS data set*/

z1 = any(box=0); /*checking for null observation*/

if z1 = 1 then box=box[,1:ncol(box)-1]||(box[,ncol(box)]+ 0.01);/*adding 0.01 to each observation*/

gm = 0;s  = 1/nrow(box);

do i = 1 to nrow(box);gm = gm + log(box[i,ncol(box)]);end;

gm=gm*(s);gm = exp(gm); /*computing Geometric mean*/

if &deg = 2 then x = design(box[,1]);/*making design matrix*/

else x = design(box[,1])||design(box[,2]);

i = -1000;sse =0;

sp = 9999999999999999999999999999;

do j = -10 to 10 by 0.01;

            if i = 0 then ny = gm#(log(box[,ncol(box)])); /*transforming observations*/

            else ny = ((box[,ncol(box)]##(i/100))-1)/((i/100)*(gm**((i/100)-1)));

            bh = ginv(x`*x)*x`*ny; /*computing parameters*/

            err = ny - x*bh;

            err = err##2; sse = err[+]; /*computing Error sum of squares*/

            if sp > sse then lamda = i/100;  /*testing  minimum SSE for Lambda value */

            sp = sse;se = se//sse;  /*making the array of all SSE*/

            l =l//(i/100);i = i+1;

end;

mn = min(se); /*taking minimum value of SSE */

print lamda; /*printing Lambda*/

t2 = box[,1:ncol(box)-1]||box[,ncol(box)]##lamda; /* Transforming the data */

create data1 from t2[colname ={&var yld}];append from t2; /* Creating a SAS data Set*/

%mend box;

/* End of Macro Box*/

/**********************************************************************************/

/**********************************************************************************/

/* Macro anal for analysis of experimental data. */

%macro anal(dat);/* dat is name of dataset*/

title "  ";

proc glm data = &dat; /*  data = mane which is in dat variable **/

class &var;  /*input variable is assigned in var*/

model yld = &var;

run;

%mend anal;

/* end of macro anal */

/*****************************************************************************/

/******************************************************************************/

/*Macro skillings is for the performing Skillings and Mack non-parametric test*/

%macro skilling;

title 'Skilling Macs Non-parametric procedure for testing equality of means';

%if &deg = 3 %then %do; /* checking for design */

proc rank data = test out = er; /*Arranging the  yield observation in ascending order*/

by blk;var yld;run;                                             /* by Block variable */

proc iml;use er; read all into s; /*Using sorted variable */

RT = j(max(S[,1]),max(S[,2]),.);T = j(max(S[,1]),max(S[,2]),.);

ST = j(max(S[,1]),max(S[,2]),1); /* Creating 3 matrix according to need */

do i = 1 to nrow(s);RT[s[i,1],s[i,2]]=s[i,3];T[s[i,1],s[i,2]]=s[i,2];end;

DO I = 1 TO nrow(rt);do j = 1 to ncol(rt);if t[i,j] = . then st[i,j] = 0;end;end;

k = st[,+];Ai = 0;

do j = 1 to ncol(rt);do i = 1 to nrow(rt);

if rt[i,j] <> . then Ai = Ai + (((12/(k[i]+1))**(1/2))*((rt[i,j]-(k[i]+1)/2)));end;

As = as//ai;ai = 0;end;

ds = 0;sigma = j(ncol(t),ncol(t),0);

do i = 1 to ncol(t); do j = 1 to ncol(t);do p = 1 to nrow(t);

ti = any(t[p,]=i);tt = any(t[p,]=j);

if ti = 1 && tt = 1 then sigma[i,j] = sigma[i,j]+1;

end;end;end;

sigma = sigma#-1;

do i = 1 to ncol(t);sigma[i,i] = (sigma[i,+]-sigma[i,i])#-1;end;

df=round(trace(ginv(sigma)*sigma));stat = as`*ginv(sigma)*as;

prob = 1 - probchi(stat,df);

print stat prob df ; 

quit;%end;

%else %do;

proc npar1way wilcoxon data=test;  /* performing Krushkal Walis test*/

      class trt;

      var yld;

 run; %end;

%mend skilling;

/*end of macro skilling */

/*****************************************************************************/

/************************************************************************************/

%start;  

 Data File
  Result File

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