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```                         WESTERN MICHIGAN UNIVERSITY
COMPUTER CENTER

LIBRARY PROGRAM #1.9.5
CALLING NAME:  ONEAOV
PROGRAMMED BY:  RUSSELL R. BARR III
PREPARED BY:  RUSSELL R. BARR III
STATISTICAL CONSULTANT:  DR. MICHAEL STOLINE
APPROVED BY:  JACK R. MEAGHER
DATE:  MARCH, 1973 (VERSION 1)

ONE-WAY ANALYSIS OF VARIANCE (UNBALANCED)

1.0  PURPOSE
2.3  STATISTICAL ANALYSIS
3.0  DATA INPUT METHODS AND EXAMPLES
4.0  HOW TO HANDLE MISSING DATA
5.0  LIMITATIONS
6.0  SPECIAL SYMBOLS
7.0  PROGRAM QUESTIONS AND HOW TO ANSWER THEM
8.0  METHOD OF USE AND SAMPLE RUNS

1.0  PURPOSE

ONEAOV IS VERY SIMILAR TO BASIC STATISTICS (BSTAT) #1.1.2.  ONEAOV ALLOWS ONE
TO OBTAIN SEVERAL IDENTICAL ANALYSES ON MORE THAN ONE VARIABLE AND ALSO ALLOWS
ONE THE ABILITY TO SPECIFY DIFFERENT GROUP COMPOSITIONS.

SUPPOSE THAT 5 VARIABLES ARE OBSERVED ON EACH OF N SUBJECTS AND THAT EACH
SUBJECT BELONGS TO ONE AND ONLY ONE OF G DISTINCT GROUPS.

ONEAOV YIELDS DESCRIPTIVE MEASURES, T-TESTS, CONFIDENCE INTERVALS, AND ONE-WAY
AOV'S FOR MAKING STATISTICAL INFERENCES ABOUT THE G GROUP MEANS.  A SEPARATE
ANALYSIS IS GIVEN FOR EACH OF THE K VARIABLES.  MORE DETAILS ABOUT THE
STATISTICAL ANALYSES ARE GIVEN IN SECTION 2.0.

GROUPS MAY BE CONSTRUCTED BY EITHER:

(A)  SPECIFYING GROUP MEMBERSHIP AS THE DATA IS ENTERED (DATA INPUT
METHOD 1), OR

(B)  SPECIFYING ONE OF THE K VARIABLES AS A BREAKDOWN VARIABLE WITH G
BREAKDOWN LIMITS FOR THE PURPOSE OF DEFINING THE G GROUPS (DATA INPUT
METHOD 2).

MISSING DATA CAN BE HANDLED BY SPECIFYING A MISSING DATA SYMBOL FOR EACH
VARIABLE.  SEE SECTION 3.0 FOR DETAILED DESCRIPTIONS OF THE DATA INPUT METHODS
AND SECTION 4.0 FOR THE USE OF THE MISSING DATA SYMBOLS.

ONEAOV IS DESIGNED TO EFFECTIVELY ANALYZE QUESTIONNAIRES WHEN SIMILAR ANALYSES
ARE WANTED ON EACH QUESTION OF THE QUESTIONNAIRE.  FOR EXAMPLE, SUPPOSE A
QUESTIONNAIRE CONSISTS OF 15 QUESTIONS AND THE SAMPLE OF PEOPLE RESPONDING TO
THE QUESTIONNAIRE CAN BE CLASSIFIED INTO G GROUPS USING EITHER A USER SUPPLIED
GROUP STRUCTURE (DATA INPUT METHOD 1) OR USING AGE LEVELS, SEX LEVELS, EDUCATION
LEVELS, INCOME LEVELS, OR SOME OTHER MEASURE OBTAINED FROM THE QUESTIONNAIRE
ITSELF TO DETERMINE THE GROUP STRUCTURE (DATA INPUT METHOD 2).  A SEPARATE
ONE-WAY AOV IS WANTED TO COMPARE THE GROUP MEAN RESPONSES FOR EACH INDIVIDUAL
QUESTION.

2.0  STATISTICAL ANALYSIS

SUPPOSE THAT THE N SUBJECT ARE CLASSIFIED INTO G GROUPS (G >= 2) WITH THE
FOLLOWING GROUP SAMPLE SIZES.

GROUP NUMBER            GROUP SAMPLE SIZE

1                        N(1)
2                        N(2)
.                        .
.                        .
.                        .
G                        N(G)
-----                    -------

N = N(1) + N(2) + .. + N(G)

EACH SUBJECT HAS K MEASUREMENTS, ONE FOR EACH VARIABLE, AND EACH SUBJECT BELONGS
TO ONE AND ONLY ONE GROUP.  A SEPARATE ANALYSIS IS GENERATED FOR EACH VARIABLE
AND EACH OF THE K ANALYSES AUTOMATICALLY INCLUDES:

(I)  MEAN(G), VAR(G), AND STANDARD DEVIATIONS S(G) FOR EACH
OF THE G GROUPS.  (G = 1,...,G),

(II)  BARTLETT'S TEST STATISTIC TO TEST THE EQUALITY OF THE G GROUP
POPULATION VARIANCES.  A CHI-SQUARE PROBABILITY VALUE P IS ALSO
GIVEN WHICH HAS G-1 DEGREES OF FREEDOM.  IF P <= ALPHA, THEN WE CONCLUDE
THAT THE POPULATION VARIANCES ARE SIGNIFICANTLY DIFFERENT AT
LEVEL ALPHA.

CAUTION:  GENERALLY IF P < .05 FOR BARTLETT'S TEST THEN INTERPRET WITH EXTREME
CAUTION THE ONE-WAY AOV AND TWO-SAMPLE T-TESTS THAT FOLLOW, UNLESS N(1) = N(2) =
... = N(G).

IT IS GENERALLY AGREED THAT THE BEST SAFEGUARD AGAINST THE LACK OF EQUALITY OF
POPULATION VARIANCES IS TO DESIGN YOUR EXPERIMENT WITH BALANCED OR EQUAL SIZED
SAMPLES.

(III)  A ONE-WAY AOV (ANALYSIS OF VARIANCE) TABLE WHICH IS USED TO TEST
THE EQUALITY OF POPULATION MEANS.  AN F PROBABILITY VALUE P IS ALSO
GIVEN WITH G-1 AND N-K * DEGREES OF FREEDOM.  IF P <= ALPHA, THEN WE
CONCLUDE THAT THE POPULATION MEANS ARE SIGNIFICANTLY DIFFERENT AT
LEVEL ALPHA.

IN ADDITION, THE FOLLOWING OPTIONS ARE AVAILABLE:

(IV)  A T-STATISTIC IS USED TO TEST THE NULL HYPOTHESIS H(O):MU(I) =MU(J)
FOR EACH PAIR OF MEANS MU(I) AND MU(J).  A T PROBABILITY VALUE P IS
GIVEN AND IF P <= ALPHA, THEN CONCLUDE THAT MU(I) NOT EQUAL MU(J) AT
LEVEL ALPHA.  FOR ONE SIDED ALTERATIONS MU(I) < MU(J) OR MU(I) > MU(J) USE
P = (T PROBABILITY VALUE)/2,

*USE N-K-M INSTEAD OF N-K DEGREES OF FREEDOM WHEN THERE ARE M MISSING
OBSERVATIONS FROM ALL OF THE G GROUPS OF THE VARIABLE BEING ANALYZED.

(V)  FOR EACH PAIR OF MEANS MU(I) AND MU(J) A 95% CONFIDENCE INTERVAL
FOR MU(I) - MU(J) IS GIVEN,

(VI)  THE USER HAS TWO CHOICES FOR THE ERROR TERM IN THE T-STATISTICS USED
FOR (IV) AND (V):

(A)  THE POOLED ERROR TERM FROM GROUP I AND J DATA ALONE WITH
N(I) + N(J) -2** DEGREES OF FREEDOM WHICH YIELDS:

** SUBTRACT ONE DEGREE OF FREEDOM FROM N(I) + N(J) - 2 FOR EACH MISSING
FROM GROUPS K AND J.

T=(MEAN(I)-MEAN(J))/SQRT(A*B)
WHERE
A=((N(I) -1)*VAR(I)+ (N(J) - 1)*VAR(J))/(N(I)+N(J)-2)

B=(N(I)+N(J))/(N(I)*N(J))

(B)  THE POOLED MEAN SQUARE ERROR TERM FROM ALL G GROUPS

(N(1) - 1)*VAR(1)  +...+ (N(G) -1)*VAR(G)
MSE = ----------------------------------------------
N-K

WHICH IS USED IN THE ONE-WAY AOV IN (III).

HENCE:              T=(MEAN(I) - MEAN(J))/SQRT(MSE*(1/N(I)+1/N(J)))
WITH
(N-K) DEGREE OF
FREEDOM.
3.0  DATA INPUT METHODS

THE USER MAY SPECIFY ONE OF TWO METHODS FOR ENTERING DATA.  FOR EITHER METHOD
THE USER MUST SPECIFY K, THE NUMBER OF VARIABLES.  IN ADDITION A MISSING
DATA SYMBOL MAY BE SPECIFIED FOR EACH VARIABLE.  (SEE SECTION 4.0).

DATA INPUT METHOD 1

IF THE GROUP COMPOSITION OR STRUCTURE IS KNOWN PRIOR TO DATA ENTRY, THEN USE
METHOD 1 TO ENTER YOUR DATA.  THE USER SPECIFIES G, THE NUMBER OF GROUPS, AND
THE GROUP SAMPLE SIZES N(1),N(2),...,N(G).  LET X(IJL) BE THE LTH OBSERVATION
FROM THE ITH GROUP OF VARIABLE J.  (I=1,...,G,J=1,...,K, AND L = 1,...,N(I))

EXAMPLE 1:  FOR G=12 GROUPS AND K=15 VARIABLES, THE DATA IS ENTERED AS FOLLOWS:

HOW MANY GROUPS? 12<CR>
ENTER NUMBER OF ELEMENTS PER GROUP (10 PER LINE)
N(1),N(2),...,N(10)<CR>
N(11),N(12)<CR>
ENTER DATA FOR GROUP 1
X(1,1,1),X(1,2,1), ..., X(1,10,1)
X(1,11,1)...,X(1,15,1)
X(1,1,2),X(1,2,2), ..., X(1,10,2)
.          .         .
.          .         .
.          .         .
X(1,1,N(1)),X(1,2,N(1)), ..., X(1,10,N(1))
X(1,11,N(1)),..., X(1,15,N(1))
ENTER DATA FOR GROUP 2
X(2,1,1),X(2,2,1), ..., X(2,10,1)
X(2,11,1), ..., X(2,15,1)
X(2,1,2),X(2,2,2), ..., X(2,10,2)
.          .         .
.          .         .
.          .         .
X(2,1,N(2)),X(2,2,N(2)), ..., X(2,10,N(2))
X(2,11,N(2)), ..., X(2,15,N(2))

(DATA FOR GROUPS 3-11 ARE ENTERED IN SIMILAR MANNER)

ENTER DATA FOR GROUP 12
X(12,1,1),X(12,2,1), ..., X(12,10,1)
X(12,11,1), ..., X(12,15,1)
.         .
.         .
.         .
X(12,1,N(12)),X(12,2,N(12)), ..., X(12,10,N(12))
X(12,11,N(12)), ..., X(12,15,N(12))

HENCE THE DATA IS ENTERED IN THE FOLLOWING ORDER FOR DATA INPUT
METHOD 1:

1-ST SUBJECT IN GROUP 1 ON ALL VARIABLES, 2-ND SUBJECT IN GROUP 1
ON ALL THE VARIABLES, ETC.  THEN 1-ST SUBJECT IN GROUP 2 ON ALL THE
VARIABLES, 2-ND SUBJECT IN GROUP 2 ON ALL THE VARIABLES, ETC.  DO THIS
FOR ALL THE GROUPS.

DATA INPUT METHOD 2

THE GROUP STRUCTURE IS NOT DEFINED UNDER DATA INPUT METHOD 2 UNTIL AFTER THE
DATA IS ENTERED.  THE USER SPECIFIES ONE OF THE K VARIABLES AS A BREAKDOWN
VARIABLE, SAY VARIABLE I.  HENCE EITHER I = 1, I = 2, ..., OR I = K.  THEN G
BREAKDOWN LIMITS:

B(1)<B(2)<...<B(G)       (G<=10)
ARE ENTERED SEPARATED BY COMMAS.

LET X(JL) BE THE LTH OBSERVATION ON VARIABLE J FOR J=1,...,K AND L=1,...,N.

THE DATA IS ENTERED:

VARIABLES ARE COLUMNS

X(1,1),X(2,1), ..., X(K,1)<CR>             OBSERVATION 1
X(1,2),X(2,2), ..., X(K,2)<CR>             OBSERVATION 2         THESE ARE ROWS.
.      .            .                         .
.      .            .                         .
.      .            .                         .
X(1,N),X(2,N), ..., X(K,N)<CR>             OBSERVATION N
^Z

THE FOLLOWING RULES ARE OBSERVED FOR DATA INPUT METHOD 2:

(I)  THE DATA IS ENTERED IN THE ORDER; VARIABLE AND THEN OBSERVATION,
(II)   ^Z (CONTROL Z) SIGNALS THE END OF DATA, AND
(III)  FOR K>10, ENTER THE DATA AS FOLLOWS.  (FOR K=15)

X(1,1),X(2,1), ..., X(10,1)<CR>
X(11,1), ..., X(15,1)<CR>
X(1,2)
.
.
.

THE G GROUPS ARE DEFINED AS FOLLOWS FROM THE G BREAKDOWN LIMITS B(1)  B(2)
...  B(G) DEFINED ON VARIABLE I.

IF THE JTH OBSERVATION ON VARIABLE I IS SUCH THAT:

(1)  X(IJ)< B(1), THEN OBSERVATION J IS IN GROUP 1
(2)  B(1)<X(IJ)<=B(2), THEN OBSERVATION J IS IN GROUP 2.
.
.
.
(G)  B(G-1) < X(IJ) <= B(G), THEN OBSERVATION J IS IN GROUP G.

IF X(IJ)>B(G), THEN OBSERVATION J IS NOT CLASSIFIED INTO ANY ONE OF THE G
GROUPS.  THEREFORE, ANY DATA POINT OBSERVED ON THE BREAKDOWN VARIABLE WHICH IS
LARGER THAN THE LARGEST BREAKDOWN LIMIT IS NOT CLASSIFIED TO ANY GROUP.

EXAMPLE 2  CONSIDER THE FOLLOWING DATA CONSISTING OF N=10 OBSERVATIONS AND K=3
VARIABLES:

VARIABLE 1        VARIABLE 2       VARIABLE 3                OBSERVATION

1                 1                7                          1
1                 6                8                          2
2                 7                7                          3
3                 5                7                          4
7                12                8                          5
2                 1                1                          6
1                 2                1                          7
6                 5                6                          8
8                 7               17                          9
10                 8                3                         10

LETTING VARIABLE 2 BE THE BREAKDOWN VARIABLE WITH THE G=3 BREAKDOWN LIMITS 2,6,
AND 8, WE NOTE THAT THE OBSERVATIONS ARE CLASSIFIED AS FOLLOWS:

OBSERVATIONS           GROUP

1,6,7                    1
2,4,8                    2
3,9,10                   3
5                    NOT CLASSIFIED

THIS IS DONE ON THE TERMINAL AS FOLLOWS:

HOW MANY VARIABLES? 3<CR>
ENTER METHOD OF INPUT (1 OR 2) 2<CR>
WHICH VARIABLE IS THE BREAKDOWN VARIABLE? 2<CR>
ENTER BREAKDOWN LIMITS (MAX 10)

2,6,8<CR>
ENTER DATA
1,1,7<CR>
1,6,8<CR>
2,7,7<CR>
3,5,7<CR>
7,12,8<CR>
2,1,1<CR>
1,2,1<CR>
6,5,6<CR>
8,7,17<CR>
10,8,3<CR>
^Z

WHEN THE DATA HAS BEEN ENTERED BY USING DATA INPUT METHOD 2, THE SAME DATA MAY
BE USED AGAIN.  THIS IS ACCOMPLISHED AS FOLLOWS:

WHEN THE PROCESSING FOR THE PRESENT DATA INPUT IS COMPLETED, THE COMPUTER
PRINTS INPUT?

AT THIS POINT THE USER HAS 3 CHOICES:

CHOICE                            METHOD

1.  ENTER NEW DATA                    INPUT? (<CR> OR FILENAME<CR>)
2.  TERMINATE THE PROGRAM             INPUT?  FINISH<CR>
3.  USE THE PREVIOUS DATA AGAIN       INPUT?  SAME<CR> *

*  IF DATA WAS ENTERED USING METHOD 1, THE ONLY VARIATION IN ANALYSIS POSSIBLE
WOULD BE THE TYPE OF POOLED MEAN SQUARE TO BE USED (SEE SECTION 7.0, LINE 16).

THE USER MAY WANT TO USE THE SAME DATA AGAIN WITH EITHER THE SAME BREAKDOWN

VARIABLE, BUT DIFFERENT BREAKDOWN LIMITS, OR A NEW BREAKDOWN VARIABLE.

THE FOLLOWING EXAMPLE ILLUSTRATES A REPEATED USE OF THE SAME INSTRUCTION.

EXAMPLE 3

SUPPOSE THAT AN ANALYSIS OF N=10 OBSERVATIONS ON 5 VARIABLES FROM A
QUESTIONNAIRE IS WANTED ON VARIOUS GROUPS DEFINED BY THE LEVELS OF INCOME AND
SEX.  ASSUME THE DATA:

V(I) = VARIABLE I

OBSERVATION     V1   V2   V3   V4   V5     LEVEL            SEX

1                                      LOW               MALE
2                                      MEDIUM          FEMALE
3                                      HIGH            FEMALE
4                                      MEDIUM          MALE
5                                      LOW             MALE
6                                      HIGH            MALE
7                                      MEDIUM          FEMALE
8                                      HIGH            MALE
9                                      LOW             FEMALE
10                                      HIGH            FEMALE

SUPPOSE THAT AN ANALYSIS OF VARIANCE (AOV) IS WANTED FOR EACH OF THE 5
VARIABLES IN DIFFERENT SITUATIONS:

(1)  COMPARING THE TWO LEVELS OF SEX,
(2)  COMPARING THE THREE LEVELS OF INCOME,
(3)  COMPARING THE AVERAGE OF LOW AND HIGH INCOME AGAINST THE MEDIUM
INCOME RESPONSES, AND
(4)  COMPARING LOW INCOME MALE AGAINST LOW INCOME FEMALE RESPONSES.

THIS IS ACCOMPLISHED BY INTRODUCING THREE NEW BREAKDOWN VARIABLES DEFINED AS
FOLLOWS:

VARIABLE
6  (SEX)               CODE:  1=MALE        2=FEMALE
7  (INCOME)            CODE:  1=HIGH,       2=LOW         3=MEDIUM
8  (SEX AND INCOME)    CODE:  1=HIGH INCOME MALE,2=HIGH INCOME FEMALE
3=OTHERS

TO OBTAIN THE DESIRED ANALYSIS WE USE THE FOLLOWING BREAKDOWN VARIABLES AND
LIMITS:

PROBLEM                       BREAKDOWN VARIABLE           BREAKDOWN LIMIT

1                                  6                         1,2
2                                  7                         1,2,3
3                                  7                         2,3
4                                  8                         1,2
----                               ----                      ---------

VARIABLE 7 IS CODED WITH HIGH INCOME = 1, LOW INCOME = 2, AND MEDIUM INCOME = 3
SO THAT A SINGLE BREAKDOWN VARIABLE CAN BE USED FOR BOTH PROBLEMS 2 AND 3.
NOTE THAT FOR PROBLEM 3, TWO GROUPS ARE DEFINED ON VARIABLE 7 WITH ONE GROUP
(HIGH INCOME, LOW INCOME) <= 2 AND ANOTHER GROUP:  2 < (MEDIUM INCOME) <= 3.

FOR PROBLEM 4 WE USE BREAKDOWN VARIABLES 8 WITH TWO GROUPS:  (HIGH INCOME
MALE) <= 1 AND 1 < (HIGH INCOME FEMALE) < 2 ALL OTHERS ARE NOT INCLUDED IN THE
ANALYSIS SINCE 3=(CODE FOR OTHERS) IS GREATER THAN 2=(LARGEST BREAKDOWN LIMIT).
THIS IS DONE ON THE TERMINAL AS FOLLOWS:

HOW MANY VARIABLES? 8<CR>
ENTER METHOD OF DATA INPUT (1 OR 2)  2<CR>
WHICH VARIABLE IS THE BREAKDOWN VARIABLE?  6<CR>
ENTER BREAKDOWN LIMITS (MAX 10)
1,2<CR>
ENTER DATA

V1,   V2,   V3,   V4,   V5,   V6,   V7,   V8,

1     2     3
2     3     3
2     1     1
1     3     3
1     2     3
1     1     1
2     3     3
1     1     1
2     2     3
2     1     2
^Z
INPUT? SAME<CR>
ENTER OUTPUT IDENTIFICATION, IF DESIRED
RUN 2<CR>
WHICH VARIABLE IS THE BREAKDOWN VARIABLE? 7<CR>
ENTER BREAKDOWN LIMITS (MAX 10)
1,2,3<CR>
.
.
.
INPUT? SAME<CR>
ENTER OUTPUT IDENTIFICATION, IF DESIRED
RUN 3<CR>
WHICH VARIABLE IS THE BREAKDOWN VARIABLE? 7<CR>
ENTER BREAKDOWN LIMITS (MAX 10)
2,3<CR>
.
.
.
INPUT? SAME<CR>
ENTER OUTPUT IDENTIFICATION, IF DESIRED
RUN 4<CR>
WHICH VARIABLE IS THE BREAKDOWN VARIABLE 8<CR>
ENTER BREAKDOWN LIMITS (MAX 10)
1,2<CR>
.
.
.
INPUT? FINISH<CR>

4.0  HOW TO HANDLE MISSING DATA

IF THERE ARE MISSING OBSERVATIONS FROM SOME OF THE VARIABLES, THEN THE USER
MAY SPECIFY K MISSING DATA SYMBOLS M(1),M(2),...M(K), ONE FOR EACH VARIABLE,
WHERE M(I) IS THE MISSING DATA SYMBOL FOR THE ITH = VARIABLE.  WHENEVER MISSING
DATA SYMBOLS ARE USED:

(I)  ONE MUST BE SPECIFIED FOR EACH OF THE K VARIABLES,
(II)  THEY ARE ENTERED ONE AT A TIME SEPARATED BY COMMAS WITH NO MORE
THAN 10 PER LINE,
(III)  THE MISSING DATA SYMBOLS MUST BE INTEGER OR FLOATING POINT NUMBER
CONSTANTS AND MAY BE POSITIVE OR NEGATIVE.
(IV)  WHENEVER THE SYMBOL M(I) APPEARS AS AN OBSERVATION FOR THE ITH
VARIABLE, THEN THAT OBSERVATION IS IGNORED FOR ALL SUBSEQUENT
CALCULATIONS AND THE GROUP SAMPLE SIZE IS REDUCED BY ONE.
(V)  SEE LINES 10 AND 11 OF SECTION 7.0 FOR FURTHER DETAILS OF TERMINAL
USE OF MISSING DATA SYMBOLS.

5.0 LIMITATIONS

1.  THE NUMBER OF GROUPS (G) AND VARIABLES (V) MAY NOT EXCEED CORMAX MINUS 14000
AS COMPUTED BY THIS FORMULA:  3GV+2G+3V.  CORMAX IS NORMALLY NOT LESS THAN
35000.
2.  A MAXIMUM OF 3 LINES OF FORMAT, IF OBJECT TIME FORMAT IS USED.
3.  ONLY F-TYPE FORMAT IS ALLOWED.
4.  NO LIMIT ON NUMBER OF OBSERVATIONS PER GROUP.
5.  NO MORE THAN 10 BREAKDOWN VALUES IS ALLOWED.

6.0  PROGRAM QUESTIONS AND HOW TO ANSWER THEM

THE FOLLOWING QUESTIONS ARE GIVEN IN THE ORDER ENCOUNTERED DURING A PROGRAM
RUN.

LINE 1  OUTPUT?
LINE 2  INPUT?

LINES 1 AND 2 DEFINE WHERE THE USER INTENDS TO WRITE HIS OUTPUT FILE (LINE 1)
AND FROM WHERE THE USER EXPECTS TO READ HIS INPUT DATA (LINE 2).  SEE NOTE (2)
BELOW FOR OTHER INPUT OPTIONS.  THE NEXT QUESTION IS LINE 3.

A PROPER RESPONSE TO EACH OF THESE QUESTIONS CONSISTS OF THREE BASIC PARTS:
A DEVICE, A FILENAME, AND A PROJECT-PROGRAMMER NUMBER.

THE GENERAL FORMAT FOR THESE THREE PARTS IS AS FOLLOWS:

DEV:FILE.EXT[PROJ,PROG]

1)  DEV:  ANY OF THE FOLLOWING DEVICES ARE APPROPRIATE WHERE INDICATED:

DEVICE LIST            DEFINITION            STATEMENT USE

TTY:                TERMINAL              INPUT OR OUTPUT
DSK:                DISK                  INPUT OR OUTPUT
LPT:                LINE PRINTER          OUTPUT ONLY
DTA0:               DECTAPE 0             INPUT OR OUTPUT
DTA1:               DECTAPE 1             INPUT OR OUTPUT
DTA2:               DECTAPE 2             INPUT OR OUTPUT
DTA3:               DECTAPE 3             INPUT OR OUTPUT
DTA4:               DECTAPE 4             INPUT OR OUTPUT
DTA5:               DECTAPE 5             INPUT OR OUTPUT
DTA6:               DECTAPE 6             INPUT OR OUTPUT
DTA7:               DECTAPE 7             INPUT OR OUTPUT
MAT0:               MAGNETIC TAPE 0       INPUT OR OUTPUT
MTA1:               MAGNETIC TAPE 1       INPUT OR OUTPUT

INPUT MAY NOT BE DONE FROM THE LINE PRINTER NOR MAY OUTPUT GO THE THE CARD

2)  FILE.EXT IS THE NAME AND EXTENSION OF THE FILE TO BE USED.  THIS PART OF
THE SPECIFICATION IS USED ONLY IF DISK OR DECTAPE IS USED.

3)  [PROJ,PROG]  IF A DISK IS USED AND THE USER WISHES TO READ A FILE IN ANOTHER
PERSON'S DIRECTORY, HE MAY DO SO BY SPECIFYING THE PROJECT-PROGRAMMER
NUMBER OF THE DIRECTORY FROM WHICH HE WISHES TO READ.  THE PROJECT NUMBER
AND THE PROGRAMMER NUMBER MUST BE SEPARATED BY A COMMA AND ENCLOSED IN
BRACKETS.  OUTPUT MUST GO TO YOUR OWN AREA.

EXAMPLE:

OUTPUT?  LPT/2
INPUT?   DSK:DATA.DAT[71171,71026]

IN THE EXAMPLE, TWO COPIES OF THE OUTPUT ARE TO BE PRINTED BY THE HIGH SPEED
LINE PRINTER.  THE INPUT DATA IS A DISK FILE OF NAME DATA.DAT IN USER DIRECTORY
[71171,71026].

DEFAULTS:

1)  IF NO DEVICE IS SPECIFIED BUT A FILENAME IS SPECIFIED THE DEFAULT DEVICE
WILL BE DSK:.

2)  IF NO FILENAME IS SPECIFIED AND A DISK OR DECTAPE IS USED THE DEFAULT ON
INPUT WILL BE FROM INPUT.DAT; ON OUTPUT IT WILL BE OUTPT.DAT.

3)  IF THE PROGRAM IS RUN FROM THE TERMINAL AND NO SPECIFICATION IS GIVEN
(JUST A CARRIAGE RETURN) BOTH INPUT AND OUTPUT DEVICES WILL BE THE
TERMINAL.

4)  IF THE PROGRAM IS RUN THROUGH BATCH AND NO SPECIFICATION IS GIVEN, (A
BLANK CARD) THE INPUT DEVICE WILL BE CDR: AND THE OUTPUT DEVICE WILL BE LPT:

5)  IF NO PROJECT-PROGRAMMER NUMBER IS GIVEN, THE USER'S OWN NUMBER WILL BE
ASSUMED.

NOTE:  (1)  IF LPT: IS USED AS AN OUTPUT DEVICE MULTIPLE COPIES MAY BE OBTAINED
BY SPECIFYING LPT:/N WHERE N REFERS TO THE NUMBER OF COPIES DESIRED.

(2)  THE FOLLOWING TWO OPTIONS ARE NOT APPLICABLE FOR THE FIRST DATA SET,
I.E., THEY ARE APPLICABLE ONLY WHEN THE PROGRAM BRANCHES BACK TO
LINE 2 UPON FIRST COMPLETION OF LINES 1-16.

(A)  SAME OPTION

UPON RETURNING FROM LINE 16 IF THE SAME DATA IS TO BE USED
AGAIN, SIMPLY ENTER "SAME<CR>", OTHERWISE, EITHER USE THE
FINISH OPTION OR ENTER ANOTHER FILENAME ETC.  INPUT FROM THE
TERMINAL IS INCLUDED IN THIS OPTION.

(B)  FINISH OPTION

THE USER MUST ENTER "FINISH<CR>" TO BRANCH OUT OF THE PROGRAM.
FAILURE TO DO SO MIGHT RESULT IN LOSING THE ENTIRE OUTPUT
FILE.

LINE 3  ENTER OUTPUT IDENTIFICATION, IF DESIRED

ENTER A LINE OF UP TO 80 CHARACTERS TO BE PRINTED ABOVE YOUR OUTPUT.  IF YOU
WANT NO HEADING TYPE "<CR>" ON THE TERMINAL OR INSERT A BLANK CARD ON BATCH
JOBS.  IF "SAME" OPTION IS USED FOR TERMINAL, THE NEXT QUESTION IS LINE 7,
OTHERWISE LINE 4.

LINE 4  FORMAT:  (F-TYPE ONLY)

THERE ARE 3 OPTIONS AVAILABLE FOR THE FORMAT, NAMELY:

(A)  STANDARD FORMAT OPTION

UNLESS OTHERWISE SPECIFIED, THE PROGRAM ASSUMES THE STANDARD OPTION.
IN THIS OPTION, THE DATA ARE ARRANGED IN GROUPS OF 10 PER LINE, TWO
VALUES BEING SEPARATED BY A COMMA.

TO USE THIS OPTION, SIMPLY TYPE IN "<CR>" ON TERMINAL JOBS OR USE A
BLANK CARD FOR BATCH JOBS.

(B)  OBJECT TIME FORMAT OPTION

IF THE DATA IS SUCH THAT A USER'S OWN FORMAT IS REQUIRED, SIMPLY
ENTER A LEFT PARENTHESIS FOLLOWED BY THE FIRST FORMAT SPECIFICATION,
A COMMA AND THE SECOND SPECIFICATION, ETC.  WHEN YOU FINISH ENTER A
RIGHT PARENTHESIS, AND THEN A CARRIAGE RETURN.  THERE CAN BE A
MAXIMUM OF 3 LINES FOR THE FORMAT, EACH LINE BEING 80 COLUMNS LONG.

NOTE THAT THE FORMAT SPECIFICATION LIST MUST USE THE FLOATING
POINT (F-TYPE) NOTATION AND MUST CONTAIN SPECIFICATION FOR EACH OF
THE VARIABLES.  THE SPECIFICATIONS FOR THE FORMAT ITSELF ARE THE
SAME AS FOR THE FORTRAN IV FORMAT STATEMENT.

(C)  SAME OPTION

IF THE FORMAT (STANDARD OR OBJECT TIME) TO BE USED IS THE SAME AS
THAT USED PREVIOUSLY, SIMPLY ENTER "SAME".

LINE 5  HOW MANY VARIABLES?

ENTER THE NUMBER OF VARIABLES TO BE USED.

LINE 6  ENTER METHOD OF INPUT (1 OR 2)

ENTER A 1 IF DATA IS TO BE ENTERED BY GROUP.  THE NEXT QUESTION IS LINE 9.
ENTER 2 IF DATA IS TO BE ENTERED USING A BREAKDOWN VARIABLE.  THE NEXT
QUESTION IS LINE 7.

LINE 7  WHICH IS THE BREAKDOWN VARIABLE?

ENTER THE NUMBER OF THE BREAKDOWN VARIABLE.

LINE 8  ENTER BREAKDOWN LIMITS (MAX 10)

ENTER NO MORE THAN 10 BREAKDOWN LIMITS, ALL ON THE SAME LINE.  ONLY POSITIVE
VALUES MAY BE USED.  THE NEXT QUESTION IS LINE 10.

LINE 9  HOW MANY GROUPS?

ENTER THE NUMBER OF GROUPS TO BE USED.

LINE 10  ARE ANY SYMBOLS TO BE USED FOR MISSING DATA? (YES OR NO)

ENTER "YES" TO USE MISSING DATA SYMBOLS.  IF "YES" IS ENTERED THE NEXT QUESTION
IS LINE 11.  IF "NO" IS ENTERED AND METHOD 1 OF INPUT IS USED, THE NEXT QUESTION
IS LINE 12.  OTHERWISE THE NEXT QUESTION IS LINE 14.

LINE 11  TYPE MISSING DATA SYMBOL FOR EACH VARIABLE (10 PER LINE)

ENTER A MISSING DATA SYMBOL FOR EACH VARIABLE.  TYPE 10 VALUES PER LINE,
SEPARATING BY COMMAS.  MISSING DATA SYMBOLS MAY BE ANY NUMBER VALUE NOT USED AS
DATA FOR THIER RESPECTIVE VARIABLE.  IF METHOD 1 OF INPUT IS USED THE NEXT
QUESTION IS LINE 12.  OTHERWISE THE NEXT QUESTION IS LINE 14.

LINE 12  ENTER NUMBER OF ELEMENTS PER GROUP (10 PER LINE)

ENTER THE NUMBERS SEPARATED BY COMMAS.

LINE 13  ENTER DATA FOR GROUP "NN"

THIS STATEMENT WILL BE REPEATED FOR EACH GROUP.  ENTER THE DATA TO CONFORM TO
THE FORMAT SPECIFIED ON LINE 4.  THE NEXT QUESTION IS LINE 15.

LINE 14  DATA IS BEING READ FROM "DEV"
OR
ENTER DATA

THE WORDING OF THE ABOVE QUESTION DEPENDS ON THE INPUT DEVICE SPECIFIED.  "DEV"
WILL BE A DEVICE OTHER THAN TTY:.

LINE 15  WOULD YOU LIKE TWO SAMPLE T'S? (YES OR NO)

ANSWER "YES" FOR TWO-SAMPLE T ANALYSIS.  IF "YES" IS ENTERED THE NEXT QUESTION
IS LINE 16.  OTHERWISE IT IS LINE 2.

LINE 16  ENTER A 1 TO USE THE POOLED MEAN SQUARE FOR JUST THE TWO GROUPS.
ENTER A 2 TO USE THE POOLED MEAN SQUARE FOR ALL 'N' GROUPS.

ENTER A 1 OR A 2.  THE NEXT QUESTION WILL BE LINE 2.

7.0  METHOD OF USE AND SAMPLE RUNS

PROCEDURE FOR TERMINAL AND BATCH JOBS ARE SIMILAR.

7.1  TERMINAL JOB

FOLLOWING LOGIN, THE USER TYPES "R ONEAOV<CR>".  INTERACTION BETWEEN USER AND
PROGRAM BEGINS AT THIS POINT.  THE PROGRAM WILL TYPE OUT THE APPROPRIATE
QUESTION OR STATEMENT AS OUTLINED IN SECTION 6.0.

EXAMPLE RUN:

THE PROBLEM SOLVED IN THIS EXAMPLE IS FROM "STATISTICAL PRINCIPLES IN
EXPERIMENTAL DESIGN", B.J. WINER, MCGRAW-HILL, 2ND EDITION, 1971, PAGE 601.

NOTE: ALL <CR> ARE ENTERED BY THE USER. WITH THE EXCEPTION OF
OUTPUT? AND INPUT? ALL INFORMATION ON THE SAME LINE AS <CR> AND
PRECEEDING <CR> ARE ENTERED BY THE USER.  ^Z IS ENTERED BY THE USER.

.R ONEAOV<CR>
--WMU ONE-WAY ANALYSIS OF VARIANCE--
OUTPUT?<CR>
INPUT?<CR>
ENTER OUTPUT IDENTIFICATION, IF DESIRED
WINER PAGE 601<CR>
FORMAT:  (F-TYPE ONLY)
<CR>
HOW MANY VARIABLES? 3<CR>
ENTER METHOD OF INPUT(1 OR 2) 1<CR>
HOW MANY GROUPS? 3<CR>
ARE ANY SYMBOLS TO BE USED FOR MISSING DATA?(YES OR NO) NO<CR>
ENTER NUMBER OF ELEMENTS PER GROUP (10 PER LINE)
3,5,4<CR>
ENTER DATA FOR GROUP 1
3,6,9<CR>
6,10,14<CR>
10,15,18<CR>
ENTER DATA FOR GROUP 2
8,12,16<CR>
3,5,8<CR>
1,3,8<CR>
12,18,26<CR>
9,10,18<CR>
ENTER DATA FOR GROUP 3
10,22,16<CR>
3,15,8<CR>
7,16,10<CR>
5,20,12<CR>
WOULD YOU LIKE TWO-SAMPLE T'S(YES OR NO) NO<CR>

WINER PAGE 601

20:31  8-Aug-78

*** VARIABLE   1 ***

GROUP        SIZE    MEANS      VARIANCE     STD DEV

1           3      6.333       12.3333      3.5119
2           5      6.600       20.3000      4.5056
3           4      6.250        8.9167      2.9861

NUMBER OF GROUPS=                3       DF=    2
BARTLETT'S STATISTIC=            0.500
WITH CHI-SQUARE PROBABILITY=      .779

ANALYSIS OF VARIANCE TABLE

SOURCE OF VAR.  D.F.     SUM OF SQ.   MEAN SQ.          F       PROB

GROUPS              2         0.300      0.150       0.010      0.990
ERROR               9       132.617     14.735
TOTAL              11       132.917

*** VARIABLE   2 ***

GROUP        SIZE    MEANS      VARIANCE     STD DEV

1           3     10.333       20.3333      4.5092
2           5      9.600       35.3000      5.9414
3           4     18.250       10.9167      3.3040

NUMBER OF GROUPS=                3       DF=    2
BARTLETT'S STATISTIC=            0.941
WITH CHI-SQUARE PROBABILITY=      .625

ANALYSIS OF VARIANCE TABLE

SOURCE OF VAR.  D.F.     SUM OF SQ.   MEAN SQ.          F       PROB

GROUPS              2       188.050     94.025       3.943      0.059
ERROR               9       214.617     23.846
TOTAL              11       402.667

*** VARIABLE   3 ***

GROUP        SIZE    MEANS      VARIANCE     STD DEV

1           3     13.667       20.3333      4.5092
2           5     15.200       57.2000      7.5631
3           4     11.500       11.6667      3.4157

NUMBER OF GROUPS=                3       DF=    2
BARTLETT'S STATISTIC=            1.817
WITH CHI-SQUARE PROBABILITY=      .403

ANALYSIS OF VARIANCE TABLE

SOURCE OF VAR.  D.F.     SUM OF SQ.   MEAN SQ.          F       PROB

GROUPS              2        30.450     15.225       0.450      0.651
ERROR               9       304.467     33.830
TOTAL              11       334.917

INPUT? FINISH<CR>

THE SECOND TERMINAL EXAMPLE USED DATA GIVEN IN EXAMPLE 2 SECTION 3.0.

HOW MANY VARIABLES? 3<CR>
ENTER THE METHOD OF INPUT(1 OR 2) 2<CR>
WHICH VARIABLE IS THE BREAKDOWN VARIABLE? 2<CR>
ENTER BREAKDOWN LIMITS (MAX 10)
2,6,8<CR>
ARE ANY SYMBOLS TO BE USED FOR MISSING DATA?(YES OR NO) NO<CR>
ENTER DATA
1,1,7<CR>
1.6,8<CR>
2,7,7<CR>
3,5,7<CR>
7,12,8<CR>
2,1,1<CR>
1,2,1<CR>
6,5,6<CR>
8,7,17<CR>
10,8,3<CR>
^Z
NUMBER OF REJECTED SAMPLES =  1
WOULD YOU LIKE TWO-SAMPLE T'S(YES OR NO) YES<CR>
ENTER A 1 TO USE THE POOLED MEAN SQUARE FOR JUST THE TWO GROUPS,
ENTER A 2 TO USE THE POOLED MEAN SQUARE FOR ALL 3 GROUPS
2<CR>

*** VARIABLE   1 ***

GROUP        SIZE    MEANS      VARIANCE     STD DEV

1           3      1.333        0.3333      0.5774
2           3      3.333        6.3333      2.5166
3           3      6.667       17.3333      4.1633

NUMBER OF GROUPS=                3       DF=    2
BARTLETT'S STATISTIC=            4.318
WITH CHI-SQUARE PROBABILITY=      .115

ANALYSIS OF VARIANCE TABLE

SOURCE OF VAR.  D.F.     SUM OF SQ.   MEAN SQ.          F       PROB

GROUPS              2        43.556     21.778       2.722      0.144
ERROR               6        48.000      8.000
TOTAL               8        91.556

TWO-SAMPLE T ANALYSIS

MEAN         T                            95.% C. I.
GRP-GRP    DIFFERANCE     VALUE      PROB    DF  LOWER LIMIT,UPPER LIMIT

1-  2       -2.00      -0.866     0.420     6   (    -6.49,     2.49)
1-  3       -5.33      -2.309     0.060     6   (    -9.82,    -0.84)
2-  3       -3.33      -1.443     0.199     6   (    -7.82,     1.16)

USING POOLED MEAN SQUARE FOR ALL    3 GROUPS

*** VARIABLE   3 ***

GROUP        SIZE    MEANS      VARIANCE     STD DEV

1           3      3.000       12.0000      3.4641
2           3      7.000        1.0000      1.0000
3           3      9.000       52.0000      7.2111

NUMBER OF GROUPS=                3       DF=    2
BARTLETT'S STATISTIC=            4.567
WITH CHI-SQUARE PROBABILITY=      .102

ANALYSIS OF VARIANCE TABLE

SOURCE OF VAR.  D.F.     SUM OF SQ.   MEAN SQ.          F       PROB

GROUPS              2        56.000     28.000       1.292      0.341
ERROR               6       130.000     21.667
TOTAL               8       186.000

TWO-SAMPLE T ANALYSIS

MEAN         T                            95.% C. I.
GRP-GRP    DIFFERANCE     VALUE      PROB    DF  LOWER LIMIT,UPPER LIMIT

1-  2       -4.00      -1.052     0.333     6   (   -11.39,     3.39)
1-  3       -6.00      -1.579     0.165     6   (   -13.39,     1.39)
2-  3       -2.00      -0.526     0.618     6   (    -9.39,     5.39)

USING POOLED MEAN SQUARE FOR ALL    3 GROUPS

INPUT? (TYPE HELP IF NEEDED)--FINISH<CR>

7.2  BATCH JOB

THE FOLLOWING IS A BATCH JOB SETUP (EACH LINE REPRESENTS ONE CARD, EACH CARD
STARTING IN COLUMN 1).  DO NOT INCLUDE COMMENTS AT RIGHT.

--------------------------------------------------------------------------------

\$JOB [#,#]                             JOB CARD; INSERT USER'S PROJECT-
PROGRAMMER NUMBER WITHIN THE BRACKETS.

\$DATA                                  SIGNIFY THE BEGINNING OF THE DATA DECK
(SEE NOTE 1 AT END OF BATCH EXAMPLE)

(DATA CARDS)                     INSERT DATA CARDS TO BE ANALYZED.

\$EOD                                   SIGNIFY THE END OF THE DATA CARD DECK.

.R ONEAOV                              EXECUTION OF PROGRAM.
(RESPONSES TO LINES 1-16 IN
SECTION 6.0 REPEATED OR NOT)

(EOF)                                  AN END-OF-FILE CARD.

--------------------------------------------------------------------------------

EXAMPLE:

IN THE EXAMPLE BELOW ONE SET OF DATA IS TO BE PROCESSED, INPUT DEVICE IS THE
CARD READER (\$DATA STATEMENT) AND THE OUTPUT DEVICE IS THE LINE PRINTER.

\$JOB [460,460]                         JOB CARD
\$DATA                                  START OF INPUT DATA
094
084
072
076
051
082
042
013
991
031
031
033
021
102                                    INPUT DATA
993
124
043
992
023
023
104
124
023
033
063
054
104
991
013
041
011
\$EOD                                   END OF DATA
.R ONEAOV                              START EXECUTION
[BLANK CARD]                           OUTPUT DEVICE IS LINE PRINTER
[BLANK CARD]                           INPUT DEVICE IS CARD READER
SAMPLE BATCH RUN                       IDENTIFICATION
(F1.0,F2.0)                            OBJECT TIME FORMAT
2                                      NUMBER OF VARIABLES
2                                      METHOD OF INPUT
2                                      BREAKDOWN VARIABLE
1,2,3,4                                BREAKDOWN LIMITS
YES                                    MISSING DATA
99                                     MISSING DATA SYMBOL
YES                                    TWO SAMPLE T'S
2                                      M.S. FOR 2 GROUPS
FINISH                                 TERMINATE PROGRAM
(EOF)                                  END-OF-FILE CARD

NOTE 1:  IF THE INPUT DEVICE IS OTHER THAN CDR: OMIT CARDS "\$DATA" THROUGH
"\$EOD" INCLUSIVE.
```