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