Accuracy: Analysis of Variance Computation
This is an example of the analysis of variance computation using one of the NIST test data sets to illustrate both the format and the accuracy of LIMDEP's computation.
The NIST data and solution file
Dataset Name: Atomic Weight of Silver (agwt.dat)
File Format: ASCII
Procedure: Analysis of Variance
Reference: Powell, L.J., Murphy, T.J. and Gramlich, J.W.
"The Absolute Isotopic Abundance & Atomic Weight
of a Reference Sample of Silver".
NBS Journal of Research, 87, pp. 9-19 (1982).
Data: 1 Factor,2 Treatments, 24 Replicates/Cell
48 Observations, 7 Constant Leading Digits
Average Level of Difficulty
Model: 3 Parameters (mu, tau_1, tau_2)
y_{ij} = mu + tau_i + epsilon_{ij}
Certified Values:
Source of Sums of Mean
Variation df Squares Squares
Between 1 3.63834187500000E-09 3.63834187500000E-09
Within 46 1.04951729166667E-08 2.28155932971014E-10
F Statistic .59467335677930E+01
Certified R-Squared 2.57426544538321E-01
Certified Residual Standard Deviation 1.51048314446410E-05
Data: Instrument: Group,AgWt
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
107.8681568 107.8681465 107.8681572 107.8681785 107.8681446 107.8681903
107.8681526 107.8681494 107.8681616 107.8681587 107.8681519 107.8681486
107.8681419 107.8681569 107.8681508 107.8681672 107.8681385 107.8681518
107.8681662 107.8681424 107.8681360 107.8681333 107.8681610 107.8681477
107.8681079 107.8681344 107.8681513 107.8681197 107.8681604 107.8681385
107.8681642 107.8681365 107.8681151 107.8681082 107.8681517 107.8681448
107.8681198 107.8681482 107.8681334 107.8681609 107.8681101 107.8681512
107.8681469 107.8681360 107.8681254 107.8681261 107.8681450 107.8681368
LIMDEP solution
+--------------------------------------------------------------------+
| Analysis of Variance for Y |
| Stratification Variable I |
| Total Sample Size .4800000000000D+02 |
| Number of Groups .2000000000000D+01 |
| Overall Sample Mean .1078681450604D+03 |
| Sample Standard Deviation .1734108072395D-04 |
| Total Sample Variance .3007130806747D-09 |
| Source of Variation Variation Deg.Fr Mean Square |
| Between Groups .3638341886916D-08 1 .3638341887D-08 |
| Within Groups .1049517291667D-07 46 .2281559330D-09 |
| Total .1413351479171D-07 47 .3007130807D-09 |
| Residual S.D. .1510483144465D-04 |
| R-squared .2574265445381D+00 MSB/MSW .24087272D-03 |
| F ratio .1594673363806D+02 P value .51741039D-05 |
+--------------------------------------------------------------------