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SAS FOR STATISTICAL PROCEDURES

Rajender Parsad

I.A.S.R.I., Library Avenue, New Delhi-110 012

rajender@iasri.res.in

1. Introduction

SAS (Statistical Analysis System) software is comprehensive software which deals with many

problems related to Statistical analysis, Spreadsheet, Data Creation, Graphics, etc. It is a layered,

multivendor architecture. Regardless of the difference in hardware, operating systems, etc., the

SAS applications look the same and produce the same results. The three components of the SAS

System are Host, Portable Applications and Data. Host provides all the required interfaces

between the SAS system and the operating environment. Functionalities and applications reside

in Portable component and the user supplies the Data. We, in this course will be dealing with the

software related to perform statistical analysis of data.

Windows of SAS

1. Program Editor : All the instructions are given here.

2. Log : Displays SAS statements submitted for execution and messages

3. Output : Gives the output generated

Rules for SAS Statements

1. SAS program communicates with computer by the SAS statements.

2. Each statement of SAS program must end with semicolon (;).

3. Each program must end with run statement.

4. Statements can be started from any column.

5. One can use upper case letters, lower case letters or the combination of the two.

Basic Sections of SAS Program

1. DATA section

2. CARDS section

3. PROCEDURE section

Data Section

We shall discuss some facts regarding data before we give the syntax for this section.

Data value: A single unit of information, such as name of the specie to which the tree belongs,

height of one tree, etc.

Variable: A set of values that describe a specific data characteristic e.g. diameters of all trees in

a group. The variable can have a name upto a maximum of 8 characters and must begin with a

letter or underscore. Variables are of two types:

Character Variable: It is a combination of letters of alphabet, numbers and special characters

or symbols.

SAS for Statistical Procedures

Numeric Variable: It consists of numbers with or without decimal points and with + or -ve

signs.

Observation: A set of data values for the same item i.e. all measurement on a tree.

Data section starts with Data statements as

DATA NAME (it has to be supplied by the user);

Input Statements

Input statements are part of data section. This statement provides the SAS system the name of

the variables with the format, if it is formatted.

List Directed Input

Data are read in the order of variables given in input statement.

Data values are separated by one or more spaces.

Missing values are represented by period (.).

Character values are followed by $ (dollar sign).

Example

Data A;

INPUT ID SEX $ AGE HEIGHT WEIGHT;

CARDS;

1 M 23 68 155

2 F . 61 102

3. M 55 70 202

;

Column Input

Starting column for the variable can be indicated in the input statements for example:

INPUT ID 1-3 SEX $ 4 HEIGHT 5-6 WEIGHT 7-11;

CARDS;

001M68155.5

2F61 99

3M53 33.5

;

Alternatively, starting column of the variable can be indicated along with its length as

INPUT @ 1 ID 3.

@ 4 SEX $ 1.

@ 9 AGE 2.

@ 11 HEIGHT 2.

@ 16 V_DATE MMDDYY 6.

;

Reading More than One Line Per Observation for One Record of Input Variables

SAS for Statistical Procedures

INPUT # 1 ID 1-3 AGE 5-6 HEIGHT 10-11

# 2 SBP 5-7 DBP 8-10;

CARDS;

001 56 72

140 80

;

Reading the Variable More than Once

Suppose id variable is read from six columns in which state code is given in last two columns of

id variable for example:

INPUT @ 1 ID 6. @ 5 STATE 2.;

OR

INPUT ID 1-6 STATE 5-6;

Formatted Lists

DATA B;

INPUT ID @1(X1-X2)(1.)

@4(Y1-Y2)(3.);

CARDS;

11 563789

22 567987

;

PROC PRINT;

RUN;

Output

Obs. ID x1 x2 y1 y2

1 11 1 1 563 789

2 22 2 2 567 987

DATA C;

INPUT X Y Z @;

CARDS;

1 1 1 2 2 2 5 5 5 6 6 6

1 2 3 4 5 6 3 3 3 4 4 4

;

PROC PRINT;

RUN;

Output

Obs. X Y Z

1 1 1 1

2 1 2 3

DATA D;

INPUT X Y Z @@;

SAS for Statistical Procedures

CARDS;

1 1 1 2 2 2 5 5 5 6 6 6

1 2 3 4 5 6 3 3 3 4 4 4

;

PROC PRINT;

RUN;

Output:

Obs. X Y Z

1 1 1 1

2 2 2 2

3 5 5 5

4 6 6 6

5 1 2 3

6 4 5 6

7 3 3 3

8 4 4 4 DATA FILES

SAS System Can Read and Write

A. Simple ASCII files are read with input and infile statements

B. Output Data files

Creation of SAS Data Set

DATA EX1;

INPUT GROUP $ X Y Z;

CARDS;

T1 12 17 19

T2 23 56 45

T3 19 28 12

T4 22 23 36

T5 34 23 56

;

Creation of SAS File From An External (ASCII) File

DATA EX2;

INFILE 'B:MYDATA';

INPUT GROUP $ X Y Z;

OR

DATA EX2A;

FILENAME ABC 'B:MYDATA';

INFILE ABC;

INPUT GROUP $ X Y Z;

;

Creation of A SAS Data Set and An Output ASCII File Using an External File

DATA EX3;

FILENAME IN 'C:MYDATA';

SAS for Statistical Procedures

FILENAME OUT 'A:NEWDATA';

INFILE IN;

FILE OUT;

INPUT GROUP $ X Y Z;

TOTAL =SUM (X+Y+Z);

PUT GROUP $ 1-10 @12 (X Y Z TOTAL)(5.);

RUN;

This above program reads raw data file from 'C: MYDATA', and creates a new variable TOTAL

and writes output in the file 'A: NEWDATA’.

Creation of SAS File from an External (*.csv) File

data EX4;

infile'C:\Users\Admn\Desktop\sscnars.csv' dlm=',' ;

/*give the exact path of the file, file should not have column headings*/

input sn loc $ year season $ crop $ rep trt gyield syield return kcal; /*give

the variables in ordered list in the file*/

/*if we have the first row as names of the columns then we can write in the above statement

firstobs=2 so that data is read from row 2 onwards*/

biomass=gyield+syield; /*generates a new variable*/

proc print data=EX4;

run;

Note: To create a SAS File from a *.txt file, only change csv to txt and define delimiter as per

file created.

Creation of SAS File from an External (*.xls) File

Note: it is always better to copy the name of the variables as comment line before Proc Import.

/* name of the variables in Excel File provided the first row contains variable name*/

proc import datafile = 'C:\Users\Desktop\DATA_EXERCISE\descriptive_stats.xls'

/*give the exact path of the file*/

out = descriptive_stats replace; /*give output file name*/

proc print;

run;

If we want to make some transformations, then we may use the following statements:

data a1;

set descriptive_stats;

x = fs45+fw;

run;

Here proc import allows the SAS user to import data from an EXCEL spreadsheet into SAS.

The datafile statement provides the reference location of the file. The out statement is used to

name the SAS data set that has been created by the import procedure. Print procedure has been

utilized to view the contents of the SAS data set descriptive_stats. When we run above codes

we obtain the output which will same as shown above because we are using the same data.

SAS for Statistical Procedures

Creating a Permanent SAS Data Set

LIBNAME XYZ 'C:\SASDATA';

DATA XYZ.EXAMPLE;

INPUT GROUP $ X Y Z;

CARDS;

.....

.....

.....

RUN;

This program reads data following the cards statement and creates a permanent SAS data set in a

subdirectory named \SASDATA on the C: drive.

Using Permanent SAS File

LIBNAME XYZ 'C:\SASDATA';

PROC MEANS DATA=XYZ.EXAMPLE;

RUN;

TITLES

One can enter upto 10 titles at the top of output using TITLE statement in your procedure.

PROC PRINT;

TITLE ‘HEIGHT-DIA STUDY’;

TITLE3 ‘1999 STATISTICS’;

RUN;

Comment cards can be added to the SAS program using

/* COMMENTS */;

FOOTNOTES

One can enter upto 10 footnotes at the bottom of your output.

PROC PRINT DATA=DIAHT;

FOOTNOTE ‘1999’;

FOOTNOTE5 ‘STUDY RESULTS’;

RUN;

For obtaining output as RTF file, use the following statements

Ods rtf file=’xyz.rtf’ style =journal;

Ods rtf close;

For obtaining output as PDF/HTML file, replace rtf with pdf or html in the above statements.

If we want to get the output in continuos format, then we may use

Ods rtf file=’xyz.rtf’ style =journal bodytitle startpage=no;

LABELLING THE VARIABLES

Data dose;

title ‘yield with factors N P K’;

input N P K Yield;

SAS for Statistical Procedures

Label N = “Nitrogen”;

Label P = “ Phosphorus”;

Label K = “ Potassium”;

cards;

...

...

...

;

Proc print;

run;

We can define the linesize in the output using statement OPTIONS. For example, if we wish

that the output should have the linesize (number of columns in a line) is 72 use Options linesize

=72; in the beginning.

2. Statistical Procedure

SAS/STAT has many capabilities using different procedures with many options. There are a

total of 73 PROCS in SAS/STAT. SAS/STAT is capable of performing a wide range of

statistical analysis that includes:

1. Elementary / Basic Statistics

2. Graphs/Plots

3. Regression and Correlation Analysis

4. Analysis of Variance

5. Experimental Data Analysis

6. Multivariate Analysis

7. Principal Component Analysis

8. Discriminant Analysis

9. Cluster Analysis

10. Survey Data Analysis

11. Mixed model analysis

12. Variance Components Estimation

13. Probit Analysis

and many more…

A brief on SAS/STAT Procedures is available at

http://support.sas.com/rnd/app/da/stat/procedures/Procedures.html

Example 2.1: To Calculate the Means and Standard Deviation:

DATA TESTMEAN;

INPUT GROUP $ X Y Z;

CARDS;

CONTROL 12 17 19

TREAT1 23 25 29

TREAT2 19 18 16

TREAT3 22 24 29

CONTROL 13 16 17

TREAT1 20 24 28

TREAT2 16 19 15

SAS for Statistical Procedures

TREAT3 24 26 30

CONTROL 14 19 21

TREAT1 23 25 29

TREAT2 18 19 17

TREAT3 23 25 30

;

PROC MEANS;

VAR X Y Z;

RUN;

The default output displays mean, standard deviation, minimum value, maximum value of the

desired variable. We can choose the required statistics from the options of PROC MEANS. For

example, if we require mean, standard deviation, median, coefficient of variation, coefficient of

skewness, coefficient of kurtosis, etc., then we can write

PROC MEANS mean std median cv skewness kurtosis;

VAR X Y Z;

RUN;

The default output is 6 decimal places, desired number of decimal places can be defined by

using option maxdec=…. For example, for an output with three decimal places, we may write

PROC MEANS mean std median cv skewness kurtosis maxdec=3;

VAR X Y Z;

RUN;

For obtaining means group wise use, first sort the data by groups using

Proc sort;

By group;

Run;

And then make use of the following

PROC MEANS;

VAR X Y Z;

by group;

RUN;

Or alternatively, me may use

PROC MEANS;

CLASS GROUP;

VAR X Y Z;

RUN;

For obtaining descriptive statistics for a given data one can use PROC SUMMARY. In the above

example, if one wants to obtain mean standard deviation, coefficient of variation, coefficient of

skewness and kurtosis, then one may utilize the following:

PROC SUMMARY PRINT MEAN STD CV SKEWNESS KURTOSIS;

CLASS GROUP;

SAS for Statistical Procedures

VAR X Y Z;

RUN;

Most of the Statistical Procedures require that the data should be normally distributed. For

testing the normality of data, PROC UNIVARIATE may be utilized.

PROC UNIVARIATE NORMAL;

VAR X Y Z;

RUN;

If different plots are required then, one may use:

PROC UNIVARIATE DATA=TEST NORMAL PLOT;

/*plot option displays stem-leaf, boxplot & Normal prob plot*/

VAR X Y Z;

/*creates side by side BOX-PLOT group-wise. To use this option first sort the file on by

variable*/

BY GROUP;

HISTOGRAM/KERNEL NORMAL; /*displays kernel density along with normal curve*/

PROBPLOT; /*plots probability plot*/

QQPLOT X/NORMAL SQUARE; /*plot quantile-quantile QQ-plot*/

CDFPLOT X/NORMAL; /*plots CDF plot*/

/*plots pp plot which compares the empirical cumulative distribution function (ecdf) of a

variable with a specified theoretical cumulative distribution function. The beta, exponential,

gamma, lognormal, normal, and Weibull distributions are available in both statements.*/

PPPLOT X/NORMAL;

RUN;

Example 2.2: To Create Frequency Tables

DATA TESTFREQ;

INPUT AGE $ ECG CHD $ CAT $ WT; CARDS;

<55 0 YES YES 1

<55 0 YES YES 17

<55 0 NO YES 7

<55 1 YES NO 257

<55 1 YES YES 3

<55 1 YES NO 7

<55 1 NO YES 1

55+ 0 YES YES 9

55+ 0 YES NO 15

55+ 0 NO YES 30

55+ 1 NO NO 107

55+ 1 YES YES 14

55+ 1 YES NO 5

55+ 1 NO YES 44

55+ 1 NO NO 27

;

PROC FREQ DATA=TESTFREQ;

SAS for Statistical Procedures

TABLES AGE*ECG/MISSING CHISQ;

TABLES AGE*CAT/LIST;

RUN:

SCATTER PLOT

PROC PLOT DATA = DIAHT;

PLOT HT*DIA = ‘*’;

/*HT=VERTICAL AXIS DIA = HORIZONTAL AXIS.*/

RUN;

CHART

PROC CHART DATA = DIAHT;

VBAR HT;

RUN;

PROC CHART DATA = DIAHT;

HBAR DIA;

RUN;

PROC CHART DATA = DIAHT;

PIE HT;

RUN;

Example 2.3: To Create A Permanent SAS DATASET and use that for Regression

LIBNAME FILEX 'C:\SAS\RPLIB';

DATA FILEX.RP;

INPUT X1-X5;

CARDS;

1 0 0 0 5.2

.75 .25 0 0 7.2

.75 0 .25 0 5.8

.5 .25 .25 0 6.3

.75 0 0 .25 5.5

.5 0 .25 .25 5.7

.5 .25 0 .25 5.8

.25 .25 .25 .25 5.7

;

RUN;

LIBNAME FILEX 'C:\SAS\RPLIB';

PROC REG DATA=FILEX.RP;

MODEL X5 = X1 X2/P;

MODEL X5 = X1 X2 X3 X4 / SELECTION = STEPWISE;

TEST: TEST X1-X2=0;

RUN;

SAS for Statistical Procedures

Various other commonly used PROC Statements are PROC ANOVA, PROC GLM; PROC

CORR; PROC NESTED; PROC MIXED; PROC RSREG; PROC IML; PROC PRINCOMP;

PROC VARCOMP; PROC FACTOR; PROC CANCORR; PROC DISCRIM, etc. Some of these

are described in the sequel.

PROC TTEST is the procedure that is used for comparing the mean of a given sample. This

PROC is also used for compares the means of two independent samples. The paired observations

t test compares the mean of the differences in the observations to a given number. The

underlying assumption of the t test in all three cases is that the observations are random samples

drawn from normally distributed populations. This assumption can be checked using the

UNIVARIATE procedure; if the normality assumptions for the t test are not satisfied, one should

analyze the data using the NPAR1WAY procedure. PROC TTEST computes the group

comparison t statistic based on the assumption that the variances of the two groups are equal. It

also computes an approximate t based on the assumption that the variances are unequal (the

Behrens-Fisher problem). The following statements are available in PROC TTEST.

PROC TTEST <options>;

CLASS variable;

PAIRED variables;

BY variables;

VAR variables;

FREQ Variables;

WEIGHT variable;

No statement can be used more than once. There is no restriction on the order of the statements

after the PROC statement. The following options can appear in the PROC TTEST statement.

ALPHA= p: option specifies that confidence intervals are to be 100(1-p)% confidence intervals,

where 0<p<1. By default, PROC TTEST uses ALPHA=0.05. If p is 0 or less, or 1 or more, an

error message is printed.

COCHRAN: option requests the Cochran and Cox approximation of the probability level of the

approximate t statistic for the unequal variances situation.

H0=m: option requests tests against m instead of 0 in all three situations (one-sample, two-

sample, and paired observation t tests). By default, PROC TTEST uses H0=0.

A CLASS statement giving the name of the classification (or grouping) variable must

accompany the PROC TTEST statement in the two independent sample cases. It should be

omitted for the one sample or paired comparison situations. The class variable must have two,

and only two, levels. PROC TTEST divides the observations into the two groups for the t test

using the levels of this variable. One can use either a numeric or a character variable in the

CLASS statement.

In the statement PAIRED PairLists, the PairLists in the PAIRED statement identifies the

variables to be compared in paired comparisons. You can use one or more PairLists. Variables

or lists of variables are separated by an asterisk (*) or a colon (:). Examples of the use of the

asterisk and the colon are shown in the following table.

The PAIRED Statements Comparisons made

PAIRED A*B; A-B

SAS for Statistical Procedures

PAIRED A*B C*D; A-B and C-D

PAIRED (A B)*(C B); A-C, A-B and B-C

PAIRED (A1-A2)*(B1-B2); A1-B1, A1-B2, A2-B1 and A2-B2

PAIRED (A1-A2):(B1-B2); A1-B1 and A2-B2

PROC ANOVA performs analysis of variance for balanced data only from a wide variety of

experimental designs whereas PROC GLM can analyze both balanced and unbalanced data. As

ANOVA takes into account the special features of a balanced design, it is faster and uses less

storage than PROC GLM for balanced data. The basic syntax of the ANOVA procedure is as

given:

PROC ANOVA < Options>;

CLASS variables;

MODEL dependents = independent variables (or effects)/options;

MEANS effects/options;

ABSORB variables;

FREQ variables;

TEST H = effects E = effect;

MANOVA H = effects E = effect;

M = equations/options;

REPEATED factor - name levels / options;

By variables;

The PROC ANOVA, CLASS and MODEL statements are must. The other statements are

optional. The CLASS statement defines the variables for classification (numeric or character

variables - maximum characters =16).

The MODEL statement names the dependent variables and independent variables or effects. If

no effects are specified in the MODEL statement, ANOVA fits only the intercept. Included in

the ANOVA output are F-tests of all effects in the MODEL statement. All of these F-tests use

residual mean squares as the error term. The MEANS statement produces tables of the means

corresponding to the list of effects. Among the options available in the MEANS statement are

several multiple comparison procedures viz. Least Significant Difference (LSD), Duncan’s New

multiple - range test (DUNCAN), Waller - Duncan (WALLER) test, Tukey’s Honest Significant

Difference (TUKEY). The LSD, DUNCAN and TUKEY options takes level of significance

ALPHA = 5% unless ALPHA = options is specified. Only ALPHA = 1%, 5% and 10% are

allowed with the Duncan’s test. 95% Confidence intervals about means can be obtained using

CLM option under MEANS statement.

The TEST statement tests for the effects where the residual mean square is not the appropriate

term such as main - plot effects in split - plot experiment. There can be multiple MEANS and

TEST statements (as well as in PROC GLM), but only one MODEL statement preceded by RUN

statement. The ABSORB statement implements the technique of absorption, which saves time

and reduces storage requirements for certain type of models. FREQ statement is used when each

observation in a data set represents ‘n’ observations, where n is the value of FREQ variable. The

MANOVA statement is used for implementing multivariate analysis of variance. The

SAS for Statistical Procedures

REPEATED statement is useful for analyzing repeated measurement designs and the BY

statement specifies that separate analysis are performed on observations in groups defined by the

BY variables.

PROC GLM for analysis of variance is similar to using PROC ANOVA. The statements listed

for PROC ANOVA are also used for PROC GLM. In addition; the following more statements

can be used with PROC GLM:

CONTRAST ‘label’ effect name< ... effect coefficients > </options>;

ESTIMATE ‘label’ effect name< ... effect coefficients > </options>;

ID variables;

LSMEANS effects < / options >;

OUTPUT < OUT = SAS-data-set>keyword=names< ... keyword = names>;

RANDOM effects < / options >;

WEIGHT variables

Multiple comparisons as used in the options under MEANS statement are useful when there are

no particular comparisons of special interest. But there do occur situations where preplanned

comparisons are required to be made. Using the CONTRAST, LSMEANS statement, we can

test specific hypothesis regarding pre - planned comparisons. The basic form of the CONTRAST

statement is as described above, where label is a character string used for labeling output, effect

name is class variable (which is independent) and effect - coefficients is a list of numbers that

specifies the linear combination parameters in the null hypothesis. The contrast is a linear

function such that the elements of the coefficient vector sum to 0 for each effect. While using the

CONTRAST statements, following points should be kept in mind.

How many levels (classes) are there for that effect. If there are more levels of that effect in the

data than the number of coefficients specified in the CONTRAST statement, the PROC GLM

adds trailing zeros. Suppose there are 5 treatments in a completely randomized design denoted

as T1, T2, T3, T4, T5 and null hypothesis to be tested is

H

o: T2+T3 = 2T1 or 2T1+T2+T3 = 0

Suppose in the data treatments are classified using TRT as class variable, then effect name is

TRT CONTRAST ‘TIVS 2&3’ TRT 2 1 1 0 0; Suppose last 2 zeros are not given, the

trailing zeros can be added automatically. The use of this statement gives a sum of squares with

1 degree of freedom (d.f.) and F-value against error as residual mean squares until specified. The

name or label of the contrast must be 20 characters or less.

The available CONTRAST statement options are

E: prints the entire vector of coefficients in the linear function, i.e., contrast.

E = effect: specifies an effect in the model that can be used as an error term

ETYPE = n: specifies the types (1, 2, 3 or 4) of the E effect.

Multiple degrees of freedom contrasts can be specified by repeating the effect name and

coefficients as needed separated by commas. Thus the statement for the above example

CONTRAST ‘All’ TRT 2 1 1 0 0, TRT 0 1 -1 0 0;

SAS for Statistical Procedures

This statement produces two d.f. sum of squares due to both the contrasts. This feature can be

used to obtain partial sums of squares for effects through the reduction principle, using sums of

squares from multiple degrees of freedom contrasts that include and exclude the desired

contrasts. Although only t1 linearly independent contrasts exists for t classes, any number of

contrasts can be specified.

The ESTIMATE statement can be used to estimate linear functions of parameters that may or

may not be obtained by using CONTRAST or LSMEANS statement. For the specification of the

statement only word CONTRAST is to be replaced by ESTIMATE in CONTRAST statement.

Fractions in effects coefficients can be avoided by using DIVISOR = Common denominator as

an option. This statement provides the value of an estimate, a standard error and a t-statistic for

testing whether the estimate is significantly different from zero.

The LSMEANS statement produces the least square estimates of CLASS variable means i.e.

adjusted means. For one-way structure, there are simply the ordinary means. The least squares

means for the five treatments for all dependent variables in the model statement can be obtained

using the statement.

LSMEANS TRT / options;

Various options available with this statement are:

STDERR: gives the standard errors of each of the estimated least square mean and the t-statistic

for a test of hypothesis that the mean is zero.

PDIFF: Prints the p - values for the tests of equality of all pairs of CLASS means.

SINGULAR: tunes the estimability checking. The options E, E=, E-TYPE = are similar as

discussed under CONTRAST statement.

Adjust=T: gives the probabilities of significance of pairwise comparisons based on T-test.

Adjust=Tukey: gives the probabilities of significance of pairwise comparisons based on Tukey's

test

Lines: gives the letters on treatments showing significant and non-significant groups

When the predicted values are requested as a MODEL statement option, values of variable

specified in the ID statement are printed for identification besides each observed, predicted and

residual value. The OUTPUT statement produces an output data set that contains the original

data set values alongwith the predicted and residual values.

Besides other options in PROC GLM under MODEL statement we can give the option: 1.

solution 2. xpx (=X`X) 3 . I (g-inverse)

PROC GLM recognizes different theoretical approaches to ANOVA by providing four types of

sums of squares and associated statistics. The four types of sums of squares in PROC GLM are

called Type I, Type II, Type III and Type IV.

SAS for Statistical Procedures

The Type I sums of squares are the classical sequential sums of squares obtained by adding the

terms to the model in some logical sequence. The sum of squares for each class of effects is

adjusted for only those effects that precede it in the model. Thus the sums of squares and their

expectations are dependent on the order in which the model is specified.

The Type II, III and IV are ‘partial sums of squares' in the sense that each is adjusted for all other

classes of the effects in the model, but each is adjusted according to different rules. One general

rule applies to all three types: the estimable functions that generate the sums of squares for one

class of squares will not involve any other classes of effects except those that “contain” the class

of effects in question.

For example, the estimable functions that generate SS (AB) in a three- factor factorial will have

zero coefficients on main effects and the (A C) and (B C) interaction effects. They will

contain non-zero coefficient on the (A B C) interaction effects, because A B C

interaction “contains” A B interaction.

Type II, III and IV sums of squares differ from each other in how the coefficients are determined

for the classes of effects that do not have zero coefficients - those that contain the class of effects

in question. The estimable functions for the Type II sum of squares impose no restriction on the

values of the non-zero coefficients on the remaining effects; they are allowed to take whatever

values result from the computations adjusting for effects that are required to have zero

coefficients. Thus, the coefficients on the higher-order interaction effects and higher level

nesting effects are functions of the number of observations in the data. In general, the Type II

sums of squares do not possess of equitable distribution property and orthogonality characteristic

of balanced data.

The Type III and IV sums of squares differ from the Type II sums of squares in the sense that the

coefficients on the higher order interaction or nested effects that contain the effects in question

are also adjusted so as to satisfy either the orthogonality condition (Type III) or the equitable

distribution property (Type IV).

The coefficients on these effects are no longer functions of the nij and consequently, are the same

for all designs with the same general form of estimable functions. If there are no empty cells (no

nij = 0) both conditions can be satisfied at the same time and Type III and Type IV sums of

squares are equal. The hypothesis being tested is the same as when the data is balanced.

When there are empty cells, the hypotheses being tested by the Type III and Type IV sums of

squares may differ. The Type III criterion of orthogonality reproduces the same hypotheses one

obtains if effects are assumed to add to zero. When there are empty cells this is modified to “the

effects that are present are assumed to be zero”. The Type IV hypotheses utilize balanced

subsets of non-empty cells and may not be unique. For a 2x3 factorial for illustration purpose

adding the terms to the model in the order A, B, AB various types sums of squares can be

explained as follows:

Effect Type I Type II Type III Type IV

General Mean R() R()

A R(A/ ) R(A/ ,B) R(A/,B,AB)

SAS for Statistical Procedures

B R(B/,A) R(B/,A) R(B/,A,AB)

A*B R(A*B/ ,A,B) R(A*B/,A,B) R(AB/,A,B)

R (A/) is sum of squares adjusted for , and so on.

Thus in brief the four sets of sums of squares Type I, II, III & IV can be thought of respectively

as sequential, each - after-all others, -restrictions and hypotheses.

There is a relationship between the four types of sums of squares and four types of data

structures (balanced and orthogonal, unbalanced and orthogonal, unbalanced and non-orthogonal

(all cells filled), unbalanced and non-orthogonal (empty cells)). For illustration, let nIJ denote

the number of observations in level I of factor A and level j of factor B. Following table

explains the relationship in data structures and Types of sums of squares in a two-way classified

data.

Data Structure Type

1 2 3 4

Effect Equal nIJ Proportionate Disproportionate Empty Cell

nIJ non-zero nIJ

A I=II=III=IV I=II,III=IV III=IV

B I=II=III=IV I=II,III=IV I=II,III=IV I=II

A*B I=II=III=IV I=II=III=IV I=II=III=IV I=II=III=IV

In general,

I=II=III=IV (balanced data); II=III=IV (no interaction models)

I=II, III=IV (orthogonal data); III=IV (all cells filled data).

Proper Error terms: In general F-tests of hypotheses in ANOVA use the residual mean squares

in other terms are to be used as error terms. For such situations PROC GLM provides the TEST

statement which is identical to the test statement available in PROC ANOVA. PROC GLM also

allows specification of appropriate error terms in MEANS LSMEANS and CONTRAST

statements. To illustrate it let us use split plot experiment involving the yield of different

irrigation (IRRIG) treatments applied to main plots and cultivars (CULT) applied to subplots.

The data so obtained can be analysed using the following statements.

data splitplot;

input REP IRRIG CULT YIELD;

cards;

. . .

. . .

. . .

;

PROC print; run;

PROC GLM;

class rep, irrig cult;

SAS for Statistical Procedures

model yield = rep irrig rep*irrig cult irrig* cult;

test h = irrig e = rep * irrig;

contrast ‘IRRIGI Vs IRRIG2’ irrig 1 -1 / e = rep* irrig;

run;

As we know here that the irrigation effects are tested using error (A) which is sum of squares due

to rep* irrig, as taken in test statement and contrast statement respectively.

In Test statement H = numerator for - source of variation and

E = denominator source of variation

It may be noted here that the PROC GLM can be used to perform analysis of covariance as well.

For analysis of covariance, the covariate should be defined in the model without specifying

under CLASS statement.

PROC RSREG fits the parameters of a complete quadratic response surface and analyses the

fitted surface to determine the factor levels of optimum response and performs a ridge analysis to

search for the region of optimum response.

PROC RSREG < options >;

MODEL responses = independents / <options >;

RIDGE < options >;

WEIGHT variable;

ID variable;

By variable;

run;

The PROC RSREG and model statements are required. The BY, ID, MODEL, RIDGE, and

WEIGHT statements are described after the PROC RSREG statement below and can appear in

any order.

The PROC RSREG statement invokes the procedure and following options are allowed with the

PROC RSREG:

DATA = SAS - data-set : specifies the data to be analysed.

NOPRINT : suppresses all printed results when only the output

data set is required.

OUT : SAS-data-set: creates an output data set.

The model statement without any options transforms the independent variables to the coded data.

By default, PROC RSREG computes the linear transformation to perform the coding of variables

by subtracting average of highest and lowest values of the independent variable from the original

value and dividing by half of their differences. Canonical and ridge analyses are performed to the

model fit to the coded data. The important options available with the model statement are:

NOCODE : Analyses the original data.

ACTUAL : specifies the actual values from the input data set.

COVAR = n : declares that the first n variables on the independent side of the model are

simple linear regression (covariates) rather than factors in the quadratic

response surface.

LACKFIT : Performs lack of fit test. For this the repeated observations must appear

together.

NOANOVA : suppresses the printing of the analysis of variance and parameter

SAS for Statistical Procedures

estimates from the model fit.

NOOPTIMAL (NOOPT): suppresses the printing of canonical analysis for quadratic response

surface.

NOPRINT : suppresses both ANOVA and the canonical analysis.

PREDICT : specifies the values predicted by the model.

RESIDUAL : specifies the residuals.

A RIDGE statement computes the ridge of the optimum response. Following important options

available with RIDGE statement are

MAX: computes the ridge of maximum response.

MIN: computes the ridge of the minimum response.

At least one of the two options must be specified.

NOPRINT: suppresses printing the ridge analysis only when an output data set is required.

OUTR = SAS-data-set: creates an output data set containing the computed optimum ridge.

RADIUS = coded-radii: gives the distances from the ridge starting point at which to compute the

optimum.

PROC REG is the primary SAS procedure for performing the computations for a statistical

analysis of data based on a linear regression model. The basic statements for performing such an

analysis are

PROC REG;

MODEL list of dependent variable = list of independent variables/ model options;

RUN;

The PROC REG procedure and model statement without any option gives ANOVA, root mean

square error, R-squares, Adjusted R-square, coefficient of variation etc.

The options under model statement are

P: It gives predicted values corresponding to each observation in the data set. The estimated

standard errors are also given by using this option.

CLM: It yields upper and lower 95% confidence limits for the mean of subpopulation

corresponding to specific values of the independent variables.

CLI : It yields a prediction interval for a single unit to be drawn at random from a

subpopulation.

STB: Standardized regression coefficients.

XPX, I: Prints matrices used in regression computations.

NOINT: This option forces the regression response to pass through the origin. With this option

total sum of squares is uncorrected and hence R-square statistic are much larger than those for

the models with intercept.

However, if no intercept model is to be fitted with corrected total sum of squares and hence usual

definition of various statistic viz R2, MSE etc. are to be retained then the option RESTRICT

intercept = 0; may be exercised after the model statement.

For obtaining residuals and studentized residuals, the option ‘R’ may be exercised under model

statement and Cook’s D statistic.

SAS for Statistical Procedures

The ‘INFLUENCE’ option under model statement is used for detection of outliers in the data and

provides residuals, studentized residuals, diagonal elements of HAT MATRIX, COVRATIO,

DFFITS, DFBETAS, etc.

For detecting multicollinearity in the data, the options ‘VIF’ (variance inflation factors) and

‘COLLINOINT’ or ‘COLLIN’ may be used.

Besides the options for weighted regression, output data sets, specification error, heterogeneous

variances etc. are available under PROC REG.

PROC PRINCOMP can be utilized to perform the principal component analysis.

Multiple model statements are permitted in PROC REG unlike PROC ANOVA and PROC

GLM. A model statement can contain several dependent variables.

The statement model y1, y2, y3, y4=x1 x2 x3 x4 x5 ; performs four separate regression analyses of

variables y1, y2, y3 and y4 on the set of variables x1, x2, x3, x4, x 5.

Polynomial models can be fitted by using independent variables in the model as x1=x, x2=x**2,

x3=x**3, and so on depending upon the order of the polynomial to be fitted. From a variable,

several other variables can be generated before the model statement and transformed variables

can be used in model statement. LY and LX gives Logarithms of Y & X respectively to the base

e and LogY, LogX gives logarithms of Y and X respectively to the base 10.

TEST statement after the model statement can be utilized to test hypotheses on individual or any

linear function(s) of the parameters.

For e.g. if one wants to test the equality of coefficients of x1 and x2 in y=

o+

1x1+

2 x2

regression model, statement

TEST 1: TEST x1 - x2 = 0;

Label: Test < equation ..., equation >;

The fitted model can be changed by using a separate model statement or by using DELETE

variables; or ADD variables; statements.

The PROC REG provides two types of sums of squares obtained by SS1 or SS2 options under

model statement. Type I SS are sequential sum of squares and Types II sum of squares are

partial SS are same for that variable which is fitted at last in the model.

For most applications, the desired test for a single parameter is based on the Type II sum of

squares, which are equivalent to the t-tests for the parameter estimates. The Type I sum of

squares, however, are useful if there is a need for a specific sequencing of tests on individual

coefficients as in polynomial models.

PROC ANOVA and PROC GLM are general purpose procedures that can be used for a broad

range of data classification. In contrast, PROC NESTED is a specialized procedure that is useful

only for nested classifications. It provides estimates of the components of variance using the

analysis of variance method of estimation. The CLASS statement in PROC NESTED has a

SAS for Statistical Procedures

broader purpose then it does in PROC ANOVA and PROC GLM; it encompasses the purpose of

MODEL statement as well. But the data must be sorted appropriately. For example in a

laboratory microbial counts are made in a study, whose objective is to assess the source of

variation in number of microbes. For this study n1 packages of the test material are purchased

and n2 samples are drawn from each package i.e. samples are nested within packages. Let

logarithm transformation is to be used for microbial counts. PROPER SAS statements are:

PROC SORT; By package sample;

PROC NESTED;

CLASS package sample;

Var logcount;

run;

Corresponding PROC GLM statements are

PROC GLM;

Class package sample;

Model Logcount= package sample (package);

The F-statistic in basic PROC GLM output is not necessarily correct. For this RANDOM

statement with a list of all random effects in the model is used and Test option is utilized to get

correct error term. However, for fixed effect models same arguments for proper error terms hold

as in PROC GLM and PROC ANOVA. For the analysis of the data using linear mixed effects

model, PROC MIXED of SAS should be used. The best linear unbiased predictors and solutions

for random and fixed effects can be obtained by using option ‘s’ in the Random statement.

PROCEDURES FOR SURVEY DATA ANALYSIS

PROC SURVEYMEANS procedure produces estimates of population means and totals from

sample survey data. You can use PROC SURVEYMEANS to compute the following statistics:

estimates of population means, with corresponding standard errors and t tests

estimates of population totals, with corresponding standard deviations and t tests

estimates of proportions for categorical variables, with standard errors and t tests

ratio estimates of population means and proportions, and their standard errors

confidence limits for population means, totals, and proportions

data summary information

PROC SURVEYFREQ procedure produces one-way to n-way frequency and crosstabulation

tables from sample survey data. These tables include estimates of population totals, population

proportions (overall proportions, and also row and column proportions), and corresponding

standard errors. Confidence limits, coefficients of variation, and design effects are also available.

The procedure also provides a variety of options to customize your table display.

PROC SURVEYREG procedure fits linear models for survey data and computes regression

coefficients and their variance-covariance matrix. The procedure allows you to specify

classification effects using the same syntax as in the GLM procedure. The procedure also

provides hypothesis tests for the model effects, for any specified estimable linear functions of the

model parameters, and for custom hypothesis tests for linear combinations of the regression

parameters. The procedure also computes the confidence limits of the parameter estimates and

their linear estimable functions.

SAS for Statistical Procedures

PROC SURVEYLOGISTIC procedure investigates the relationship between discrete responses

and a set of explanatory variables for survey data. The procedure fits linear logistic regression

models for discrete response survey data by the method of maximum likelihood, incorporating

the sample design into the analysis. The SURVEYLOGISTIC procedure enables you to use

categorical classification variables (also known as CLASS variables) as explanatory variables in

an explanatory model, using the familiar syntax for main effects and interactions employed in the

GLM and LOGISTIC procedures.

The SURVEYSELECT procedure provides a variety of methods for selecting probability-based

random samples. The procedure can select a simple random sample or a sample according to a

complex multistage sample design that includes stratification, clustering, and unequal

probabilities of selection. With probability sampling, each unit in the survey population has a

known, positive probability of selection. This property of probability sampling avoids selection

bias and enables you to use statistical theory to make valid inferences from the sample to the

survey population.

PROC SURVEYSELECT provides methods for both equal probability sampling and sampling

with probability proportional to size (PPS). In PPS sampling, a unit's selection probability is

proportional to its size measure. PPS sampling is often used in cluster sampling, where you

select clusters (groups of sampling units) of varying size in the first stage of selection. Available

PPS methods include without replacement, with replacement, systematic, and sequential with

minimum replacement. The procedure can apply these methods for stratified and replicated

sample designs.

3. Exercises

Example 3.1: An experiment was conducted to study the hybrid seed production of bottle gourd

(Lagenaria siceraria (Mol) Standl) Cv. Pusa hybrid-3 under open field conditions during

Kharif-2005 at Indian Agricultural Research Institute, New Delhi. The main aim of the

investigation was to compare natural pollination and hand pollination. The data were collected

on 10 randomly selected plants from each of natural pollination and hand pollination on

number of fruit set for the period of 45 days, fruit weight (kg), seed yield per plant (g) and

seedling length (cm). The data obtained is as given below:

Grou

p

No. of fruit Fruit wei

g

ht Seed

y

ield/

p

lant Seedlin

g

len

g

th

1 7.0 1.85 147.70 16.86

1 7.0 1.86 136.86 16.77

1 6.0 1.83 149.97 16.35

1 7.0 1.89 172.33 18.26

1 7.0 1.80 144.46 17.90

1 6.0 1.88 138.30 16.95

1 7.0 1.89 150.58 18.15

1 7.0 1.79 140.99 18.86

1 6.0 1.85 140.57 18.39

1 7.0 1.84 138.33 18.58

SAS for Statistical Procedures

2 6.3 2.58 224.26 18.18

2 6.7 2.74 197.50 18.07

2 7.3 2.58 230.34 19.07

2 8.0 2.62 217.05 19.00

2 8.0 2.68 233.84 18.00

2 8.0 2.56 216.52 18.49

2 7.7 2.34 211.93 17.45

2 7.7 2.67 210.37 18.97

2 7.0 2.45 199.87 19.31

2 7.3 2.44 214.30 19.36

{Here 1 denotes natural pollination and 2 denotes the hand pollination}

1. Test whether the mean of the population of Seed yield/plant (g) is 200 or not.

2. Test whether the natural pollination and hand pollination under open field conditions are

equally effective or are significantly different.

3. Test whether hand pollination is better alternative in comparison to natural pollination.

Procedure:

For performing analysis, input the data in the following format. {Here Number of fruit (45

days) is termed as nfs45, Fruit weight (kg) is termed as fw, seed yield/plant (g) is termed as syp

and Seedling length (cm) is termed as sl. It may, however, be noted that one can retain the same

name or can code in any other fashion}.

data ttest1; /*one can enter any other name for data*/

input group nfs45 fw syp sl;

cards;

. . . . .

. . . . .

. . . . .

;

*To answer the question number 1 use the following SAS statements

proc ttest H0=200;

var syp;

run;

*To answer the question number 2 use the following SAS statements;

proc ttest;

class group;

var nfs45 fw syp sl;

run;

To answer the question number 3 one has to perform the one tail t-test. The easiest way to

convert a two-tailed test into a one-tailed test is take half of the p-value provided in the output of

2-tailed test output for drawing inferences. The other way is using the options sides in proc

SAS for Statistical Procedures

statement. Here we are interested in testing whether hand pollination is better alternative in

comparison to natural pollination, therefore, we may use Sides=L as

proc ttest sides=L;

class group;

var nfs45 fw syp sl;

run;

Similarly this option can also be used in one sample test and for right tail test Sides=U is used.

Exercise 3.2: A study was undertaken to find out whether the average grain yield of paddy of

farmers using laser levelling is more than the farmers using traditional land levelling methods.

For this study data on grain yield in tonne/hectare was collected from 59 farmers (33 using

traditional land levelling methods and 26 using new land leveller) and is given as:

Traditional Lase

r Traditional Laser

3.67 3.6 3.79 3.95

4.04 3.7 3.17 5.3

3.49 5.3 3.58 5.8

2.75 4.4 4.08 2.8

2.63 5.4 4.25 3.0

2.46 3.4 5.21 4.78

2.50 3.5 5.63 4.07

2.88 8.2 3.42 4.88

2.45 7.5 3.88 4.37

2.46 7.6 3.29

2.67 7.0 3.92

2.38 7.4 2.25

2.42 3.4 2.58

2.54 3.6 3.25

3.88 5.6 3.46

3.88 5.6 3.79

3.42 5.4

Test whether the traditional land levelling and laser levelling give equivalent yields or are

significantly different.

Procedure:

For performing analysis, input the data in the following format. {Here traditional land levelling

is termed as LL, laser levelling as LL, method of levelling as MLevel and grain yield in t/ha as

gyld. It may, however, be noted that one can retain the same name or can code in any other

fashion}.

data ttestL; /*one can enter any other name for data*/

input MLevel gyld;

SAS for Statistical Procedures

cards;

. . . . .

. . . . .

. . . . .

;

*To answer the question number 1 use the following SAS statements

proc ttest data =ttestL;

var gyld;

run;

Exercise 3.3: The observations obtained from 15 experimental units before and after application

of the treatment are the following:

Unit No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Before 80 73 70 60 88 84 65 37 91 98 52 78 40 79 59

After 82 71 95 69 100 71 75 60 95 99 65 83 60 86 62

1. Test whether the mean score before application of treatment is 65.

2. Test whether the application of treatments has resulted into some change in the score of the

experimental units.

3. Test whether application of treatment has improved the scores.

Procedure:

data ttest;

input sn preapp postapp;

cards;

1 80 82

2 73 71

3 70 95

4 60 69

5 88 100

6 84 71

7 65 75

8 37 60

9 91 95

10 98 99

11 52 65

12 78 83

13 40 60

14 79 86

15 59 62

;

*For objective 1, use the following;

PROC TTEST H0=65;

VAR PREAPP;

RUN;

SAS for Statistical Procedures

*For objective 2, use the following;

PROC TTEST;

PAIRED PREAPP*POSTAPP;

RUN;

*For objective 3, use the following;

PROC TTEST sides=L;

PAIRED PREAPP*POSTAPP;

RUN;

Exercise 3.4: In F2 population of a breeding trial on pea, out of a total of 556 seeds, the

frequency of seeds of different shape and colour are: 315 rounds and yellow, 101 wrinkled and

yellow, 108 round and green , 32 wrinkled and green. Test at 5% level of significance whether

the different shape and colour of seeds are in proportion of 9:3:3:1 respectively.

Procedure:

/*rndyel=round and yellow, rndgrn=round and green, wrnkyel=wrinkled and yellow,

wrnkgrn=wrinkled and green*/;

data peas;

input shape_color $ count;

cards;

rndyel 315

rndgrn 108

wrnkyel 101

wrnkgrn 32

;

proc freq data=peas order=data;

weight count ;

tables shape_color / chisq testp=(0.5625 0.1875 0.1875 0.0625);

exact chisq;

run;

Exercise 3.5: The educational standard of adoptability of new innovations among 600 farmers are given

as below: Educational standard

Adoptability Matric Graduate Illiterate

Adopted 100 60 80

Not adopted 50 20 290

Draw the inferences whether educational standard has any impact on their adoptability of innovation.

Procedure:

data innovation;

input edu $ adopt $ count;

cards;

Matric adopt 100

SAS for Statistical Procedures

Matric Noadopt 50

grad adopt 60

grad Noadopt 20

illit adopt 80

illit Noadopt 290

;

proc freq order=data;

weight count ;

tables edu*adopt / chisq ;

run;

Exercise 3.6: An Experiment was conducted using a Randomized complete block design in 5

treatments a, b, c, d & e with three replications. The data (yield) obtained is given below:

Treatment(TRT)

Replication(REP) a b c d e

1 16.9 18.2 17.0 15.1 18.3

2 16.5 19.2 18.1 16.0 18.3

3 17.5 17.1 17.3 17.8 19.8

1. Perform the analysis of variance of the data.

2. Test the equality of treatment means.

3. Test H0: 2T1=T2+T3, where as T1, T2, T3, T4 and T5 are treatment effects.

Procedure:

Prepare a SAS data file using

DATA Name;

INPUT REP TRT $ yield;

Cards;

. . .

. . .

. . .

;

Print data using PROC PRINT. Perform analysis using PROC ANOVA, obtain means of

treatments and obtain pairwise comparisons using least square differences, Duncan’s New

Multiple range tests and Tukey’s Honest Significant difference tests. Make use of the following

statements:

PROC Print;

PROC ANOVA;

Class REP TRT;

Model Yield = REP TRT;

Means TRT/lsd;

Means TRT/duncan;

Means TRT/tukey;

Run;

Perform contrast analysis using PROC GLM.

Proc glm;

SAS for Statistical Procedures

Class rep trt;

Model yld = rep trt;

Means TRT/lsd;

Means TRT/duncan;

Means TRT/tukey

Contrast ‘1 Vs 2&3’ trt 2 -1 -1; Run;

Exercise 3.7: In order to select suitable tree species for Fuel, Fodder and Timber an experiment

was conducted in a randomized complete block design with ten different trees and four

replications. The plant height was recorded in cm. The details of the experiment are given below:

Plant Height (Cms): Place – Kanpur

Name of Tree Spacing Replications

1 2 3 4

A. Indica 4x4 144.44 145.11 104.00 105.44

D. Sisso 4x2 113.50 118.61 118.61 123.00

A. Procer 4x2 60.88 90.94 80.33 92.00

A. Nilotic 4x2 163.44 158.55 158.88 153.11

T. Arjuna 4x2 110.11 116.00 119.66 103.22

L. Loucoc 4x1 260.05 102.27 256.22 217.80

M. Alba 4x2 114.00 115.16 114.88 106.33

C. Siamia 4x2 91.94 58.16 76.83 79.50

E. Hybrid 4x1 156.11 177.97 148.22 183.17

A. Catech 4x2 80.2 108.05 45.18 79.55

Analyze the data and draw your conclusions.

Exercise 3.8: An experiment was conducted with 49 crop varieties (TRT) using a simple lattice

design. The layout and data obtained (Yld) is as given below:

REPLICATION (REP)-I

BLOCKS(BLK)

1 2 3 4 5 6 7

22(7) 10(12) 45(22) 37(25) 18(33) 30(33) 5(28)

24(20) 14(26) 44(21) 41(23) 19(17) 34(31) 6(74)

28(25) 8(42) 43(16) 40(11) 21(13) 35(10) 7(14)

27(68) 9(13) 47(37) 42(24) 17(10) 32(12) 2(14)

25(4) 13(10) 49(13) 36(30) 15(36) 29(22) 1(16)

26(11) 12(21) 48(21) 39(34) 20(30) 33(33) 3(11)

23(45) 11(11) 46(12) 38(15) 16(14) 31(18) 4(7)

REPLICATION (REP)-II

BLOCKS(BLK)

1 2 3 4 5 6 7

22(29) 18(64) 20(25) 23(45) 5(19) 3(13) 14(60)

8(127) 25(31) 27(71) 16(22) 19(47) 24(23) 49(72)

43(119) 46(85) 13(51) 2(13) 47(86) 17(51) 21(10)

SAS for Statistical Procedures

1(24) 11(51) 48(121) 37(85) 40(33) 10(30) 42(23)

36(58) 4(39) 41(22) 9(10) 12(48) 31(50) 35(54)

29(97) 39(67) 6(75) 30(65) 33(73) 38(30) 28(54)

15(47) 32(93) 34(44) 44(5) 26(56) 45(103) 7(85)

1. Perform the analysis of variance of the data. Also obtain Type II SS.

2. Obtain adjusted treatment means with their standard errors.

3. Test the equality of all adjusted treatment means.

4. Test whether the sum of 1 to 3 treatment means is equal to the sum of 4 to 6 treatments.

5. Estimate difference between average treatment 1 average of 2 to 4 treatment means.

6. Divide the between block sum of squares into between replication sum of squares and

between blocks within replications sum of squares.

7. Assuming that the varieties are a random selection from a population, obtain the genotypic

variance.

8. Analyze the data using block effects as random.

PROCEDURE

Prepare the DATA file.

DATA Name;

INPUT REP BLK TRT yield;

Cards;

. . . .

. . . .

. . . .

;

Print data using PROC PRINT. Perform analysis of 1 to 5 objectives using PROC GLM. The

statements are as follows:

Proc print;

Proc glm;

Class rep blk trt;

Model yld= blk trt/ss2;

Contrast ‘A’ trt 1 1 1 -1 -1 -1;

Estimate ‘A’ trt 3 -1 -1 -1/divisor=3;

Run;

The objective 6 can be achieved by another model statement.

Proc glm;

Class rep blk trt;

Model yield= rep blk (rep) trt/ss2;

run;

The objective 7 can be achieved by using the another PROC statement

Proc Varcomp Method=type1;

Class blk trt;

Model yield = blk trt/fixed = 1;

Run;

SAS for Statistical Procedures

The above obtains the variance components using Hemderson’s method. The methods of

maximum likelihood, restricted maximum likelihood, minimum quadratic unbiased estimation

can also be used by specifying method =ML, REML, MIVQE respectively.

Objective 8 can be achieved by using PROCMIXED.

Proc Mixed ratio covtest;

Class blk trt;

Model yield = trt;

Random blk/s;

Lsmeans trt/pdiff;

Store lattice;

Run;

PROC PLM SOURCE = lattice;

LSMEANS trt /pdiff lines;

RUN;

Exercise 3.9: Analyze the data obtained through a Split-plot experiment involving the yield of 3

Irrigation (IRRIG) treatments applied to main plots and two Cultivars (CULT) applied to

subplots in three Replications (REP). The layout and data (YLD) is given below:

Replication-I Replication -II Replication-III

I1 I2 I3 I1 I2 I3 I1 I2 I3

C1

(1.6) C1

(2.6) C1

(4.7) C1

(3.4) C1

(4.6) C1

(5.5) C1

(3.2) C1

(5.1) C1

(5.7)

C2

(3.3) C2

(5.1) C2

(6.8) C2

(4.7) C2

(1.1) C2

(6.6) C2

(5.6) C2

(6.2) C2

(4.5)

Perform the analysis of the data. (HINT: Steps are given in text).

Remark 3.9.1: Another way proposed for analysis of split plot designs is using replication as

random effect and analyse the data using PROC MIXED of SAS. For the above case, the steps

for using PROC MIXED are:

PROC MIXED COVTEST;

CLASS rep irrig cult;

MODEL yield = irrig cult irrig*cult / DDFM=KR;

RANDOM rep rep*irrig;

LSMEANS irrig cult irrig*cult / PDIFF;

STORE spd;

run;

/* An item store is a special SAS-defined binary file format used to store and restore information with a hierarchical

structure*/

/* The PLM procedure performs post fitting statistical analyses for the contents of a SAS item store that was

previously created with the STORE statement in some other SAS/STAT procedure*/

PROC PLM SOURCE = SPD;

LSMEANS irrig cult irrig*cult /pdiff lines;

RUN;

SAS for Statistical Procedures

Remark 3.9.2: In Many experimental situations, the split plot designs are conducted across

environments and a pooled is required. One way of analysing data of split plot designs with two

factors A and B conducted across environment is

PROC MIXED COVTEST;

CLASS year rep a b;

MODEL yield = a b a*b / DDFM=KR;

/* DDFM specifies the method for computing the denominator degrees of freedom for the tests of fixed effects

resulting from the MODEL*/

RANDOM year rep(year) year*a year*rep*a year*a*b;

LSMEANS a b a*b / PDIFF;

STORE spd1;

run;

PROC PLM SOURCE = SPD1;

LSMEANS a b a*b/pdiff lines;

RUN;

Exercise 3.10: An agricultural field experiment was conducted in 9 treatments using 36 plots

arranged in 4 complete blocks and a sample of harvested output from all the 36 plots are to be

analysed blockwise by three technicians using three different operations. The data collected is

given below: Block-1

Technician

Operation 1 2 3

Block-2

Technician

Operation 1 2 3

1 1(1.1) 2(2.1) 3(3.1) 1 1(2.1) 4(5.2) 7(8.3)

2 4(4.2) 5(5.3) 6(6.3) 2 2(3.2) 5(6.7) 8(9.9)

3 7(7.4) 8(8.7) 9(9.6) 3 3(4.5) 6(7.6) 9(10.3)

Block-3

Technician

Operation 1 2 3

Block-4

Technician

Operation 1 2 3

1 1(1.2) 6(6.3) 8(8.7) 1 1(3.1) 9(11.3) 5(7.8)

2 9(9.4) 2(2.7) 4(4.8) 2 6(8.1) 2(4.5) 7(9.3)

3 5(5.9) 7(7.8) 3(3.3) 3 8(10.7) 4(6.9) 3(5.8)

1. Perform the analysis of the data considering that technicians and operations are crossed with

each other and nested in the blocking factor.

2. Perform the analysis by considering the effects of technicians as negligible.

3. Perform the analysis by ignoring the effects of the operations and technicians.

Procedure:

Prepare the data file.

DATA Name;

INPUT BLK TECH OPER TRT OBS;

Cards;

. . . .

SAS for Statistical Procedures

. . . .

. . . .

;

Perform analysis of objective 1 using PROC GLM. The statements are as follows:

Proc glm;

Class blk tech oper trt;

Model obs= blk tech (blk) oper(blk) trt/ss2;

Lsmeans trt oper(blk)/pdiff;

Run;

Perform analysis of objective 2 using PROC GLM with the additional statements as follows:

Proc glm;

Class blk tech oper trt;

Model obs= blk oper(blk) trt/ss2;

run;

Perform analysis of objective 3 using PROC GLM with the additional statements as follows:

Proc glm;

Class blk tech oper trt;

Model obs = blk trt/ss2;

run;

Exercise 3.11: A greenhouse experiment on tobacco mossaic virus was conducted. The

experimental unit was a single leaf. Individual plants were found to be contributing significantly

to error and hence were taken as one source causing heterogeneity in the experimental material.

The position of the leaf within plants was also found to be contributing significantly to the error.

Therefore, the three positions of the leaves viz. top, middle and bottom were identified as levels

of second factor causing heterogeneity. 7 solutions were applied to leaves of 7 plants and

number of lesions produced per leaf was counted. Analyze the data of this experiment.

Plants

Leaf Position 1 2 3 4 5 6 7

Top 1(2) 2(3) 3(1) 4(5) 5(3) 6(2) 7(1)

Middle 2(4) 3(3) 4(2) 5(6) 6(4) 7(2) 1(1)

Bottom 4(3) 5(4) 6(7) 7(6) 1(3) 2(4) 3(7)

The figures at the intersections of the plants and leaf position are the solution numbers and the

figures in the parenthesis are number of lesions produced per leaf.

Procedure:

Prepare the data file.

DATA Name;

INPUT plant posi $ trt count;

Cards;

. . . .

. . . .

. . . .

SAS for Statistical Procedures

;

Perform analysis using PROC GLM. The statements are as follows:

Proc glm;

Class plant posi trt count;

Model count= plant posi trt/ss2;

Lsmeans trt/pdiff; Run;

Exercise 3.12: The following data was collected through a pilot sample survey on Hybrid Jowar

crop on yield and biometrical characters. The biometrical characters were average Plant

Population (PP), average Plant Height (PH), average Number of Green Leaves (NGL) and Yield

(kg/plot).

1. Obtain correlation coefficient between each pair of the variables PP, PH, NGL and yield.

2. Fit a multiple linear regression equation by taking yield as dependent variable and

biometrical characters as explanatory variables. Print the matrices used in the regression

computations.

3. Test the significance of the regression coefficients and also equality of regression

coefficients of a) PP and PH b) PH and NGL

4. Obtain the predicted values corresponding to each observation in the data set.

5. Identify the outliers in the data set.

6. Check for the linear relationship among the biometrical characters.

7. Fit the model without intercept.

8. Perform principal component analysis.

No. PP PH NGL Yield

1 142.00 0.5250 8.20 2.470

2 143.00 0.6400 9.50 4.760

3 107.00 0.6600 9.30 3.310

4 78.00 0.6600 7.50 1.970

5 100.00 0.4600 5.90 1.340

6 86.50 0.3450 6.40 1.140

7 103.50 0.8600 6.40 1.500

8 155.99 0.3300 7.50 2.030

9 80.88 0.2850 8.40 2.540

10 109.77 0.5900 10.60 4.900

11 61.77 0.2650 8.30 2.910

12 79.11 0.6600 11.60 2.760

13 155.99 0.4200 8.10 0.590

14 61.81 0.3400 9.40 0.840

15 74.50 0.6300 8.40 3.870

16 97.00 0.7050 7.20 4.470

17 93.14 0.6800 6.40 3.310

18 37.43 0.6650 8.40 1.570

19 36.44 0.2750 7.40 0.530

20 51.00 0.2800 7.40 1.150

21 104.00 0.2800 9.80 1.080

22 49.00 0.4900 4.80 1.830

23 54.66 0.3850 5.50 0.760

24 55.55 0.2650 5.00 0.430

SAS for Statistical Procedures

25 88.44 0.9800 5.00 4.080

26 99.55 0.6450 9.60 2.830

27 63.99 0.6350 5.60 2.570

28 101.77 0.2900 8.20 7.420

29 138.66 0.7200 9.90 2.620

30 90.22 0.6300 8.40 2.000

31 76.92 1.2500 7.30 1.990

32 126.22 0.5800 6.90 1.360

33 80.36 0.6050 6.80 0.680

34 150.23 1.1900 8.80 5.360

35 56.50 0.3550 9.70 2.120

36 136.00 0.5900 10.20 4.160

37 144.50 0.6100 9.80 3.120

38 157.33 0.6050 8.80 2.070

39 91.99 0.3800 7.70 1.170

40 121.50 0.5500 7.70 3.620

41 64.50 0.3200 5.70 0.670

42 116.00 0.4550 6.80 3.050

43 77.50 0.7200 11.80 1.700

44 70.43 0.6250 10.00 1.550

45 133.77 0.5350 9.30 3.280

46 89.99 0.4900 9.80 2.690

Procedure:

Prepare a data file

Data mlr;

Input PP PH NGL Yield;

Cards;

. . . .

. . . .

;

For obtaining correlation coefficient, Use PROC CORR;

Proc Corr;

Var PP PH NGL Yield;

run;

For fitting of multiple linear regression equation, use PROC REG

Proc Reg;

Model Yield = PP PH NGL/ p r influence vif collin xpx i;

Test 1: Test PP =0; Test 2: Test PH=0;

Test 3: Test NGL=0;

Test 4: Test PP-PH=0;

Test 4a: Test PP=PH=0;

Test 5: Test PH-NGL=0;

Test 5a: Test PH=NGL=0;

SAS for Statistical Procedures

Model Yield = PP PH NGL/noint;

run;

Proc reg;

Model Yield = PP PH NGL;

Restrict intercept =0;

Run;

For diagnostic plots

Proc Reg plots(unpack)=diagnostics;

Model Yield = PP PH NGL;

run;

For variable selection, one can use the following option in model statement:

Selection=stepwise sls=0.10;

For performing principal component analysis, use the following:

PROC PRINCOMP;

VAR PP PH NGL YIELD;

run;

Example 3.13: An experiment was conducted at Division of Agricultural Engineering, IARI,

New Delhi for studying the capacity of a grader in number of hours when used with three

different speeds and two processor settings. The experiment was conducted using a factorial

completely randomised design in 3 replications. The treatment combinations and data obtained

on capacity of grader in hours given as below:

Replicatio

n speed Processor setting trt cgrade

r

1 1 1 1 1852

1 1 2 2 1848

1 1 3 3 1855

1 2 1 4 2270

1 2 2 5 2279

1 2 3 6 2272

1 3 1 7 3035

1 3 2 8 3042

1 3 3 9 3028

2 1 1 1 1845

2 1 2 2 1855

2 1 3 3 1860

2 2 1 4 2276

2 2 2 5 2275

2 2 3 6 2248

2 3 1 7 3036

2 3 2 8 3033

2 3 3 9 3038

3 1 1 1 1851

3 1 2 2 1840

3 1 3 3 1840

SAS for Statistical Procedures

3 2 1 4 2265

3 2 2 5 2280

3 2 3 6 2278

3 3 1 7 3040

3 3 2 8 3028

3 3 3 9 3040

Experimenter was interested in identifying the best combination of speed and processor setting

that gives maximum capacity of the grader in hours.

Solution: This data can be analysed as per procedure of factorial CRD and one can use the

following SAS steps for performing the nalysis:

Data ex1a;

Input rep speed proset cgrader;

/*here rep: replication; proset: processor setting and cgrader: capacity of the grader in hours*/

Cards;

1 1 1 1852

1 1 2 1848

1 1 3 1855

. . . .

. . . .

. . . .

3 3 1 3040

3 3 2 3028

3 3 3 3040

;

Proc glm data=ex1;

Class speed prost;

Model cgrader=speed post speed*post;

Lsmeans speed post speed*post/pdiff adjust=tukey lines;

Run;

The above analysis would identify test the significance of main effects of speed and processor

setting and their interaction. Through this analysis one can also identify the speed level

(averaged over processor setting) {Processor Setting (averaged over speed levels)} at which the

capacity of the grader is maximum. The multiple comparisons between means of combinations

of speed and processor setting would help in identifying the combination at which capacity of

the grader is maximum.

Exercise 3.14: An experiment was conducted with five levels of each of the four fertilizer

treatments nitrogen, Phosphorus, Potassium and Zinc. The levels of each of the four factors and

yield obtained are as given below. Fit a second order response surface design using the original

data. Test the lack of fit of the model. Compute the ridge of maximum and minimum responses.

Obtain predicted residual Sum of squares.

N P2O5 K

2O Zn Yield

SAS for Statistical Procedures

40 30 25 20 11.28

40 30 25 60 8.44

40 30 75 20 13.29

40 90 25 20 7.71

120 30 25 20 8.94

40 30 75 60 10.9

40 90 25 60 11.85

120 30 25 60 11.03

120 30 75 20 8.26

120 90 25 20 7.87

40 90 75 20 12.08

40 90 75 60 11.06

120 30 75 60 7.98

120 90 75 60 10.43

120 90 75 20 9.78

120 90 75 60 12.59

160 60 50 40 8.57

0 60 50 40 9.38

80 120 50 40 9.47

80 0 50 40 7.71

80 60 100 40 8.89

80 60 0 40 9.18

80 60 50 80 10.79

80 60 50 0 8.11

80 60 50 40 10.14

80 60 50 40 10.22

80 60 50 40 10.53

80 60 50 40 9.5

80 60 50 40 11.53

80 60 50 40 11.02

Procedure:

Prepare a data file.

/* yield at different levels of several factors */

title 'yield with factors N P K Zn';

data dose;

input n p k Zn y ; label y = "yield" ;

cards;

. . . . .

. . . . .

. . . . .

;

*Use PROC RSREG.

ods graphics on;

proc rsreg data=dose plots(unpack)=surface(3d);

model y= n p k Zn/ nocode lackfit press;

SAS for Statistical Procedures

run;

ods graphics off; *If we do not want surface plots, then we may

proc rsreg;

model y= n p k Zn/ nocode lackfit press;

Ridge min max;

run;

Exercise 3.15: Fit a second order response surface design to the following data. Take

replications as covariate.

Fertilizer1 Fertilizer2 X1 X2 Yields(lb/plot)

Replication I Replication II

50 15

117.52 8.12

120 15 +1 112.37 11.84

50 25

1+1 13.55 12.35

120 25 +1 +1 16.48 15.32

35 20

208.63 9.44

134 20

+

20 14.22 12.57

85 13 0 27.90 7.33

85 27 0 +216.49 17.40

85 20 0 0 15.73 17.00

Procedure:

Prepare a data file.

/* yield at different levels of several factors */

title 'yield with factors x1 x2';

data respcov;

input fert1 fert2 x1 x2 yield ;

cards;

. . . . .

. . . . .

. . . . .

;

/*Use PROC RSREG.*/

ODS Graphics on;

proc rsreg plots(unpack)=surface(3d);

model yield = rep fert1 fert2/ covar=1 nocode lackfit ;

Ridge min max;

run;

ods graphics off;

Exercise 3.16: Following data is related to the length(in cm) of the ear-head of a wheat variety

9.3, 18.8, 10.7, 11.5, 8.2, 9.7, 10.3, 8.6, 11.3, 10.7, 11.2, 9.0, 9.8, 9.3, 10.3, 10, 10.1 9.6, 10.4.

Test the data that the median length of ear-head is 9.9 cm.

Procedure:

This may be tested using any of the three tests for location available in Proc Univariate viz.

Student’s test, the sign test, and the Wilcoxon signed rank test. All three tests produce a test

statistic for the null hypothesis that the mean or median is equal to a given value 0 against the

SAS for Statistical Procedures

two-sided alternative that the mean or median is not equal to 0. By default, PROC

UNIVARIATE sets the value of 0 to zero. You can use the MU0= option in the PROC

UNIVARIATE statement to specify the value of 0. If the data is from a normal population, then

we can infer using t-test otherwise non-parametric tests sign test, and the Wilcoxon signed rank

test may be used for drawing inferences.

Procedure:

data npsign;

input length;

cards;

9.3

18.8

10.7

11.5

8.2

9.7

10.3

8.6

11.3

10.7

11.2

9.0

9.8

9.3

10.3

10.0

10.1

9.6

10.4

;

PROC UNIVARIATE DATA=npsign MU0=9.9;

VAR length;

HISTOGRAM / NOPLOT ;

RUN;

QUIT;

Exercise 3.17: An experiment was conducted with 21 animals to determine if the four different

feeds have the same distribution of Weight gains on experimental animals. The feeds 1, 3 and 4

were given to 5 randomly selected animals and feed 2 was given to 6 randomly selected animals.

The data obtained is presented in the following table.

Feeds Weight gains (kg)

1 3.35 3.8 3.55 3.36 3.81

2 3.79 4.1 4.11 3.95 4.25 4.4

3 4 4.5 4.51 4.75 5

4 3.57 3.82 4.09 3.96 3.82

Procedure:

SAS for Statistical Procedures

data np;

input feed wt;

datalines;

1 3.35

1 3.80

1 3.55

1 3.36

1 3.81

2 3.79

2 4.10

2 4.11

2 3.95

2 4.25

2 4.40

3 4.00

3 4.50

3 4.51

3 4.75

3 5.00

4 3.57

4 3.82

4 4.09

4 3.96

4 3.82

;

PROC NPAR1WAY DATA=np WILCOXON; /*for performing Kruskal-Walis test*/;

VAR wt;

CLASS feed;

RUN;

Example 3.18: Finney (1971) gave a data representing the effect of a series of doses of carotene

(an insecticide) when sprayed on Macrosiphoniella sanborni (some obscure insects). The Table

below contains the concentration, the number of insects tested at each dose, the proportion dying

and the probit transformation (probit+5) of each of the observed proportions.

Concentratio

n (mg/1) No. of

insects (n) No. of

affected (r) %kill (P) Log

concentration

(x)

Empirical

probit

10.2 50 44 88 1.01 6.18

7.7 49 42 86 0.89 6.08

5.1 46 24 52 0.71 5.05

3.8 48 16 33 0.58 4.56

2.6 50 6 12 0.41 3.82

0 49 0 0 - -

Perform the probit analysis on the above data.

SAS for Statistical Procedures

Procedure

data probit;

input con n r;

datalines;

10.2 50 44

7.7 49 42

5.1 46 24

3.8 48 16

2.6 50 6

0 49 0

;

ods html;

Proc Probit log10 ;

Model r/n=con/lackfit inversecl;

title ('output of probit analysis');

run;

ods html close;

Model Information

Data Set WORK.PROBIT

Events Variable r

Trials Variable n

Number of Observations 5

Number of Events 132

Number of Trials 243

Name of Distribution Normal

Log Likelihood -120.0516414

Number of Observations Read 6

Number of Observations Used 5

Number of Events 132

Number of Trials 243

Algorithm converged.

Goodness-of-Fit Tests

Statistic Value DF Pr > ChiSq

Pearson Chi-Square 1.7289 30.6305

L.R. Chi-Square 1.7390 30.6283

Response-Covariate Profile

Response Levels 2

Number of Covariate Values 5

Since the chi-square is small (p > 0.1000), fiducial limits will be calculated using a t value of 1.96

Type III Analysis of Effects

Effect DF Wald

Chi-Square Pr > ChiSq

Log10(con) 177.5920 <.0001

SAS for Statistical Procedures

Analysis of Parameter Estimates

Parameter DF Estimate Standard

Error 95% Confidence

Limits Chi-Square Pr > ChiSq

Intercept 1 -2.8875 0.3501 -3.5737 -2.2012 68.01 <.0001

Log10(con) 1 4.2132 0.4783 3.2757 5.1507 77.59 <.0001

Probit Model in Terms of

Tolerance Distribution

MU SIGMA

0.68533786 0.23734947

Estimated Covariance Matrix for

Tolerance Parameters

MU SIGMA

MU 0.000488 -0.000063

SIGMA -0.000063 0.000726

Probit Analysis on Log10(con)

Probability Log10(con) 95% Fiducial Limits

0.01 0.13318 -0.03783 0.24452

0.02 0.19788 0.04453 0.29830

0.03 0.23893 0.09668 0.33253

0.04 0.26981 0.13584 0.35834

0.05 0.29493 0.16764 0.37940

0.06 0.31631 0.19466 0.39737

0.07 0.33506 0.21832 0.41316

0.08 0.35184 0.23946 0.42733

0.09 0.36711 0.25866 0.44026

0.10 0.38116 0.27631 0.45218

0.15 0.43934 0.34898 0.50192

0.20 0.48558 0.40618 0.54202

0.25 0.52525 0.45467 0.57700

0.30 0.56087 0.49759 0.60904

0.35 0.59388 0.53666 0.63942

0.40 0.62521 0.57295 0.66905

0.45 0.65551 0.60716 0.69861

0.50 0.68534 0.63983 0.72870

0.55 0.71516 0.67142 0.75986

0.60 0.74547 0.70240 0.79265

0.65 0.77679 0.73330 0.82766

0.70 0.80980 0.76480 0.86563

0.75 0.84543 0.79777 0.90761

0.80 0.88510 0.83352 0.95533

0.85 0.93133 0.87427 1.01188

0.90 0.98951 0.92456 1.08401

0.91 1.00357 0.93658 1.10155

0.92 1.01883 0.94960 1.12065

0.93 1.03562 0.96387 1.14170

0.94 1.05436 0.97976 1.16526

0.95 1.07574 0.99783 1.19218

0.96 1.10086 1.01898 1.22388

0.97 1.13174 1.04490 1.26294

0.98 1.17279 1.07924 1.31498

0.99 1.23750 1.13315 1.39721

SAS for Statistical Procedures

Probit Analysis on con

Probability con 95% Fiducial Limits

0.01 1.35888 0.91657 1.75599

0.02 1.57718 1.10799 1.98745

0.03 1.73353 1.24935 2.15043

0.04 1.86129 1.36724 2.28215

0.05 1.97212 1.47110 2.39553

0.06 2.07163 1.56554 2.49671

0.07 2.16302 1.65317 2.58917

0.08 2.24825 1.73565 2.67506

0.09 2.32868 1.81410 2.75586

0.10 2.40526 1.88932 2.83257

0.15 2.75005 2.23349 3.17629

0.20 3.05900 2.54788 3.48353

0.25 3.35157 2.84884 3.77571

0.30 3.63808 3.14478 4.06477

0.35 3.92538 3.44084 4.35935

0.40 4.21897 3.74068 4.66710

0.45 4.52389 4.04724 4.99582

0.50 4.84549 4.36343 5.35423

0.55 5.18995 4.69265 5.75260

0.60 5.56506 5.03963 6.20374

0.65 5.98127 5.41132 6.72450

0.70 6.45363 5.81830 7.33883

0.75 7.00531 6.27722 8.08377

0.80 7.67532 6.81590 9.02252

0.85 8.53758 7.48633 10.27723

0.90 9.76143 8.40534 12.13411

0.91 10.08243 8.64132 12.63428

0.92 10.44313 8.90434 13.20233

0.93 10.85466 9.20181 13.85792

0.94 11.33346 9.54469 14.63036

0.95 11.90537 9.95006 15.56609

0.96 12.61427 10.44674 16.74479

0.97 13.54388 11.08927 18.32046

0.98 14.88655 12.00168 20.65263

0.99 17.27807 13.58779 24.95808

Interpretation: The goodness-of-fit tests (p-values = 0.6305, 0.6283) suggest that the

distribution and the model fits the data adequately. In this case, the fitting is done on normal

equivalent deviate only without adding 5. Therefore, log LD50 or lof ED50 corresponds to the

value of Probit=0. Log LD50 is obtained as 0.685338. Therefore, the stress level at which the

50% of the insects will be killed is (100.685338=4.845 mg/l). Similarly the stress level at which

65% of the insects will be killed is (100.776793 = 5.981 mg/l). Although both values are given in

the table above.

4. Discussion

We have initiated a link “Analysis of Data” at Design Resources Server

(www.iasri.res.in/design) to provide steps of analysis of data generated from designed

experiments by using statistical packages like SAS, SPSS, MINITAB, and SYSTAT, MS-

SAS for Statistical Procedures

EXCEL etc. For details and live examples one may refer to the link Analysis of data at

http://www.iasri.res.in/design/Analysis%20of%20data/Analysis%20of%20Data.html.

How to see SAS/STAT Examples?

One can learn from the examples available at

http://support.sas.com/rnd/app/examples/STATexamples.html

How to use HELP?

Help SAS help and Documentation Contents Learning to use SAS Sample SAS

Programs SAS/STAT …

5. Strengthening Statistical Computing for NARS

NAIP Consortium on Strengthening Statistical Computing for NARS (www.iasri.res.in/sscnars)

targets at providing

‐ research guidance in statistical computing and computational statistics and creating sound

and healthy statistical computing environment

‐ Providing advanced, versatile, and innovative and state-of the art high end statistical

packages to enable them to draw meaningful and valid inferences from their research.

The efforts also involve designing of intelligent algorithms for implementing statistical

techniques particularly for analysing massive data sets, simulation, bootstrap, etc.

The objectives of the consortium are:

‐ To strengthen the high end statistical computing environment for the scientists in NARS;

‐ To organize customized training programmes and also to develop training modules and

manuals for the trainers at various hubs; and

‐ To sensitize the scientists in NARS with the statistical computing capabilities available

for enhancing their computing and research analytics skills.

This consortium has provided the platform for closer interactions among all NARS

organizations.

Capacity Building

For capacity building of researchers in the usage of high end statistical computing facility and

statistical techniques,

‐ 209 trainers have been trained through 30 working days training programmes;

‐ 2166 researchers have been trained through 104 training programmes of one week duration

each in the usage.

The capacity building efforts have paved the way for publishing research papers in the high

impact factor journals.

Indian NARS Statistical Computing Portal

For providing service oriented computing, developed and established Indian NARS Statistical

Computing portal, which is available to NARS users through IP authentication at

http://stat.iasri.res.in/sscnarsportal. Any researcher from Indian NARS may obtain User name

and password from Nodal Officers of their respective NARS organizations, list available at

SAS for Statistical Procedures

www.iasri.res.in/sscnars. It is a paradigm of computing techniques that operate on software-as-

a-service). There is no need of installation of statistical package at client side. Following 24

different modules of analysis of data are available on this portal, which have been classified

into four broad categories as

Basic Statistics

• Descriptive Statistics

• Univariate Distribution Fitting

• Test of Significance based on t-test

• Test of Significance based on Chi-square test

• Correlation Analysis

• Regression Analysis

Designs of Experiments

• Completely randomized designs

• Block Designs (includes both complete and incomplete block designs)

• Combined Block Designs

• Augmented Block Designs

• Resolvable Block Designs

• Nested Block Designs

• Row-Column Designs

• Cross Over Designs

• Split Plot Designs

• Split-Split-Plot Designs

• Split Factorial (main A, sub B C) designs

• Split Factorial (main AB, sub CD) designs

• Strip Plot Designs

• Response Surface Designs

Multivariate Analysis

• Principal Component Analysis

• Linear Discriminant Analysis

Statistical Genetics

• Estimation of Heritability from half- sib data

• Estimation of variance-Covariance matrix from Block Designs

The above modules can be used by uploading *.xlsx, *.csv and *.txt files and results can be

saved as *.RTF or *.pdf files. This has helped them in analyzing their data in an efficient

manner without losing any time.

SAS for Statistical Procedures

Requirements of Excel Files during analysis over Indian NARS Statistical Computing

Portal

1. Excel file must have the .xls, .xlsx, .csv or .txt extensions

2. This system will only consider the first sheet of the excel file which has name appearing

first in lexicographic order. It will not analyze the data which lies in subsequent sheets in

excel file.

3. Do not put period (.) or Zero (0) to display missing values in the treatment. It will not

consider as missing. Please leave the missing observations as blank cells.

4. If you are getting some wrong analysis then kindly check your excel file. Go to First

Column, first cell and then press Ctrl+Shift+End. It will select all the filled rows and

columns. If it selects some missing rows and columns then kindly delete those rows and

columns otherwise it will give wrong analysis result.

5. Do not use special characters in the variable/column names. Also variable names should

not start with spaces.

6. Do not use any formatting to the Excel sheet including formats or expressions to the cell

values. It should be data value.

7. If the First row cells has been merged then it will not detect as Column/Variable names.

8. If any rows or columns are hidden then it will be displayed during the analysis.

Basic Statistics

SAS for Statistical Procedures

9. Descriptive Statistics: The data file should contain at least one quantitative analysis

variable.

10. Univariate Distribution Fitting: The data file should contain at least one quantitative

numeric variable.

11. Test of Significance based on t-distribution: The data file should contain at least one

quantitative variable name and one classificatory variable.

12. Chi-Square Test: The data file should contain at least one categorical variable and

weights or frequency counts variable if frequencies are entered in a separate column.

Data may also have classificatory in it.

13. Correlation: The data file should contain at least two quantitative variables.

14. Regression Analysis: The data file should contain at least one Dependent and one

Independent variable.

Design of Experiments

15. Unblock Design: Prepare a data file containing one variable to describe the Treatment

details and at least one response/ dependent variable in the experimental data to be

analyzed. Also, the treatment details may be coded or may have actual names (i.e. data

values, for variable describing treatment column may be in numeric or character). The

maximum length of treatment value is 20 characters. The variables can be entered in any

order.

16. Block Design: Prepare a data file containing two variables to describe the block and

treatment details. There should be at least one response/ dependent variable in the

experimental data to be analyzed. Also, the block/treatment details may be coded or may

have actual names (i.e. data values, for variables describing block and treatment column

may be in numeric or character). The maximum length of treatment value is 20 character.

The variables can be entered in any order. (These conditions are applicable to other

similar experimental designs also)

17. Combined Block Design: The data file should contain three variables to describe

Environment, Block, Treatment variables and at least one Dependent variable.

18. Augmented Block Design: The data file should contain two variables to describe Block

& Treatment variables and at least one Dependent variable. At present, Portal supports

only numeric treatment and block variables for augmented designs. An augmented block

design involves two sets of treatments known as check or control and test treatments. The

treatments should be numbered in such a fashion that the check or control treatments are

numbered first followed by test treatments. For example, if there are 4 control treatments

and 8 test treatments, then the control treatments are renumbered as 1, 2, 3, 4 and tests are

renumbered as 5, 6, 7, 8, 9, 10, 11, 12.

19. Resolvable Block Design: The data file should contain three variables to describe the

Replication, Block, Treatment variables and at least one Dependent/ response variable.

20. Nested Block Design: The data file should contain three variables to describe Block,

SubBlock, Treatment variables and at least one Dependent variable.

21. Row Column Design: The data file should contain three variables to describe Row,

Column, Treatment variables and at least one Dependent variable.

22. Crossover Design: Create a data file with at least 5 variables, one for units, one for

periods, one treatments, one for residual, and one for the dependent or analysis variable.

For performing analysis using the portal, please rearrange the data in the following order:

animal numbers as units; periods can be coded as 1, 2, 3, and so on, treatments as

SAS for Statistical Procedures

alphabets or numbers (coding could be done as follows: for every first period the number

one has assigned (fixed) and for other periods code 1 to 3 are given according to the

treatment received by the unit in the previous period) and residual effect as residual. It

may, however, be noted that one can retain the same name or can code in any other

fashion. A carry-over or residual term has the special property as a factor, or class

variate, of having no level in the first period because the treatment in the first period is

not affected by any residual or carry over effect of any treatment. When we consider the

residual or carryover effect in practice the fact that carry-over or residual effects will be

adjusted for period effects (by default all effects are adjusted for all others in these

analysis). As a consequence, any level can be assigned to the residual variate in the first

period, provided the same level is always used. An adjustment for periods then removes

this part of the residual term. (For details a reference may made to Jones, B. and

Kenward,M.G. 2003. Design and Analysis of Cross Over Trials. Chapman and

Hall/CRC. New York . Pp: 212)

23. Split Plot Design: The data file should contain three variables to describe Replication,

Main Plot, Sub Plot variables and at least one Dependent variable.

24. Split Split Plot Design: The data file should contain four variables to describe

Replication, Main Plot, Sub Plot, and Sub-Sub Plot Treatment variables and at least one

Dependent variable.

25. Split Factorial (Main A, Sub B×C) Plot Design The data file should contain four

variables to describe Replication, Main Plot, Sub Plot(1){levels of factor 1 in sub plot} ,

and Sub Plot(2) ){levels of factor 21 in sub plot} Treatment variables and at least one

Dependent variable.

26. Split Factorial (Main A×B, Sub C×D) Plot Design: Create a data file with at least 6

variables, one for block or replication, one for main plot- treatment factor 1, one main

plot- treatment factor 2, one for subplot- treatment factor 1, one for subplot- treatment

factor 2 and at least one for the dependent or analysis variable. If the data on more than

one dependent variable is collected in the same experiment, the data on all variables may

be entered in additional columns. One may give actual levels used for different factors

applied in main plot-treatment factor 1, main plot- treatment factor 2, subplot- treatment

factor 1 and subplot- treatment factor 2. Please remember that there should not be any

space between a single data value. Main plot- treatment factor 1, main plot- treatment

factor 2, subplot- treatment factor 1, subplot- treatment factor 2 treatments and block

numbers may be coded as 1, 2, 3 and so on. One can have character values also.

27. Strip Plot Design: The data file should contain at least 4 variables to describe

Replication, Horizontal Strip, Vertical Strip variables and at least one Dependent

variable.

28. Response Surface Design: The data file should contain at least one treatment factor

variable and at least one dependent variable

Multivariate Analysis

29. Principal Component Analysis: The data file should contain at least one quantitative

analysis variable.

30. Discriminant Analysis: The data file should contain at least one quantitative analysis

variable and a classificatory variable.

Statistical Genetics

SAS for Statistical Procedures

31. Genetic Variance Covariance: Create a data file with at least 4 variables, one for

blocking variable, one for treatments and at least two analysis variable.

32. Heritability Estimation from Half-Sib Data: The data file should contain at least one

quantitative analysis variable and a classificatory variable.

Other IP Authenticated Services

Following can also be accessed through IP authenticated networks:

Web Report Studio: http://stat.iasri.res.in/sscnarswebreportstudio

BI DashBoard: http://stat.iasri.res.in/sscnarsbidashboard

Web OLAP Viewer: http://sas.iasri.res.in:8080/sscnarswebolapviewer

E-Miner 6.1: http://sas.iasri.res.in:6401/AnalyticsPlatform

E-Miner 7.1: http://stat.iasri.res.in/SASEnterpriseMinerJWS/Status

Accessing SAS E-Miner through URL (IP Authenticated Services)

For Accessing E-miner 6.1 and 7.1 through URLs, following ports should be open

Server Ports

1) Metadata serve

r

8561

2) Object spawner 8581

3) Table Server 2171

4) Remote Server 5091

5) SAS App. Olap Server 5451

6) SAS Deployment Tester Server 10021

7) Analytics Platform Server 6411

8) Framework Server 22031

However, if you are accessing only E-miner 6.1, then following port need not be opened.

Framework Server 22031

Steps for accessing SAS Enterprise Miner 6.1 and SAS Enterprise Miner 7.1 separately

SAS Enterprise Miner 6.1

Pre-requisite:

‐ JRE 1.5 Update 15

‐ If Firewall and proxy has been implemented then kindly open following ports:

Server Ports

1) Metadata server 8561

2) Object spawner 8581

3) Table Server 2171

4) Remote Server 5091

5) SAS App. OLAP Server 5451

6) SAS Deployment Tester Server 10021

7) Analytics Platform Server 6411

Steps to be followed:

‐ If you have installed multiple Java Runtime Environment then

SAS for Statistical Procedures

Go to Control Panel Java Java tab View Keep check on JRE 1.5.0_15 and

Uncheck all others

‐ Check the entry of the sas.iasri.res.in in the host file, if not then open host file

C:\Windows\System32\drivers\etc and edit the host file by entering the IP as shown

below or specify the internal/external IP given by IASRI. Internal IP is to be specified

only at IASRI, New Delhi. All other NARS organizations should specify external IP

only which is: 203.197.217.209 sas.iasri.res.in sas as shown below

‐

‐ Now Go to URL: http://sas.iasri.res.in:6401/AnalyticsPlatform

‐ Click on Launch and then Run

SAS Enterprise Miner 7.1

Pre-requisite:

‐ JRE 1.6 Update 16 or higher

‐ If Firewall and/or proxy has been implemented then kindly open the following ports:

Server Ports

1) Metadata server 8561

2) Object spawner 8581

3) Framework Server 22031

4) Remote Server 5091

5) SAS App. Olap Server 5451

6) SAS Deployment Tester Server 10021

Steps to be followed:

‐ If you have installed multiple Java Runtime Environment then

Go to Control Panel Java Java tab View Keep check on JRE 1.6.0_16 or

higher available version and Uncheck all other

Check the entry of the stat.iasri.res.in in the host file, if not then open host file

C:\Windows\System32\drivers\etc and edit the host file by entering the IP as shown below

or specify the internal/external IP given by IASRI, New Delhi. Internal IP is to be

SAS for Statistical Procedures

specified only at IASRI, New Delhi. All other NARS organizations should specify external

IP only which is: 14.139.56.156 stat.iasri.res.in stat (earlier 203.197.217.221 stat.iasri.res.in

stat) as shown below stat.iasri.res.in stat as shown below

‐ Now Go to URL: http://stat.iasri.res.in/SASEnterpriseMinerJWS/Status

‐ Click on Launch and then Run

Please note: You cannot run both E-Miner 6.1 and E-Miner 7.1 together. If you want to

run JMP 6.1 then JAVA 1.5.0_15 should be available and for running JMP 7.1, JAVA

version 1.6 onwards should be available on your system.

Indian NARS Statistical Computing Portal and other IP authenticated services are best viewed in

Internet Explorer 6 to 8 and Firefox 2.0.0.11 and 3.0.6

Macros Developed

Macros have been developed for some commonly used statistical analysis and made available at

Project Website www.iasri.res.in/sscnars. Following macros have been developed:

1. Analysis of data from Augmented Block designs

http://www.iasri.res.in/sscnars/augblkdsgn.aspx

2. Analysis of data from Split Factorial ( main A, Sub B C) designs

http://www.iasri.res.in/sscnars/spltfctdsgn.aspx

3. Analysis of data from Split Factorial (Main AB, Sub C) designs

http://www.iasri.res.in/sscnars/spltfctdsgnm2s1.aspx

4. Analysis of data from Split Factorial ( main AB, Sub C D) designs

http://www.iasri.res.in/sscnars/spltfactm2s2.aspx

5. Analysis of data from Split Split Plot designs

http://www.iasri.res.in/sscnars/spltpltdsgn.aspx

6. Analysis of data from Strip Plot designs

http://www.iasri.res.in/sscnars/StripPlot.aspx

7. Analysis of data from Strip-Split Plot designs

SAS for Statistical Procedures

http://www.iasri.res.in/sscnars/stripsplit.aspx.

8. Econometric Analysis ((diversity indices, instability index, compound growth rate, Garret

scoring technique and Demand analysis using LA-AIDS model) and available at

http://www.iasri.res.in/sscnars/ecoanlysis.aspx

9. Estimation of heritability along with its standard error from half sib data

http://www.iasri.res.in/sscnars/heritability.aspx

10. Generation of Polycross designs

http://www.iasri.res.in/sscnars/polycrossdesign.aspx

11. Generation of TFNBCB designs

http://www.iasri.res.in/sscnars/TFNBCBdesigns.aspx

How to see updated version of reference manual?

Reference manual is updated regularly and updated version may be downloaded from

http://www.iasri.res.in/sscnars/contentmain.htm

How to Renew License Files for SAS 9.2M2?

1. Go to http://stat.iasri.res.in/sscnarsportal/public

2. Click on SAS License Downloads 2011-12. It will redirect to New Page. It will start the

Download of the SAS_Licenses11-12.zip. If it does not start automatically, then it would

show Yellow Bar below the URL bar. Click on the Yellow Bar and Select Download

File. Dialog box showing Open/Save/Cancel would appear. Click on Save and Browse the

desired Location for saving the file.

3. Click on Portal Page link which is on top of the Page to go back to the main page.

4. Click on How to apply License Files?. Again it will redirect to the New Page and will start the

Download Renew_the_licenses_for_SAS92_JMP8_JMPGenomics4.doc If it does not start

automatically, then it would show Yellow Bar below the URL bar. Click on the Yellow Bar

and Select Download File. Dialog box showing Open/Save/Cancel would appear. Click on

Save and Browse the desired Location for saving the file.

You can also follow the following links for renewal of SAS Licenses:

http://support.sas.com/kb/31/187.html

Following link is only for Windows 7 and Windows Vista:

http://support.sas.com/kb/31/290.html

SAS 9.3

In SAS 9.3, the default destination in the SAS windowing environment is HTML, and ODS

Graphics is enabled by default. These new defaults have several advantages. Graphs are

integrated with tables, and all output is displayed in the same HTML file using a new style. This

new style, HTML Blue, is an all-color style that is designed to integrate tables and modern

statistical graphics. The default settings in the Results tab are as follows:

The Create listing check box is not selected, so LISTING output is not created.

The Create HTML check box is selected, so HTML output is created.

The Use WORK folder check box is selected, so both HTML and graph image files are

saved in the WORK folder (and not your current directory).

The default style, HTMLBlue, is selected from the Style drop-down list.

SAS for Statistical Procedures

The Use ODS Graphics check box is selected, so ODS Graphics is enabled.

Internal browser is selected so results are viewed in an internal SAS browser

We can view and modify the default settings by selecting

ToolsOptionsPreferencesResult Tab from the menu at the top of the SAS window

usually known as TOPR pronounced "topper". Snap shot is as under.

To get SAS listing instead of HTML, Select check box Create listing option and deselect

Create HTML check box.

Once HTML checkbox is deselected "Use work folder " get deselected automatically.

Select View results as they are generated , if ODS Graphics is not required as default

output. In many cases, graphs are an integral part of a data analysis. If we do not need

graphics, ODS Graphics should be disabled, which will improve the performance of our

program in terms of time and memory. One can disable and re-enable ODS Graphics in

our SAS programs with the ODS GRAPHICS OFF and ODS GRAPHICS ON statements.

References

Littel, R.C., Freund, R.J. and Spector, P.C. (1991). SAS System for Linear Models, Third

Edition. SAS Institute Inc.

Searle, S.R. (1971). Linear Models. John Wiley & Sons, New York.

Searle, S.R., Casella, G and McCulloch, C.E. (1992). Analysis of Variance Components. John

Wiley & Sons, New York.

www.sas.com

www.support.sas.com

www.iasri.res.in/design

www.iasri.res.in/sscnars

http://stat.iasri.res.in/sscnarsportal