AONEW
Analyzes a one-way classification model.
Required Arguments
NI — Vector of length NGROUP containing the number of responses for each group. (Input)
Y — Vector of length NI(1) + NI(2) +  + NI(NGROUP) containing the responses for each group. (Input)
AOV — Vector of length 15 containing statistics relating to the analysis of variance. (Output)
I
AOV(I)
1
Degrees of freedom for among groups
2
Degrees of freedom for within groups
3
Total (corrected) degrees of freedom
4
Sum of squares for among groups
5
Sum of squares for within groups
6
Total (corrected) sum of squares
7
Among-groups mean square
8
Within-groups mean square
9
F -statistic
10
p-value
11
R2 (in percent)
12
Adjusted R2 (in percent)
13
Estimated standard deviation of the error within groups
14
Overall mean of Y
15
Coefficient of variation (in percent)
Optional Arguments
NGROUP — Number of groups. (Input)
Default: NGROUP = size (NI,1).
IPRINT — Printing option. (Input)
Default: IPRINT = 0.
IPRINT
Action
0
No printing is performed.
1
AOV is printed only.
2
STAT is printed only.
3
All printing is performed.
STATNGROUP by 4 matrix containing information concerning the groups. (Output)
Row I contains information pertaining to the I-th group. The information in the columns is as follows:
Col
Description
1
Group number
2
Number of nonmissing observations
3
Group mean
4
Group standard deviation
LDSTAT — Leading dimension of STAT exactly as specified in the dimension statement in the calling program. (Input)
Default: LDSTAT= size (STAT , 1)
NMISS — Number of missing values. (Output)
Elements of Y containing NaN (not a number) are omitted from the computations.
FORTRAN 90 Interface
Generic: CALL AONEW (NI, Y, AOV [])
Specific: The specific interface names are S_AONEW and D_AONEW.
FORTRAN 77 Interface
Single: CALL AONEW (NGROUP, NI, Y, IPRINT, AOV, STAT, LDSTAT, NMISS)
Double: The double precision name is DAONEW.
Description
Routine AONEW performs an analysis of variance of responses from a one-way classification design. The model is
yij = μi + ɛ ij     i = 1, 2, , k; j = 1, 2, , ni
where the observed value of yij constitutes the j-th response in the i-th group, μi denotes the population mean for the i-th group, and the ɛ ij’s are errors that are identically and independently distributed normal with mean zero and variance σ2. AONEW requires the yij’s as input into a single vector Y with responses in each group occupying contiguous locations. The analysis of variance table is computed along with the group sample means and standard deviations. A discussion of formulas and interpretations for the one-way analysis of variance problem appears in most elementary statistics texts, e.g., Snedecor and Cochran (1967, Chapter 10).
Example
This example computes a one-way analysis of variance for data discussed by Searle (1971, Table 5.1, pages 165179). The responses are plant weights for 6 plants of 3 different types3 normal, 2 off-types, and 1 aberrant. The responses are given by type of plant in the following table:
Type of Plant
Normal
Off-Type
Aberrant
101
84
32
105
88
 
94
 
 
Note that for the group with only one response, the standard deviation is undefined and is set to NaN (not a number).
 
USE AONEW_INT
 
IMPLICIT NONE
INTEGER NGROUP, NOBS
PARAMETER (NGROUP=3, NOBS=6)
!
INTEGER IPRINT, NI(NGROUP)
REAL AOV(15), Y(NOBS)
!
DATA NI/3, 2, 1/
DATA Y/101.0, 105.0, 94.0, 84.0, 88.0, 32.0/
!
IPRINT = 3
CALL AONEW (NI, Y, AOV, IPRINT=IPRINT)
END
Output
 
Dependent R-squared Adjusted Est. Std. Dev. Coefficient of
Variable (percent) R-squared of Model Error Mean Var. (percent)
Y 98.028 96.714 4.83 84 5.751
 
* * * Analysis of Variance * * *
Sum of Mean Prob. of
Source DF Squares Square Overall F Larger F
Among Groups 2 3480 1740.0 74.571 0.0028
Within Groups 3 70 23.3
Corrected Total 5 3550
 
Group Statistics
Standard
Group N Mean Deviation
1 3 100 5.568
2 2 86 2.828
3 1 32 NaN