CIDMS
Computes a confidence interval on a variance component estimated as proportional to the difference in two mean squares in a balanced complete experimental design.
Required Arguments
DF1 — Degrees of freedom for effect 1. (Input)
EFMS1 — Mean square for effect 1. (Input)
DF2 — Degrees of freedom for effect 2. (Input)
EFMS2 — Mean square for effect 2. (Input)
VCHAT — Estimated variance component. (Input)
VCHAT = (EFMS1 ‑ EFMS2)/a, where a is some positive constant.
CONINT — Vector of length 2 containing the lower and upper endpoints of the confidence interval, respectively. (Output)
Optional Arguments
CONPER — Confidence level for two-sided interval estimate on the variance component, in percent. (Input)
Default: CONPER = 95.0.
A CONPER percent interval is computed, hence, CONPER must be in the interval [0.0, 100.0). CONPER often will be 90.0, 95.0, or 99.0. For a one-sided interval with confidence level ONECL, ONECL in the interval [50.0, 100.0), set
CONPER = 100.0 ‑ 2.0 * (100.0 ‑ ONECL).
IMETH — Method option. (Input)
Default: IMETH = 0.
IOPT | Action |
|---|
0 | Graybill’s Method |
1 | Bross’ Method |
FORTRAN 90 Interface
Generic: CALL CIDMS (DF1, EFMS1, DF2, EFMS2, VCHAT, CONINT [, …])
Specific: The specific interface names are S_CIDMS and D_CIDMS.
FORTRAN 77 Interface
Single: CALL CIDMS (DF1, EFMS1, DF2, EFMS2, VCHAT, CONPER, IMETH, CONINT)
Double: The double precision name is DCIDMS.
Description
Routine CIDMS computes a confidence interval on a variance component that has been estimated as proportional to the difference of two mean squares. Let
(stored in EFMS1 and EFMS2, respectively) be the two mean squares. The variance component estimate
(stored in VCHAT) is assumed to be of the form
where a is some positive constant. Two methods for computing a confidence interval on σ2 can be used. For IMETH = 0, the method discussed by Graybill (1976, Theorem 15.3.5, page 624, and Note 4, page 620) is used. The result was proposed by Williams (1962). For IMETH = 1, the method due to Bross (1950) and discussed by Anderson and Bancroft (1952, page 322) is used.
Routine CIDMS can also be used when a variance component is estimated by the difference of two linear combinations of mean squares, each linear combination contains nonnegative coefficients, and the two linear combinations do not use any of the same mean squares. Let
be the two linear combinations (stored in EFMS1 and EFMS2, respectively). The variance component estimate
(stored in VCHAT) is assumed to be of the form
where a is some positive constant, the ci’s and di’s are nonnegative, and for i = 1, 2, …, k, cidi = 0. Satterthwaite (1946) approximations as discussed by Graybill (1976, pages 642‑ 643) can be used to arrive at approximate degrees of freedom for each linear combination of mean squares for input into CIDMS. Let νi be the degrees of freedom associated with the i-th mean square
The degrees of freedom stored in DF1 and DF2 should be taken to be
and
respectively.
Comments
Informational error
Type | Code | Description |
|---|
1 | 1 | One or more endpoints of CI are set to zero. |
Example
This example computes a confidence interval on a variance component estimated by a difference of mean squares using a nested design discussed by Graybill (1976, pages 635‑636). The nested design gave the following analysis of variance table:
Source | DF | MS | EMS |
|---|
A | 5 | 385.4 | |
B within A | 18 | 85.4 | |
Error | 48 | 12.3 | |
A confidence interval of
is computed using the method of Graybill. (Note that the lower endpoint of the confidence interval, which is 3.136, is given incorrectly by Graybill [page 636]. Graybill uses an incorrect value for F0.975;5, 18 in his computations.)
USE CIDMS_INT
USE UMACH_INT
IMPLICIT NONE
INTEGER NOUT
REAL CONINT(2), DF1, DF2, EFMS1, EFMS2, VCHAT
!
DF1 = 5.0
EFMS1 = 385.4
DF2 = 18.0
EFMS2 = 85.4
VCHAT = (EFMS1-EFMS2)/12.0
!
CALL CIDMS (DF1, EFMS1, DF2, EFMS2, VCHAT, CONINT)
!
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) CONINT
99999 FORMAT (' Lower confidence limit', F9.3, /' Upper confidence ', &
'limit', F9.3)
END
Output
Lower confidence limit 3.136
Upper confidence limit 186.464
