Download Procedure TABLES: A Two-way Table Generator with Statistics for Control Versus Treated Comparisons

PROCEDURE TABLES: A Two-way Table Generator
With Statistics For Contro1 Verses
Treated Comparisons
S. Stanley Young
George F. Fraction
Lilly Research Laboratories
ABSTRACT
PROCEDURE TABLES produces a two-way. treatment by parameters~ table containing various statistics
(mean, standard deviation, number of observations, standard error, t-statistic, variance, etc.) and
compares multiple treatments
to a common control group.
either a Student, Dunnett, Williams, or Bonferroni t.
of Bartlett (P~.OOl).
Statistical testing can be computed using
Variance homogeneity ;s tested using a procedure
Raw or ranked data can be analyzed.
KEYWORDS
One-way ANOVA, Two-way tables, Multiple comparisons, Student t, Dunnett t, Williams t, Banferron; t,
Nonparametric t tests, SAS PROC TABLES
statistics are given in the PROCEDURE TABLES
section.
The BY
feature
allows multiple
INTRODUCTION
Quite often one des; res a two-way tab le with
treatment
groups
indexed
vertically
and
response parameters horizonally.
In €ach cell
of such a two~way table, various statistiCS,
mean~ standard deviation, etc., should be given
vertically.
It is also desirable to be able to
test
treated
each
control group.
group
a-gainst
a
tables.
In many
cases~
the table construction
capabilities of TABLES will be a sufficient and
attractive
summarization
results so that
unnecessary.
common
special
of
experimental
programming
will
be
STATISTICAL TESTING
PROC TABLES accomplishes all of
the above.
The various statistics available in each cell
are as follows:
by default - mean, standard
Table 1 summarizes the error rate considerations and dose response characteristics of four
types of contro 1 verses treatment stati sti ca 1
tests.
deviation and number of observations and by
request - sum~ standard error of mean, number
Tab1e I
of missing
values,
minimum,
maximum,
PROC TABLES Statistics Options
range,
variance, corrected sum of squares, uncorrected
Type of
Statistics
sum of squares, and at-statistic.
Error Rate
Each group can be compared to a common control
Dose Response
group by any of the following techniques:
Student, Dunnett, Williams or Bonferroni t.
Student
Per Comparison
No Requirement
One or two-tailed testing can be requested and
the level of the test can be specified: .05 or
.01 for Dunnett or Williams; .05 to .000001 for
Student or Bonferroni.
Dunnett
Per Parameter
Treatments Unrelated
Williams
Per Parameter
Monotone Increasing
or Decreasing
The
Sanferron;
tabulated
statistics
and
statistical
True
No Requirement
Experiment-Wi se
(upper bo und)
testing can be computed on either the raw data
- parametric testing, or On the ranked data -
non parametric testing.
The
Student t is classically used to test
two sample means are sufficiently
different as to be considered not to have come
The variability is
from a single population.
measured in each sample as the sample variance
and pooled.
TeChnically, the test requires
that the observations in each population be
normally and independently distributed and that
the samples be drawn frOm populations with
equal
va~iance.
Practically,
the test is
rather rob'ust to departures from normality and
equality of variance.
whether
Additionally Bartlettls test for homogeneity is
applied to
the variance of each group.
Statistical testing is impaired only if P~.OOl,
therefore S1 gnif i cance is dec 1ared at th i s
poi nt.
TABLE CONSTRUCTION
PROC TABLES constructs
CLASSES variable defines
two-way tables;
a
vertical margin, and
the response variables are given horizontally.
In each ce 11 of the table any of a number of
statistics can be specified; these statistics
will
be
printed
vertically.
The
The Dunnett t is designed to test multiple
treatments against a common control. The error
various
482
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Ha.lnut Creek, CA 94595.
494
Avenue~
rate is controlled per variable; the error rate
is experiment-wise (as long as there is but one
response variable tested).
Classically the
treatments are unrelated to one another; but an
example in Dunnett's paper and common practice
among experimenters use the test when the
treatments are progressively higher doses of a
common treatment.
8ecause the error rate is
fixed experiment-wise, pretesting with an AN'OVA
is superfluous as long as the control verses
treatment comparisons are the comparisons of
; nterest.
assumptions, homogeneity and
should. analyze the ranked data.
1.
l.
0
Bonferroni t is described by Miller; the test
error rate is experiment-wise across treatment
groups within a parameter and across parameters.
The error rate is an upper bound on the total
numbers
of
tests
and
does
not
require
independence Qf the comparisons being made.
The error rate is almost exact if the per
comparison error rate is small and th€ comparisons independent. It is overly conservative
if the comparisons and/or parameters are not
independent.
Figure 1 gives the
hypothesis testing.
Figure 1
for
Third. the «,- leve 1 depends upon· the wi 11 i ngness
to make a type I error - false positive mistake.
Custom usually sets theO<-level at .05 or .01,
but these levels need not be followed slavishly.
Finally. one or two-tailed testing? If one has
strong theoretical or empirical information'. it
can be appropriate to test only in qne
direction.
Othei"wise. two-tai led testing is
appropriate. There is a mistaken practice in
statistical hypothesis testing of testing in
only one dir.ection because the investigator is
only lI;nterested U in changes in a specified
direction.
The purpose of experimentation is
to discover the effects of treatment and unless
there
is
strong theoretical
Of'
empirical
evidence to the contrary, testing must be for
increases or decreases. One can always adjust
the level of testing (someWhat) for power
considerations.
statistical
Diagram of Statistical Options
Raw
Data
Ranked
Data
options
-
one
Second, the method of statistical testing must
be chosen.
Table 1 gives the pertinent
attributes of the four available tests. If one
is comparing a single treatment to control, or
if only one statistical compa~ison ;s being
made,
the Student t
is appropriate.
If
multiple
unrelated
treatments
are
being
compared to a common control on just a single
parameter~ then Dunnett1s t is. appropriate.
If
the dose
response
is monotone and each
treatment group is being compared to control
within' a single parameter, then Wiliiams t is
appropriate. Multiple treatments and multiple
parameters require a Bonferroni t.
It should
be noted that seldom is a single response
parameter tested;
it
is more
usua 1 that
multiple responses are measured and tested. If
this is so~ then it is imperative that either
the per parameter error rate be adjusted to
give a desired experiment-wise error rate or
that investigators be fully informed of the
experiment-wise Type I error rate and be
prepared to consider observed results as false
positives.
Williams t is designed to test progressively
higher doses against an untreated, common
contra 1 and requires the dose response to be
monotone.
The error rate is experiment-wise
(as long as there is but one response variable
tested).
It requires pre-specification (or
scrutiny of the data) of the direction of the
testing.
In our formulation of the Williams
test, the following mathematical formulation of
treatment meanS and numbers of. observations
give the direction of testing:
D ~ (Li·n:(x.-x »)!L(i·u.).
1.
normality,
Student
or
One-Tail
Dunnett
or
or
--l"'-Leve lJ.Wi 11i ams
or
Tw.o Tailed
Bonferroni
THE TABLES PROCEDURE
Support Type: U
question naturally arises: Which of these
statistical options is most appropriate? The
anSwer natura 11y depends upon the circumstances.
First, if the error structures of the various
groups is homogenous and normally distributed,
analysis of the raw data ;s appropriate;
departures from these requirements must be
rattlBr severe before the error rates of
statistical testing are upset markedly. If the
departures are marked, then some form of
nonparametric analysis is appropriate.
TABLES
uses the ranked data to compute a nonparametric
analysis.
Use of the ranked data, even when
the unranked data is appropriate, extracts a
very modest price in terms of the experiments
ability to detect real changes - about 5:, loss
of power - so that many theoreticians argue
that if there is any question about the usual
S. Stanley Young
George F. fraction
Lilly Research laboratories
The
PROCEDURE TABLES computes and tabulates simple
univariate
statistics
for
all
applicable
variables for a control group and up to
nineteen treated groups.
The procedure wi 11 mark those treatment means
are significantly different from the
control mean at a specified level using a one
or two tai led t test ali raw or ranked data
according to any of the following methods:
(1) Student
(2) Dunnett
(3) Williams
(4) Bonferroni
Which
483
LEVEL = ",-Leve 1
This
parameter
specifies
the
significance
leve 1.
For
the
Student
or
Sonferroni
statistic, the value may range from 0.001 to
0.1; for Dunnett or Williams, the value must be
either .05 or .01.
If this parameter is
omitted, the significance level defaults to
.05. The word LEVEL may be abbreviated as L.
procedure will also check for homogeniety
variance using Bartlett 1 s procedure
at
P~.OOl, the level given by Anderson and McLean
beyond which statistical hypothesis testing is
upset. Th;s procedure requires the data set to
be sorted by the CLASSES variable within the BY
variable(s) .
The
of
OUTPUT
TAILS = 1 or 2
This parameter specifies whether a on'e or two
Two-way tables (classes variable by response
variables) show the statistics computed on all
numeric variables or on all variables given in
the var-i ab les sta'tement.
The pr inted values
are formatted such that the standard deviation
will contain at least three (3) significant
digits
(all
integer
digits
are
kept).
Significant means (Student, Dunnett~ Williams,
or Bonferroni t} and standard deviations of
unusual variability (Bartlett, P ~ .D01) are
marked.
Each table is footnoted to indicate
the t test method employed, the alpha 1eve 1,
nlJ11ber of tails, variables which do not meet
Bartlett's test for homogeniety of variance,
and whether the analyses are done 011 raw or
ranked data.
The PROC attempts to conserve
paper by formatting and folding the table if
necessary.
tailed test will be used.
If it is omitted,
the default is a two tai led test.
The word
TAILS may be abbreviated as T.
RANKED
This
option,
when
used,
indicates
the
statistics are to be computed on the ranks of
the variable(s) rather than the raw values.
PROC
TABLES
performs
its
own
ranking,
preserving missing values and giving the
average rank to tied values.
The word RANKED
may be abbreviated as RANK or R. or may even be
\>If itt en as NPAR.
LABEL
This option, when used, forces the printing of
labels with each variable analyzed as well as
the CLASSES variable.
It requires that the
labels be defined on the data set. The first
eight characters of the label definition are
printed. The word LABEL may be abbreviated as
lBL or L.
When no statistical options are specified on
the PROC TABLES statement, TABLES prints, for
each applicable variable and group:
(1) The mean
(2) The standard deviation
(3) The number of non-missing values
STATISTICAL OPTIONS
THE PROCEDURE TABLES STATEMENT
*MEAN
*STD
STDERR
PROC TABLES Options and Parameters;
The options and parameters that can appear are
as follows:
*N
NMISS
SUM
MIN
MAX
RANGE
VAR
USS
CSS
T
DATA = Data Set Name
The data parameter tell s TABLES the SAS data
set to be ana lyzed. If it is omitted t then the
last data set created will be used.
CONTROL = Control Group Value
This parameter is-used-to specify a value which
I f the par ameter
i dent if i es the contra 1 gro up.
is coded, TABLES takes as the control group
that group which has this specified value in
the explicit Or implicit CLASSES variable.
If
this parameter is omitted, TABLES uses the
first (lowest valued) group of the classes
variable as the control group.
The word
CONTROL may be abbrevi ated as CNTl or C. _
Mean
Standard Deviation
Standard Error or the Mean
Number of Non-MiSSing Values
Number of Missing Values
Sum
Minimum Va 1ue
Max imum Va 1 ue
Range
Var i ance
Uncorrected Sums of Squares
Corrected Sums of Squares
Control Group: Tabular (Critical) T
for the statistical method, «-level,
and number of tails
Treated Group: Sample T comparing the
treated group to the control group.
'Default Statistics
PROCEDURE INFORMATION STATHifNTS
STATISTIC = Type of Statistics
This parameter
the user to specify the
type of significance test to be performed. If
this parameter is omitted, a formatted means
table will be produced, but no statistical
testing will
be performed.
The allowable
statistics are as follows:
STUDENT, DUNNETT,
WILLIAMS,
and
BONFERRONI;
these
may
be
abbreviated as $, 0, W, and 8, respectively.
The word STATISTIC may be abbrevi ated as STAT
or S.
allows
CLASSES
STATEMENT - The
CLASSES statement
defines
the
variable
which
controls
the
vertical margin. The different values of this
variable control the printing and statistical
testing.
Only the first variable in the
CLASSES statement list of variables will be
used.
The data set must be sorted by this
variable.
If the CLASSES statement is not
used, TABLES will consider the first variab1e
in the explicit or implicit VARIABLES list as
the CLASSES variable. The word CLASSES may be
484
abbreviated as CLASS. The CLASSES variable is
treated as an alpha variable and the first
eight characters are used.
EXAMPLE 1. PROC TABLES; CLASSES TRT; BY SEX;
VARIABLES STATEMENT - Computations will be
performed on all numeric variables listed in
the VARIABLES statement.
When the CLASSES
statement is omitted, TABLES uses the first
variable as the CLASSES variable.
If the
VARIABLES statement is not present, statistics
will
PROCEDURE
DEtlONSTRA nON
TABLES
BY FPACTION AND YOUNG
ELI LILLY & CO.
RAT GRO}lTH DATA
~~~-~~~.-~----~~---------- SEX~f
---------------------------
be computed on all non-classes, non-by
nll11eric variables in the data seL
VARIABLES may be abbreviated as VAR.
TRT
The word
0.0000
BY STATEMENT - If a BY statement is used, the
data set must be sorted by the variables in the
BY statement. TABLES will treat each BY group
as a separate set of control verses treatment
groups. The CLASSES variable must be sorted
within the lowest order BY variable.
STAT
""
MEAN
92.89
137.78
8.81
9
10.3-7
9
STO
"
1.0'00'0'
TREATMENT OF MISSING VALUES
2.0'0'00
MEAN
95.70
123.90
STO
N
4,62
10
4,25
10
MEAN
92.80
116.50
STO
5.35
10
7.49
10
STO
90.2:0'
6.94-
109,30
10.3S
N
10
"
A11 forms of mi ss i n9 va 1ues are ignored in the
computations. In handling ranked data, missing
values are not assigned a rank but remain
mi ssing.
3.0000
""
MEAN
W8
""'
171,$9
9,48
1<J8.78
157,nD
181.30'
10'.01
10.0'4
10
,
10
,
9.65
148.70'
168.80
4,08
4.59
10
10
129.20'
7.91
10
10
151.50
6.47
10
REFERENCES
Anderson, V. L., and McLean, R. A. Design of
Exper'iments:
A Realistic Approach Marcel
Dekker, Inc. New York, 1974, pp 16-22.
PROCEDURE
TAB L E 5
BY
FRACTlOt~
Ell LIllY & CO.
w. ~ llA Multiple Comparison
C.
Procedure for Comparing Several Treatments With
a Contro 1"
'-"'-""--"-""-"-'-""'---"-".2.""-'. 50,
pp 1096-11
Du"nett~
PAl GROWTH DATA
---------~-------------.-- SEX~N ---------------------------
Ounnett, C. W.,
"New Table For Multiple
Comparisons with a Control" Biometrics Vol 20.
pp 482-491 1964.
TOT
STAT
0.0'000
MEAN
STO
N
Leyman.
E.L •• Nonparametrics:
Statistica1
~M~e~t~ho~d~s~~B~ar,s~e~d~~o~n,--~R~a~n~k"s.
Holden-Day,
San
Francisco 1975.
1.00cn
Miller, Rupert G.
Simultaneous Statistical
Inference McGraw-Hill Book Company 1966
pp 67-70, 129-172.
2.0'000
D.
3.0000
A~,
"A Test for Differences
Means When Severa 1 Dose
Leve 1s are Compared With a Zero Dose Contro 1"
Biometrics
Vol 27 t pp 103-117 1971.
Between
Williams,
Dose
Treatment
D.
Leve 15
A.•
with
"The Comparison
a
Zero
Biometrics Vol 28, pp 519-531
Dose
of Several
Contro pI
1972.
485
"4
103,ZO
193.2
11.2:5
10
14.1
98,40'
152.7
15,n3
N
10
15,310
MEAN
92.0'0
MEAN
STO
N
6,09
10
337.50
16.2b
10
MEAt>!
STO
Steel, R. G. D., Torrie, J. H. Principles and
Procedures
of
Statistics McGraw-Hill
Book
Company 1960 pp 73-76.
WI
STO
N
Williams,
OHIONSTRATION
At-.'O YOUNG
147.0
13.4
10
144.5
14.1
10
10
20$.1
13.9
10
241.70
13,44
10
200.3
234.80
10.05
10
10'.7
10
194.9
10.7
10
227.80
9.65
10
EXAMPLE 4. PROC TABLES STAT=OUN TAILS=] LEVEL=.01
MEAN MIN MAX RANGE T LABEL RANKCLASSES TRT; BY SEX;
,
EXAMPLE 2. PROC TABLES STAT=STUDENT TAILS=2
LEVEL =.05 LABEL MEAN STO N T;
CLASSES TRT; BY SEX;
PROCEDURE
TAB l
E 5
PPOCEOURE
ELI LILLY & CO.
RAl
tiArA
GRO~TH
SEX~F
-~---------------~~--~~~-* SEX~F
I)
STAT
.0000
MEAN
sm
N
TABLE T
1. 0(01)
MEAN
Wl
W4
W8
W14
GRAMS
GRAMS
GRAtIS
GRAMS
n.89
131.18
~.97
3.22:
9
2:.030
95.70
STO
N
T
10
MEAN
SID
N
T
1.
2:.15
198.78
3.11
9
2.030
17l,89
3,08
9
2.030
123.90*
157.00*
181. 30*
0.0000
1. 0000
3.17
10
1.
-3.576
-3.968
-'+.777
n.80
116.50*
168.80*
2:.31
2.74
10
-5.483
148,79*
2,02:
10
-6,179
W14
GRAMS
GRA""
20.11
1.00
33.00
13.00
33.56
.34.17
Z8.eo
MAX
RANGE
TASLE T
38.50
37.50
38.50
2'5.50
2'4.0'0
39.00
flEAN
25.10
11.00
36.00
t5.00
0.969
MEAN
MIN
2.030
3.16
L06
wa
GRAMS
HIN
MAX
RANtiE
T
2.0000
-0.030
2.14
2.0000
10
-8.193
MEAN
HIN
HAX
;VHlGE
3.0UOO
MEAN
510
'90.~G
N
10
-0.893
2:.63
T
•
•
p
<~
P
<~
---------------------------
GRAMS
STAT
MG/KG
,
10
0.933
OEtl0NSTRATION
--------------------------TRT
TRT
HG/KG
TAB L E S
6Y FRACTION AND YOUNG
ELI LILLY & CO,
RAT GROWTH O-ATA
DEMONSTRATION
BY FRACTION AND YOUNG
r
109.30·
3.22
129.2tl*
2.81
10
-11. 376
10
-7.:338
Wl
2.8-37
19.95
7.00
36.00
29.00
-0,031
W4
39.00
11.0'0
15.0'0
2.a37
Z.837
24.30
24.65*
25.00*
15.50
8.00
34.00
26.00
-3.665
12.50
17 .35*
16.60*
2.e37
31.00
15.50
-2,6-63
14.95*
34.00
21.50
-4.468
4.fH)
H.ne
£6.50
;':2.50
-5.524
23.00
11.00
12.5-0
-6.669
-8.562
9.05*
5.80,*
5.65*
9.50
22.00
151.50*
2.54
10
3.0000
-lz.9Z1
MEAI-t
MIN
HAX
RAt\GE
.05, TWO TAILED STUOENT T ON RA~ DATA .
.001. UNUSUAL VARIABILITY, BARTLETT.
T
14.85
2.00
38.50
1.00
20.1)0
1.00
11.00
1.00
11 ,co
10.00
-13.899
36.S0
19.00
10.00
-1.U22
-7.330
-11.423
* : p <= .01. ONE iAILED DL~N£TT T eN RANKED DATA.
• ; p <~ .001. UNUSUAL VARIABILITY. BARTLETT.
NOTE: UNITS EXPRESSED ARE THOSE Of THE RAW DATA.
EXA~lPLE
EXAMPLE 5. PROC TABLES STAT=BON TAILS=2 LEVEL=.Ol
MEAN STO N T CONTROL=3 LABEL'
CLASSES TRT; BY SEX;
,
3. PROC TABLES STAT=BON TAILS=2 LEVEL=.05
MEAN STD N T LABEL RANK;
CLASSES TRT; BY SEX;
PROCEDURE
TABLES
PROCEDURE
DEMONSTRATICN
BY FRACTION ANO YOUNG
Ell LILLY 3. CO.
RAT GR()I.lTH OATA
-------------------------TRr
STAt
HGIKG
0.0000
MEAN
STO
N
TA8LE
1.'0000
* :
we
Wl
W4
GRAMS
GRAMS
GRAtIS
W14
GRAtIS
20.11
33.00
14.50
7.84
33,56
4.92
34,17
3.77
•
3,06b
9
3.066-
•
3.066
24.30
7.e5
5,60
24.65*
7.9'
T
10
0,969
10
-2.663
1.
-3.665
MEAN
STO
19.95
10.02
14.95*
8.16
17.35*
N
1.
T
-t).031
"-5.524
MEAN
STO
14.85
9.05*
6.64
N
11.80
10
1.
T
-1.022
-7,330
N
3.0000
SEX;F ---------------------------
25.10
MEAN
STO
2.0001}
T
3.5"3
10
-6.669
5,80*
3,39
1.
-11.423
TRT
0.0000
9
3.066
1.0000
25.0(1'1f
6.19
10
HEAN
STO
2.00UO
16.60*
4.00
10
HEAN
STO
HEm
STD
3.0(1).0;:' MEAN
STO
"TABlE T
-13.eQ9
•
••
OATA.
486
W8
GRAI15
SRANS
92.89
8.81
137.78lt
10.37
171.89l!
9.48
198.78*
9.65
0.893
T
5.65.
3.27
10
"4
T
N
-8.562
GRAMS
N
T
-4.468
W1
GRAMS
,
N
# : P <= .O{!l. UNUSUAL VARIABILITY, BNHlETT.
UNITS EXPRESSED ARE TliOSE OF THE PAW
STAT
MG/KG
p <= .05. r~o TAILED SONFERPONI T ON RANKED DATA.
PER COMPARISON ERROR RATE
.oo~oe33,
NOTE~
TAg l E S
DEMONSTRATION
BY FRACTION ANO YOUNG
ELI LILLY &.CO.
RAT tiROWTH DATA
•
W14
,
9
7.338
11.376
12.921
95.70
4.62
10
1.876
123.90lt
4.25
10
3.865
157.0U*
10,01
181.30*
lO.U4
10
8.367
n.M
116.50
148.70*
5.35
10
0.M7
7.49
10
1.906
90,2"0
6.94
10
3.t-57
109.30
10.38
10
3.657
10
7.611
4.08
168.ao*
4.59
10
10
5.339
U:9.20
7.91
4.857
151.50
10
3.657
6.47
10
3.657
P <= .01. TWO TAILED BONFERRONI T ON RAW DATA.
PER CQ?"tPMHSCN ERROR RATE ,. .0004167.
P <= .001. ~~USUAL VARIABILITY, 8ARTLETT.
TREATED AS CQN7ROl CROUP fOR STATISTICAL TEST1NG.
,,',
EXAMPLE 6. PROC TABLES LABEL;
CLASSES TRT; BY SEX;
PROCEDURE
TABLES
DEMONSTRATION
BY FRACTION "NO YOUNG
Ell LILLY S CO.
RAT (ORQWrH DATA
------------------------------TRT
MG/KG
0.00000
MEAN
5TO
"
1.0000
11EAN
SlD
2.01100
--------------------------------
W,
W3
""
GRAMS
GRAMS
GRAMS
GRANS
92.89
8.81
9
106.33
123.56
137.78
150.89
9.86
9
11.59
9
10.3'
U.50
9
9
95.70
98.40
110.00
123.90
4.62
S.25
5.23
4.25
136.40
4.65
10
10
10
10
10
MEAN
92.80
95.80
103.80
116.5U
STO
5.35
10
6.48
10
8.42
7.49
10
90,20
6.94
88,80
98.50
STO
8.52
N
10
10
9.78
10
MEAN
W5
GRAtIS
"
N
3.0000
"'
STAT
SEX=f
10
109.10
10.38
10
129.30
6.88
10
119.10
10.83
10
---------------------------------------------------------------------TRT
MS/KG
U.OOOO
STAT
MEAN
STO
N
1.(1000
MEAN
5TO
N
2.0000
MEAN
STO
N
3.0000
MEAN
STO
"
W,
W7
W8
"'
"10
GRAMS
GRAMS
GRAtIS
GRAMS
GRANS
158.67
11.9Z
170.11
171.89
9.48
182.89
9
9
184.67
9,(18
9
10.37
•
8.87
9
146.10
7.16
10
155.00
7.97
10
157.00
10.01
10
166,$0
167,80
9.4-0
9.11
lO
136.5(1
5.76
145.20
148.70
155.60
4.24
4.0$
5.17
10
10
121. 90
9.87
10
10
128.60
1(1.17
10
10
129.20
7.91
10
10
136.10
6.82
10
154.00
6.18
10
138.00
7.77
10
487
j-sUGrsi"siiiiiE"lNOllX
BY KEYiCiii--1
I
I
I ___________________
INDEX .---KEYlIORD
I
1
1
6---AIIOVA
22---B1SE
S---~I ASIlD
2---81T
11---BIT
3---ClLCO~1'
"--CA!.CO~P
16--CHlRTS
21--C!.USTER
~--CORT:USTS
22---DlTl
17---D1TlSllT
10---D1STRIBUtION
1---DISTRIBUtIONS
18---EllUC! TIOR
1---ESTIIIATICII
S---ESTI!llTICII
10---ESTI!1TION
lS---EtPONENTI1L
4---l'ACTORIH
17---l'ORTRlN
9---GR lPH1CS
16---GlIlPHICS
8---GR1PHS
S---EY STOGRl liS
19---IIIDllX
l---UPLAN-UIR
13--KOL!OGOROV-SIIIRBOV
14---KOLIIOGORCY-SII1RBOY
18---LURUY
15---LILLIEFOFS
22---IIUAGl!lIUT
2---1I1I11PUL1T10II
11---1I1IlIPUL17IOIl
18---QILINE
15---0PER!'T10llS
17---OIITPUT
1---PLOT
3---PLOTTl!R
3---PLOTT1I!G
9---PLOTTIIIG
15---1'01550N
22--RlIlIS
10---RlNDOIl
12---llECODIIIG
S---REGRESSIOIl
15---RELI1B1LITY
15---llESl!A ilca
5---RIllGE
10---SA~pt.IlIG
20---SPSS
2---SUBSTRING
, l---SUBSTRIN G
'---SURVIVAL
20---5Y STl!K
21---STSTE!
22---SYSTEft
~---TlBULAR
15---Tl! STI JIG
18---rRUIIIlIG
'2---TR!MSFOR!ATIOM
488
SUGI SASW1RE INDI!X OF
COKPUTER CODES DEVELOPED AND DOCUKENTED BY SAS USERS
nux
I
,
,,
,
,
,,
,
1 1
1
NA!ll:
---------
KleBO K!I
------------
DI!SCRIPTION:THIS !lACRO HlS ONE-HAtF PAGE OF COOl! FOR KlPLIN-IIEIE
ESTI!ATIOII OP SURVIVAL PISTRIBUTIONS
I
1 REQUIl1E!lUTS:
I
I
Bl!FEREIICE:
CONTlCT
&
ADDRESS
1
HARRELL, FRlN~
BICSTATISTICS DEPT.
U~IVERSITY NORTH CAROLINA
CSlUL HILL
NC 2"'5111
_I
IN t1!X I
,
2,
---=lIi-!lE-,-r-U-,c-TtOR PU=T=BI"'T::----·
---------------------
1)1! SCBIPTIOII: ALLOWS USERS TO STORI! AllY BIT STRING SUBSET OF A SAS
, VlRIABLE
1
1
,
,
1
,,
I
I
RI!QUIRI!~1!8TS:~
~
REFERENCE:
COIITACT
HABREtL, PRAHK
I S , BICSTATISnCS DEPT.
,
ADDRESS
tiN IVERSITY 1I0RT H
ClROLIlIl
, ___________________________
CHAPEL HILL
IIC 2'151 q_
_______ 1
rNfixT3I-----NiiE: n"Cc-PLOTTEII
,
,
1
._--------------------
DESCRIPTION:LIRE/ptOT PLOTTIRG rOR CALC08P PLOTTER
I
1
1
1 REQrrIRE~RNTS:LOC1LL! WRITTEN BAstC SYMBOL AND L!NEPtOTTING SUBROUTINES
1 IND CllCO~P PLOT'ER WITH "OK OF CORE.
REfERENCE:
1
1
,,
,
I
CORTACT
&
ADDRESS
BURELL, !'RAllII:
BICSTATISTICS DEPT.
U~IVERSITY NORTH CAROLINA
CHAPEL HILL
HC 27514
489
[NCEX'
NAME: MlCRO TABULAR
4
DESC~IPTION:OSES TABULAR METHOD OF ANALYSIS TO COMPUTE USER SPEC1FIEJ
SINGLE IlESREE 01' FREEDOM LINEAR CONTRASTS ON TBEATSENT KEAIIS FROM
BALAIICED FACTORIAL EXPERIMENTS. EASIER AND MOBE CONVENIENT THAN GtM.
~EQUI~EMENTs:a5
CARD IMAGES
llEl'!~I!IICB:
CUMER, SAMUEL
CONTlCT
lGMROMY DEPT.
OBIVERS1TY lLLIII01S
lJREANl
&
ADDRESS
ncu
t
It
6 laO 1
NAKE: MAellO RIDGREGR
5
DESCRIPTION:CALClJL1TES COEF. or RIDGE REGRESS. lND ALLOWS SELECTION OF
APPROPBIATE COEF. VALUES. USER SPECIFIES DEP. VARIABLE & RANGE OF K
(BIAS) VALUES FOR ANALYSI S. OUTPUTS MEANS, VlRUNCl!S, CORR. MATRIX, EIG
UR. IHl'LlTION UCTORS & OTHER STAT. WITH RIDGE TRACE PLOT.
BEQUIRE"ENTS:USES SAS 76.5 PROC'S FORMAT, ftATRIX, AND PLOT
RllFEREIICE:
CONTACT
r,
BOGERS, ROBl!RT
:
ADDRESS
IMtEX'
HILDEBRAND, E.
USDA FOREST SERVICE
UNIVERSITY "Is50UR1
COLUMBIA
ftO 65201
-------------------
6
DESCRIPT10N:PER!OR!S A ONE-WAY 10V USING GROUP SIZES, BEANS AND
STANDARD DEVI1TICNS AS INPUT. T-TllSTS FOR 3 TYPES OF COMPARISONS: ALL
GROUPS WITH THE FIRST GROUP, ALL POSSIBLE PAIRS OF GROUPS, AND USER
sOPPLIED CONTRASts
REQUIREMENTS: 37.8K
REl'EREIICE:
COllT1CT
&
lDDRESS
TESAR, T. P.
UPJOl!5 COMPANY
7293-32-1
lUtA!AZOO
_ _ _ _ _ tI
III 4900 f
------------------------_.
m=E=-X-':-..,7:-:1-----:M,.,Ac::~::J!"': P ROC
CCPLoT-----------
---------
I
I DESCRIPTION: PRODUCES A CALCO!P PLOT WIT!! AS !ANY AS fIVE l'U:lCTIONS Oli
I ONE SET OF AXES. EACH F~NCTION IS DEFINED BY 1 PAIR OF V!R!ABLEs.
t USER CONTROLS PLOT SIZE, sY!BOLS FOR EACH FUNCTION, AXIS LABELS, LEGEND
I UD SCAL1!S.
I
t
I
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t
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t
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______ 1
,
REQUIRE!EIITS:_8.q~
RI!FEREIICE:
CORTACT
&
ADDRESS
TESAR. T. P.
UPJOIIII COIIPA!!Y
7293-32-1
KlLA!A'ZOO
III 49001
-----490
-----------