Indian Institutes of Technology

Some Results on Linear Algebra, Matrix Theory and Distributions

Consider the set-up of a complete factorial experiment, say 2k. If there are four factors, then the total number of plots needed to conduct the experiment is 4 2 16.  When the number of factors increases to six, then the required number of plots to conduct the experiment becomes 6 2 64  and so on. Moreover, the number of treatment combinations also becomes large when the number of factors increases.

We consider the models which are used in designing an experiment. The experimental conditions, experimental setup and the objective of the study primarily determine that what type of design is to be used and hence which type of design model can be used for the further statistical analysis to conclude about the decisions. These models are based on one-way classification, two-way classifications (with or without interactions), etc. We discuss them now in detail in a few setups which can be ex...

The completely randomized design and randomized block design may not be suitable in such situations because they will require a large number of experimental units to accommodate all the treatments. In such cases, when the a sufficient number of homogeneous experimental units are not available to accommodate all the treatments in a block, then incomplete block designs can be used.

Factorial experiments involve simultaneously more than one factor and each factor is at two or more levels. Several factors affect simultaneously the characteristic under study in factorial experiments and the experimenter is interested in the main effects and the interaction effects among different factors.

Any scientific experiment is performed to know something that is unknown about a group of treatments and to test certain hypothesis about the corresponding treatment effect. When variability of experimental units is small relative to the treatment differences and the experimenter do not wishes to use experimental design, then just take large number of observations on each treatment effect and compute its mean. The variation around mean can be made as small as desired by taking more observat...

Design of experiment means how to design an experiment in the sense that how the observations or measurements should be obtained to answer a query in a valid, efficient and economical way. The designing of the experiment and the analysis of obtained data are inseparable. If the experiment is designed properly keeping in mind the question, then the data generated is valid and proper analysis of data provides the valid statistical inferences. If the experiment is not well designed, the validit...

The same linear model is used in the linear regression analysis as well as in the analysis of variance. So it is important to understand the role of a linear model in the context of linear regression analysis and analysis of variance

The balanced incomplete block designs have several advantages. They are connected designs as well as the block sizes are also equal. A restriction on using the BIBD is that they are not available for all parameter combinations.

The objective of confounding is to mix the less important treatment combinations with the block effect differences so that higher accuracy can be provided to the other important treatment comparisons. When such mixing of treatment contrasts and block differences is done in all the replicates, then it is termed as total confounding.