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Programmes → I.M.Sc. in Mathematical Sciences and M.Sc. in Statistics-OR

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Design and Analysis of Experiments

Course Code: IM 403; ST 503  |  Credits: 4  |  Prerequisite: Linear Algebra and Matrix Theory

Syllabus Details

  • ANOVA and Basic Designs: Review of linear estimation and basic designs; elimination of heterogeneity in two directions; ANOVA: fixed effect models (2-way classification with equal, unequal and proportional number of observations per cell), random and mixed effect models (2-way classification with m (> 1) observations per cell).
  • Block Designs: Connectedness, orthogonality, balance and efficiency; resolvable designs; properties of BIB designs, designs derived from BIB designs; intrablock analysis of BIB, recovery of inter-block information in BIB designs; row column and Youden square designs; missing plot technique; elementary ideas of lattice and PBIB designs.
  • Finite Fields, Finite Geometries and Constructions: Finite fields; finite geometries: projective geometry and Euclidean geometry; construction of complete set of mutually orthogonal latin squares (MOLS); construction of BIBD using finite Abelian groups, MOLS, finite geometry and method of differences.
  • Factorial Designs: Analysis, confounding and balancing in symmetric factorials; response surface designs.

Course Learning Objective

  1. Apply ANOVA for 1- and 2-way classification, for (a) fixed effect models with equal, unequal and proportional number of observations per cell, and (b) random and mixed effect models with m (> 1) observations per cell.
  2. Discuss and use incomplete block designs, and discuss the concepts of orthogonality, connectedness and balance.
  3. Discuss the concepts of finite fields and finite geometries and apply them in construction of Latin squares, balanced incomplete block designs and confounded factorial experiments.
  4. Identify the effects of different factors and their interactions and analyze factorial experiments.
  5. Apply appropriate factorial designs and perform their analysis, explain the practical utility of split-plot designs, and understand the effects of independence or dependence of different factors under study.
  6. Discuss the background and utility of response surface designs.
  1. Chakrabarti, M. C. Mathematics of Design and Analysis of Experiments. Asia Publishing House, Bombay, 1962
  2. Mardia, K. V., Kent, J. T. and Bibby, J. M. Multivariate Analysis. Academic Press, 1979
  3. Dey, A. Theory of Block Designs. John Wiley & Sons, 1986
  4. Montgomery, D. C. Design and Analysis of Experiments. 6th ed. John Wiley & Sons, 2005
  5. Raghavarao, D. and Padgett, L. V. Block Designs: Analysis, Combinatorics, and Applications. World Scientific, 2005
  6. Raghavarao, D. Construction and Combinatorial Problems in Design of Experiments. John Wiley & Sons, 1970
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