Useful for UGC NET · ASRB NET · ISS
This is the complete study package for Design and Analysis of Experiments (STS-203) together with Section A of STS-206, Designs and Analysis of Experiments and Sampling Theory (Conventional). The Foundation course laid out three designs — completely randomised, randomised block, Latin square — and analysed each. This course is about what to do when those three are not enough: when a cell holds several observations, when several factors must be studied at once, when the block is too small to hold every treatment, and when the factor levels are quantities and the question is where the optimum lies.
What a second observation per cell buys — a pure error term and a testable interaction; proportional cell frequencies, which keep the design orthogonal, and disproportionate ones, which do not, worked to the point where the naive arithmetic produces a negative sum of squares; Fisher's LSD, Duncan's multiple range and Tukey's HSD with the studentized-range points computed rather than quoted; and the analysis of covariance.
UNIT 2Begins where the Foundation factorial section stops. The generating form that writes any contrast down without thinking about signs; Yates's algorithm through the three passes of a \(2^{3}\), with the two checks the \(2^{2}\) case is too small to motivate; the variance every effect shares; the \(3^{2}\) factorial split into linear and quadratic single-degree components that add back to the whole; and what a three-factor interaction measures.
UNIT 3Confounding as a trade of one contrast for a smaller block, with the block sum of squares shown to equal the confounded effect's; partial confounding and its relative information; aliasing, defining relations and resolution for the half fraction of \(2^{4}\) and the quarter fraction of \(2^{5}\); split-plot designs and their two error terms; and balanced incomplete blocks, analysed in full with adjusted means and the efficiency factor.
UNIT 4Two associate classes and what regularity buys, verified on the triangular scheme; simple lattices and Youden squares; then response surface methodology — the first-order model, the curvature test that only centre points can provide, the path of steepest ascent, and the central composite design whose rotatability condition \(\alpha = F^{1/4}\) is derived from the design moments and then checked numerically.
PRACTICALAll sixteen prescribed experiments: thirteen worked in the units, plus one-way analysis of covariance worked from scratch on data where the adjustment reverses the ranking of two treatments, the two-way case, and the identification and construction of confounded arrangements in \(2^{3}\), \(2^{4}\) and \(3^{2}\).
REFERENCEThe prescribed unit-wise outline for STS-203 and the Section A practical list for STS-206, as printed, with the objectives, outcomes, the stated pre-requisite and the reading list.
| What is built here | Where it is used |
|---|---|
| Interaction, and the pure error that makes it testable | Every factorial analysis; the curvature test of Unit 4; and the reason a two-way table with one observation per cell in the Foundation Unit 1 has to assume additivity |
| Non-orthogonal analysis by fitting constants | The same \(R(A \mid \mu, B)\) reduction as the multiple regression \(t\) statistic in Multivariate Analysis, Unit 2, and the rank-deficient normal equations of Linear Algebra and Linear Models, Unit 4 |
| Contrasts and orthogonal polynomial components | Any test aimed at a specific alternative rather than at “some difference”; trend analysis over ordered levels |
| Confounding and fractional replication | Screening designs wherever runs are expensive; the fractional factorial profiles of conjoint analysis in Multivariate Analysis, Unit 4 |
| Incomplete block designs | Any comparison where the natural block is smaller than the treatment set — tasting panels, machine positions, litters |
| Response surface methodology | Process optimisation; the quadratic form and its eigenvalues from Linear Algebra, Unit 3 classify the stationary point |