Balanced factorial experiments.II

Pun and Nigam(1976) have developed the theory of Balanced Factorial Experiments (BFE) in varying replicates and varying block sizes. The present work gives some further results on BFE. It is established that any BFE with merged treatments (or collapsed levels in the sense of Addleman, 1962) is again a BFE, It is shown that BFE implies and is implied by a Partially Efficiency Balanced (PEB) design. Interestingly, the results of Pearce (1971) on merging of two treatments can also be obtained as particular cases.     

Analysis of covariance as an alternative approach to the analysis of non-orthogonal lay-outs

Though the analysis of two, three, and four-way non-orthogonal lay-outs is available in literature, it involves tedious calculations, and experimenters refrain using higher-way non-orthogonal lay-outs where computer facilities are not available. This paper will show that the analysis of a n-way lay-out can be considered as the analysis of a (n-1) lay-out with covariance and this approach is expected to minimize the calculations when the analysis has to be carried through desk calculators.     

On screening samples in the laboratory and factors in factorial investigations

Procedures such as group testing and fractional replication can greatly reduce the workload. The former is especially efficient when the presence of a characteristic in samples is low. Fractional replication can greatly reduce the amount of experimentation when some of the parameters associated with a factorial are nonexistent or negligible. Supersaturated fractional replication can be used to efficiently screen factors when it is suspected that they may not affect a process but it is desired to check this suspicion. There are many types of grouping and pooling material in an investigation. Some of these are discussed as are the interrelationships among the above procedures.     

A monte carlo study of the f test and three tests based on ranks of treatment effects in randomized block designs

The F test is compared with three procedures based on ranks for testing treatment effects in the randomized complete block, fixed effects, model with one observation per cell.     

Robustness group divisible designs

Robustness of group divisible (GD) designs is investigated, when one block is lost, in terms of efficiency of the residual design. The exact evaluation of the efficiency can be made for singular GD and semi-regular GD designs as ell as regular GD designs with λ₁ = 0. In a regular GD design with λ₁ > 0, the efficiency may depend upon the lost block and sharp upper and lower bounds on the efficiency are presented. The investigation shows that GD designs are fairly robust in terms of efficiency. As a special case, we can also show the robustness of balanced incomplete block design when one block is lost.     

Breaking alias chains in fractional factorials

Some experimenters carry out their investigation in stages. They begin with an initial 2^n-p fraction of resolution IV, in which the main effects are clean and the interactions are aliased in chains, Then, having analyzed the initial experiment, they plan further runs to isolate certain interactions by breaking the chains. In this paper a method called semifolding, for choosing the points in the second experiment, is presented.     

Designs balanced for circular residual effects

Magda (1980) introduced a model for repeated measurements designs with a circular structure of the residual effects. He proved the universal optimality of circular balanced uniform designs over a subclass of the possible designs. We strengthen his result to optimality over the set of all designs with the same number of experimental units, periods and treatments.     

Stability and Validity of the Holden Psychological Screening Inventory (HPSI) in Psychiatric Inpatients

Abstract

Forty-seven psychiatric inpatients in a Canadian psychiatric hospital participated in an evaluation of the stability and validity of the Holden Psychological Screening Inventory (HPSI). Stability coefficients over a 1-month period were .85, .79, and .66 for the HPSI Psychiatric, Social, and Depression Symptomatology scales, respectively, and coefficient alpha reliabilities for these scales ranged between .76 and .89 across both time periods. Staff rating composite scales corresponding to the self-report HPSI scales had stability coefficients of .74, .85, and .82, respectively. As well, they had inter-rater reliabilities that ranged between .65 and .84 across both time periods. The 3 staff rating composites at time 1 correlated equivalently with the corresponding 3 primary HPSI scales at times 1 and 2 (p > .05). Similarly, the 3 staff rating composites at time 2 correlated equivalently with the corresponding 3 primary HPSI scales at times 1 and 2 (p > .05). Over a 1-month period, HPSI scale scores were very stable and correlations with criterion ratings were stable. Using a confirmatory factor analysis, with each of the 3 dimensions defined by the time 1 and 2 measures for the 3 HPSI scales and 3 staff rating composites, evidence for discriminant as well as convergent validity was obtained. In summary, the self-report HPSI and the staff rating composite measures evidenced sufficient reliability and validity to meet the requirements for routine clinical assessment work with psychiatric inpatients. Additionally, the stability data provide effects of retesting baseline data for assessing treatment outcome in this population.     

On choosing between fixed and random block effects in some no-interaction models

The purpose of this article is to strengthen the understanding of the relationship between a fixed-blocks and random-blocks analysis in models that do not include interactions between treatments and blocks. Treating the block effects as random has been recommended in the literature for balanced incomplete block designs (BIBD) because it results in smaller variances of treatment contrasts. This reduction in variance is large if the block-to-block variation relative to the total variation is small. However, this analysis is also more complicated because it results in a subjective interpretation of results if the block variance component is non-positive. The probability of a non-positive variance component is large precisely in those situations where a random-blocks analysis is useful – that is, when the block-to-block variation, relative to the total variation, is small. In contrast, the analysis in which the block effects are fixed is computationally simpler and less subjective. The loss in power for some BIBD with a fixed effects analysis is trivial. In such cases, we recommend treating the block effects as fixed. For response surface experiments designed in blocks, however, an opposite recommendation is made. When block effects are fixed, the variance of the estimated response surface is not uniquely estimated, and in practice this variance is obtained by ignoring the block effect. It is argued that a more reasonable approach is to treat the block effects to be random than to ignore it.     

Designs with Repeated Measurements on Any Number of Units over Varying Periods

In the usual repeated measurements designs (RMDs), the subjects are all observed for the same number of periods and the optimum RMDs require specified numbers of subjects, usually depending on the number of treatments to be used. In practice, it is sometimes not feasible to meet these requirements. To overcome this problem, alternative designs are suggested where any number of available subjects may be used and they may be observed for different periods. These designs are based on suitable serially balanced sequences which are shown to be optimal. Moreover, besides the usual direct and residual effects, the model considered has an extra term due to the interaction effect between them. The recommended designs are universally optimal in a very general class.