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. |
STAT — NGROUP 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 165‑179). The responses are plant weights for 6 plants of 3 different types‑3 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
