Other Special Designs - Designs with Cell N of 1
In some instances the observations for the study are not easy to come by, and costs are associated with obtaining an observation. Economic aspects then have to be weighed against design aspects. One way to design economical experiments is to select only single observations for different cells in the design.
If the design is a full factorial design with an N of 1 in each cell, then estimating the sums of squares for all effects exhausts the degrees of freedom, and no SS error can be computed. To analyze such designs, first compute the complete table of all effects; of course, because no SS-error can be computed, no F-tests can be computed either. Then examine the reported Means Squares (MS; SS divided by the respective degrees of freedom). Their size is an estimate of the size of the respective effect. Use that information to decide which effects to pool into the error term (the small, non-significant effects). Usually, one discards higher order interactions in these types of designs. Finally, use the GLM and ANOVA More Results - Custom Tests tab to "build" the chosen error term and to test the statistical significance of effects. However, remember that the statistical significance tests here are not to be taken too literally because this procedure capitalizes on chance (only small effects are pooled into the error).