This research consists of two parts involving non-parametric procedures for assessing interaction and main effects. The first part is concerned with the problem of interaction in two-way layouts with one observation per cell. After a survey of the work done so far attention is centred on the work carried out by Wolfe et al. based on orthogonal Latin squares. Analysis is made of the three procedures proposed and it is shown that for one of them the critical values for the test involved and hence the powers are highly dependent on the main effects. Proposals are made to adjust the data for the main effects by aligning the data within the levels of the two factors through row and column means or medians. A power comparison based on a Monte-Carlo simulation study reveals that the modified procedures do stabilise the critical points of the tests and lead to a more consistent power performance. The second part of the research originates from a blocked factorial experiment at Cambridge Laboratory, Cereals Research Department involving two factors. Measurement of the response variable is not possible and hence a non-parametric procedure is sought for analysis. A Friedman-type procedure is proposed for the analysis which leads to over-estimation of the residual variance and hence reduced power performance when testing one effect in the presence of the others. Two modifications are made to the proposed procedure and through a power study based on simulations it is shown that one of the modifications mitigates the drop in power performance and leads to a procedure which is comparable to the ANOVA under normality and is more efficient when severe deviations from normality occur.