Type I Analysis by Projections

사영에 의한 제1종 분석

  • Received : 20110100
  • Accepted : 20110300
  • Published : 2011.04.30


This paper discusses how to get the sums of squares due to treatment factors when Type I Analysis is used by projections for the analysis of data under the assumption of a two-way ANOVA model. The suggested method does not need to calculate the residual sums of squares for the calculation of sums of squares. There-fore, the calculation is easier and faster than classical ANOVA methods. It also discusses how eigenvectors and eigenvalues of the projection matrices can be used to get the calculation of sums of squares. An example is given to illustrate the calculation procedure by projections for unbalanced data.


Projection;Type I Analysis;unbalanced data;projection matrix;eigenvector;eigenvalue


  1. 최재성 (2008). 반복측정의 다가 반응자료에 대한 일반화된 주변 로짓모형, <응용통계연구>, 32, 621-630.
  2. Corbeil, R. R. and Searle, S. R. (1976). A comparison of variance component estimators, Biometrics, 32, 779-791.
  3. Graybill, F. A. (1976). Theory and Application of the Linear Model, Wadsworth, California.
  4. Milliken, G. A. and Johnson, D. E. (1984). Analysis of Messy Data, Van Nostrand Reinhold, New York.
  5. Montgomery, D. C. (1976). Design and Analysis of Experiments, John Wiley & Sons, New York.
  6. Searle, S. R., Casella, G. and McCulloch, C. E. (1992). Variance Components, John Wiley & Sons, New York.
  7. Steel, R. G. and Torrie, J. H. (1980). Principles and Procedures of Statistics, McGraw-Hill, New York.

Cited by

  1. Variance Components of Nested Designs vol.28, pp.6, 2015,
  2. Projection analysis for balanced incomplete block designs vol.26, pp.2, 2015,
  3. Estimable functions of mixed models vol.29, pp.2, 2016,
  4. Interblock Information from BIBD Mixed Effects vol.28, pp.2, 2015,
  5. Type II analysis by projections vol.23, pp.6, 2012,
  6. Type III sums of squares by projections vol.25, pp.4, 2014,
  7. Projection analysis for two-way variance components vol.25, pp.3, 2014,
  8. The analysis of random effects model by projections vol.26, pp.1, 2015,


Supported by : 계명대학교