In such situations with only one replication a better way is to measure several factors for each plot and analyse them with Ordination or Classification methods. But, be careful of this, because the size of plots is very determinant. The smaller the size of plots, the higher the significant differences by chance. The larger the size, the lower the uniformity of within plot data.

Good Luck

Thanks very much Ehsan, we'll try your recommendation.

Cheers!.

This depends very much on your experimental design. Highly factorial designs, for example, often have no replication, and indeed are frequently fractional. Error variability estimates are generated by assuming that high order interactions are negligible. Whether or not this makes sense depends on the scientific context. In very highly factorial designs, the higher order interactions generally are unimportant. But you wouldn't want to do this with just a few factors. This page may help you: http://methodology.psu.edu/ra/most/fefaq#t41n264

If you have unreplicated trials in several locations, you can use the treatment x location interaction MS as an error term, and previously test the interaction MS using the Tukey one degree for additivity test. For individual analysis, moving averages can be used to adjust plot data.

Another alternative is to include replicated checks randomly or systematically interspersed and adjust plot data by check neighbors.

There is a good review in a Symposium on Unreplicated experiments in Crop Science, Vol. 46 (Nov–Dec 2006). See articles by Payne and Perrett.

Thanks very much Mervyn and Francisco, we'll read the suggested information.

Cheers!.

Another tip: If you have a rectangular array with +50 entries (i. e 5 rows, 10 cols), you can use spatial analysis; see Burgueño et al "User's Guide for Spatial Analysis of Field Variety Trials Using ASREML" (http://repository.cimmyt.org/xmlui/bitstream/handle/10883/584/73230.pdf). Good luck

What all of these answers have in common is that you find a reduced model for the effects of interest, so that if you have 50 plots with 50 treatments, your model has < 50 parameters. The residuals from that model are then used to estimate variance.

But, if you have a small number of treatments, (and one plot per treatment) then you are most unlikely to be able to find a reduced model. In which case, there isn't a lot that you can do unless you have very good estimates of uncertainty from previous work. That would be very dangerous.

This is true for factorial designs. For variety trials is more complicated, we want to adjust means against fertility trends or spatial variability and secondly test differences. In that situation we need some kind of replication, mainly in space with different locations (not necessarily with the same set of varieties in all places), or use pseudoreplication and then adjust using results from past works. I agree that it is hard to work with this kind of data.

I work on field also, and i found similar problems with using data without replication. I use Chi-squared test in this case to compare treatments.

All the best