Advanced search
Publication Cover
Journal of Quality Technology
A Quarterly Journal of Methods, Applications and Related Topics
Volume 6, 1974 - Issue 3
Submit an article Journal homepage
8
Views
9
CrossRef citations to date
0
Altmetric
Articles

Computation and Use of Expected Mean Squares in Analysis of Variance

Ronald D. SneeE. I. du Pont de Nemours and Company, Inc., Wilmington, Delaware19898View further author information
Pages 128-137 | Published online: 27 Feb 2018

References

Periodicals

  • Bainbridge, T. R., “Staggered, Nested Designs for Estimating Variance Components,”, Industrial Quality Control, Vol. 22, No. 1, July 1965, pp. 12–20.
  • Cochran, W. G., “Testing a Linear Relation Among Variances,”, Biometrics, Vol. 7, 1951, pp. 17–32.
  • Cornfield, J., and Tukey, J. W., “Average Values of Mean Squares in Factorials,”, Annals of Mathematical Statistics, Vol. 27, 1956, pp. 907–949.
  • Davenport, J. M., and Webster, J. T., “Type-I Error and Power of a Test Involving a Satterthwaite's Approximate F-Statistic,”, Technometrics, Vol. 14, No. 3, August 1972, pp. 555–569.
  • Eisen, E. J., “The Quasi-F Test for an Unnested Factor in an Unbalanced Hierarchal Design with a Mixed Model,”, Biometrics, Vol. 22, No. 4, December 1966, pp. 937–942.
  • Gaito, J., “Expected Mean Squares in Analysis of Variance Techniques,”, Psychological Reports, Vol. 7, 1960, pp. 3–10.
  • Ganguli, M., “A Note on Nested Sampling,”, Sankhyā, Vol. 5, 1931, pp. 449–452.
  • Gates, C. E., and Shive, C., “The Analysis of Variance of the S-stage Hierarchal Classification,”, Biometrics, Vol. 18, 1962, pp. 529–536.
  • Gaylor, D. W., and Hartwell, T. D., “Expected Mean Squares for Nested Classifications,”, Biometrics, Vol. 25, No. 2, June 1969, pp. 427–430.
  • Gaylor, D. W., and Hopper, F. N., “Estimating the Degrees of Freedom for Linear Combinations of Mean Squares by Satterthwaite's Formula,”, Technometrics, Vol. 11, No. 4, November 1969, pp. 691–706.
  • Gaylor, D. W., Lucas, H. L., and Anderson, R. L., “Calculation of Expected Mean Squares by the Abbreviated Doolittle and Square Root Methods,”, Biometrics, Vol. 26, No. 4, December 1970, pp. 641–656.
  • Gower, J. C., “Variance Component Estimation for Unbalanced Hierarchal Classifications,”, Biometrics, Vol. 18, 1962, pp. 537–542.
  • Hartley, H. O., “Expectation, Variances and Co-variances of ANOVA Mean Squares by ‘Synthesis,’”, Biometrics, Vol. 23, No. 1, March 1967, pp. 105–114, 853.
  • Hicks, C. R., “Fundamentals of Analysis of Variance,”, Industrial Quality Control, Vol. 13, 1956, No. 3, pp. 5–8, No. 4, pp. 13–16.
  • Howe, R. B., and Myers, R. H., “An Alternative to Satterthwaite's Test Involving Positive Linear Combinations of Variance Components,”, Journal of the American Statistical Association, Vol. 65, No. 329, March 1970, pp. 404–412.
  • Hudson, J. D., and Krutchkoff, R. G., “A Monte Carlo Investigation of the Size and Power of Tests Employing Satterthwaite's Synthetic Mean Squares,”, Biometrika, Vol. 55, No. 2,1968, pp. 431–433.
  • Mahamunulu, D. M., “Sampling Variances of the Estimates of Variance Components in the Unbalanced 3-Way Nested Classification,” Annals of Mathematical Statistics, Vol. 34, 1963, pp. 521–527.
  • Rao, J. N. K., “On Expectations, Variances, and Co-variances of ANOVA Mean Squares by ‘Synthesis,’”, Biometrics, Vol. 24, No. 4, December 1968, pp. 963–978.
  • Satterthwaite, F. E., “Synthesis of Variance,”, Psychometrika, Vol. 6, 1941, pp. 309–316.
  • Satterthwaite, F. E., “An Approximate Distribution of Estimates of Variance Components,”, Biometrics Bulletin, Vol. 2, 1946, pp. 110–114.
  • Searle, S. R., and Fawcett, R. F., “Expected Mean Squares in Variance Components Models having Finite Populations,”, Biometrics, Vol. 26, No. 2, June 1970, pp. 243–254.
  • Schultz, E. F., Jr., “Rules of Thumb for Determining Expectations of Mean Squares in Analysis of Variance,”, Biometrics, Vol. 11, No. 2, June 1955, pp. 123–135.
  • Smith, H., “The Analysis of Data from a Designed Experiment,”, Journal of Quality Technology, Vol. 1, No. 4, October 1969, pp. 259–263.
  • Tietjen, G. L., and Moore, R. H., “On Testing Significance of Components of Variance in the Unbalanced Nested Analysis of Variance,”, Biometrics, Vol. 24, No. 2, June 1968, pp. 423–429.

Books

  • Anderson, R. L., and Bancroft, T. A., Statistical Theory in Research, McGraw-Hill, New York, 1952, pp. 327–330.
  • Bennett, C. A., and Franklin, N. L., Statistical Analysis in Chemistry and the Chemical Industry, John Wiley & Sons, Inc., New York, 1954, Chapter 7.
  • Brownlee, K., Statistical Theory and Methodology in Science and Engineering, First Edition, John Wiley & Sons, New York, 1960, Chapter 13.
  • Hicks, C. R., Fundamental Concepts in Design of Experiments, Holt, Rinehart, and Winston, New York, 1964, pp. 153–163.
  • Ostle, B., Statistics in Research, Second Edition, Iowa State University Press, Ames, Iowa, 1963, Chapters 11 and 12.
  • Scheffé, H., Analysis of Variance, John Wiley & Sons, Inc., New York, 1959, pp. 247–248, 284–289.
  • Searle, S. R., Linear Models, John Wiley & Sons, New York, 1971, pp. 411–413.
  • Steel, R. D. G., and Torrie, J., Principles and Procedures of Statistics, McGraw-Hill, New York, 1960, Chapter 11.
  • Winer, B., Statistical Principles in Experimental Design, McGraw-Hill, New York, 1962, Chapter 5.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.