Best way, and commonly used in field experiments, is to start with a proper experimental design. If soil differences (such as physical properties, commonly associated to mineral availability) are suspected, a Block Design should be used, blocking (grouping the various treatments, such as varieties) perpendicular to the direction of change in the varying environmental factor (Disturbing factor: soil fertility, moisture availability, soil physical properties, etc.). Blocking reduces the errors induced by the disturbing factors. A closer look at the advantages and disadvantages should be looked before implementation of the experimental design.

Hi Noam,

You can see A Practical Guide to Geostatistical

Mapping of Environmental Variables, there you can find some help.

See: http://eusoils.jrc.ec.europa.eu/esdb_archive/eusoils_docs/other/eur22904en.pdf

Toni

Hi Noam, if you haven’t yet started your experiment and you are planning to do it on an area with extremely variable soil, you should use a DOE (design of experiment) like a Randomized blocks design or, better, a Split-plot design.

Best way, and commonly used in field experiments, is to start with a proper experimental design. If soil differences (such as physical properties, commonly associated to mineral availability) are suspected, a Block Design should be used, blocking (grouping the various treatments, such as varieties) perpendicular to the direction of change in the varying environmental factor (Disturbing factor: soil fertility, moisture availability, soil physical properties, etc.). Blocking reduces the errors induced by the disturbing factors. A closer look at the advantages and disadvantages should be looked before implementation of the experimental design.

The previous two answers are right, you should test your soil so that you can map the variability in soil fertility and assign your varieties to plots in the field so that each variety occurs at least once in plots of the same fertility. Another possibility might be to fertilize the plots so as to bring them all up to the same fertility level before you plant your varieties.

Simple answer is DON'T NEGLECT -- your paper's reviewers certainly won't.

I) Assuming you are working in standard field plots consider the following case scenarios:

i) YOU DON'T KNOW WHICH ARE GOOD/BAD PLOTS IN YOUR STUDY --Try just adding Papadakis covariates to your ANOVA. This is usually just called Papadakis ANOVA or Papadakis Analysis.

ii) YOU DO KNOW WHICH ARE GOOD/BAD PLOTS IN YOUR STUDY -- Perhaps you even have categorical or quantitative data backing this up. Try Bayesian ANOVA model

II) If your site is not well organized into plots but you have some quatitiative covariates that relate to the GOOD/BAD then might consider spatial kriging or Bayesian kriging ideas discussed above.

III) Otherwise randomizing treatments to plots and replicating are always recommendable and (given enough replication) will also provide a purely "Frequentist" approach to addressing this kind of issue. Probably not applicable to your situation since you are likely don't have more time or resources for more data.

** Consult an applied statistician who works with experimentalist or in an extension service capacity soon.

There isn't really enough information given to answer the question fully, but "ignoring" the fertility effect won't make it go away. You need to compensate for the fertility effects. This can be done in several ways:

1. Blocking in one dimension (Randomized [in]complete block design structures).

2. Blocking in two dimensions (Latin square design structures, Latin rectangles, and their generalizations).

3. Covariance analysis, if measures of soil fertility are available for the various plots, or if standards can be planted and measured on the plots.

Covariance analysis can be used in conjunction with design structures.

Randomization is the key response. This was the main contribution of Fisher to statistics, precissely to avoid soil fertility differences in their agronomy experiments.

How do you use randomization? Dennis Clason give the three main and relatively simple ways but it depends of the extent of the experiment

If the experiment was not done, consult an applied statistician soon or find a good design in Cochran & Cox or Kuehl´s books. Sometimes I use materials from a good course of Marcia "Experimental Design for Spatial Layouts".

If you need to analyze experimental data with spatial variability without proper blocking, see the work of Federer (Biometrics 54:471) and the criticism of Gilmour (Biometrics 56:944) and references therein.

The simplest way is to apply principles of Design of Experiments (DoE) by dividing your experimental area into small and more homogeneous blocks. Then you divide each of the blocks in a number of plots equal to the number of varieties. Finally you assign, randomly for each block, one of the varieties to one of the plots of a given block. You continue the procedure to finish one block and you do the same for the remaining blocks. However, if you have a large number of varieties, which is common in early plant breeding programs you should consider incomplete block designs like alpha design.

The second solution is to sample enough your study area, use geostatistical tools (variogram and kriging) to describe, model and spatially interpolate the spatial variability of soil fertility. It is better to use a variante of kriging, i.e block kriging, such that the size of the block is the one corresponding to the size of the plot. Then you can use this information as a covariate in a analysis of covariance of a classical design like Randomized Complete Block or a more elaborate one like alpha design.

I would add to all the right answers only this concerning replications: larger number is better. You simply can’t "neglect" the soil variability, you have to tackle it, trying to handle in order to identify its effect and therefore “subtract” from your analysis. So definitively I would suggest you to increase as much as possible (reasonable) the number of replications

I would suggest to use the appropriate experimental design for your experiment. And if you still suspect there will be variation in soil fertility within blocks then take soil samples from each plot and and analyze for different parameters. Conduct your experiment and finally use the parameters from soil analysis as covariate for your variety related data. I have doubt on controlling this type of variation by increasing the replications. It is true we can reduce error by increasing replication. But we cannot eliminate the variation within blocks by increasing the number off replication.

The physico-chemical properties of soils have influence on the occurrence and distribution of microbial populations.

Thus, populations of bacteria (CFU / gr soil) change dramatically with the amount of micronutrients, pH, salinity and sand content of silt and clay.

Let me add a case study that may have some relevance here. We had a situation where soybean cyst nematode (SCN) population density was correlated with crop yield, which would usually lead a nematologist to recommend use of SCN-resistant cultivars as a management option. Yield was also correlated with soil nutrient, which would lead an agronomist/soil scientist to recommend nutrient amendment. In fact, neither recommendation alone would solved the problem in sustainable ways because there was a soil structural problem below the usual 6-12-in sampling zone. The solution is to address SCN and soil nutrient management simultaneously.

Therefore, accounting for the statistical design alone may not give you the answers that you are looking for or avoid the nutrient problem that you are facing. You may want to incorporate an integrated soil biology/physiochemical component to your experimental design.

It is not easy to separate the effect of spatial variability.

If you have knowledge of geostatistics can correct the experimental error due to the effect of spatial variability (such as nitrate-nitrogen, moisture, etc.) in the model: for exemple,SAS software has developped some macros for this purpose.

Spatial placements by randomized or latin sq designs alleviate the problem for AGRONOMY TRIALS/Research...... In selection work you are TRYING TO SEE that one plant that will give you the superior combination of traits...... this can be masked by the difference of the square meter where your plant is standing ..... you'll never know that the JACKPOT plant was ther but you missed it. In Phase 3 evaluation trials all the above mentioned advice holds true and we have found the Latin square with subsequent ANOVA analyses the top.

Selection of appropriate experimental design will handle the problem of differences in the experimental fields especially where there are differences in soil factors. if variation is in two way direction you can use lattice design. Secondly, try to block along the variation gradient, the error term will be minimized and degree of precision will be increased in the course of data analysis. I believe this will solve the problem.

Sorry I mean Latin square design.

The number of varieties to be tested can influence the decision of what type of design to use. The "complete block designs" (randomized block, Latin squares, and others) are inefficient for testing a large number of varieties. The reason is that these designs do not adequately minimize the effect of soil heterogeneity with large numbers (>25). In this situation Lattice designs (incomplete block designs) are used. In these designs each block contains fewer varieties than the total number - hence the term "incomplete". They are very well-suited for plant breeding experiments. I think Yates first developed this concept - paper attached.

I thought no one could to neglect the siol heterogeneities, the only way is to avoid these interference sources by good field experimental design as suggested information above. You may try a new method by small unmanned (remoting controlled) aircraft, with airborne far-infrared or optical camera, to take photos or video over the test site before you layout. And through the analysis of the remote sensing images, you could extract response frame, analyzing the soil heterogeneity among plots or blocks. It would be the background of experimental error control, the test data might be calibrated. Of course, the premise is to have the equipment condition and be familiar with the remote sensing image processing. if interested, you can try.

The plot can be divided into homogenous blocks. Each block should be made perpendicular to the observed fertility gradient. Complete or incomplete blocks may be used depending on the number of varieties to be tested. If the number of varieties to be compared are less (e.g. 25 incomplete blocks are efficient, i.e., each block will be divided into sub-blocks (incomplete blocks) and a subset of the test varieties are randomly assigned to each incomplete block within a block.

1. The exactness of a trial may be increased by replication number and / or plot size. The way you choose depends on the mode of spatial variation: random or consistent. If possible, first you may set a fractional plot trial to learn this.

2. That means that you should sow some area with one cultivar, divide it into 1-m^2 plots and harvest all them separately. Then calculate yield dispersion of these small plots. Then unite neighbor plots into 2 m2, 4 m2, 8 m2 and so on, and calculate s^2 as well. Finally, you obtain a hyperbolic trend: s^2 drops as plot size increases (Smith's law).

3. If the exponent of the equation

If you actually know the soil attributes across your field (I am assuming you have already conducted your study), use the soil attributes as covariates in an analysis of covariance. Including variety by covariate interactions enable one to determine if one variety is better at low nitrogen levels than another.

Use of some soil attributes as covariate may be a statistical problem. the Variability in soil characteristics is associated to neighbor effects and, so, don't can to assume indenpendence presumption on soil observations.

i fully agree with Claudio that making blocks perpendicular to the direction of change of soil factors can help in minimising the soil heterogeneity. Replication, Randomisation and local error control and proper experimental plot design will collectively help in reducing the soil variation.

Soil heterogeneity should be taken into account in each field experiment in order to make the results meaningful. For planning experiments you may wish to consult the following standard work:

Experimental Designs, 2nd Edition, by William G. Cochran and Gertrude M. Cox

Noam, you may have to look into spatial autocorrelation effects. Spatial autocorrelation tells you whether things that are close together are more similar on some attribute than things are further apart.

You can include spatial effects in a regression analysis using a spatial autoregressive (SAR) model, for example the Stata program will do it:

http://repec.org/snasug08/drukker_spatial.pdf

This paper SPATIAL AUTOCORRELATION AND AUTOREGRESSIVE MODELS

IN ECOLOGY , LICHSTEIN et al migt also be useful.

http://www4.ncsu.edu/~simons/Lichstein%20et%20al%20Ecol%20Monog.pdf

We are usually use the "control" or "check" variety during field experiment (plus to other described methods). Usually it is a well known variety with low level of adaptability. We sow it every 10-20-30 experimental varieties (this depends from number of experimental varieties, type and shape of field...). For ex.:

C 1 2 3 4 5 6 7 8 9 10 C 11 12 13 14 15 16 17 18 19 20 C 21...

31 32 33 34 35 C 36 37 38 39 40 41 42 43 44 45 C 46 ...

The variation of productivity of this variety describes the differences in the places of field. As a result, it is possible to design the "map" of experimental field and use the "correction coefficient" to calculate the potential plant's productivity to simulate the situation when all points of field have the same conditions.

You should be able to look for row and columnn effects and correct for these within a REML analysis in Genstat. First off I would plot the residuals from the anova using the layout of the trial so you can see if there are evident spatial effects ... you can do this as a further output from anova in Genstat. You can then use REML analysis to look for autoregressive effects of rows and columns in the random model.

Noam, using the word neglect soil spatial differences is not good. Usually, when we plan for a field experiment we aim at testing the treatments under real conditions, and in case of varietal evaluation we can get results that can have direct bearing on farmer's fields. Thus instead of ignoring the spatial variability, accommodate it during design of the experiment. The field can vary in many ways, including soil moisture retention, fertility, particles size and distribution, organic matter content, etc. In order to account for this natural variability, you should use a correct design and correct layout of your plots with appropriate number of replications (see previous answers on this question). Knowing your field conditions, layout your blocks such that you may accommodate as uniform a variability as possible. You could be guided by the slope of the field. You could replicate your blocks contour-wise to achieve this recommendation. Good luck and hope that I understood your problem.

In order to neglect the effects of spatial soil differences in an agricultural field experiments, development of most adequate Lattice desig could be one of best possibilities. Optimal number of replications, size of plots, number of treatments (varieties) and checks, also must be taken into consideration.

See:

http://www.cabi.org/gara/FullTextPDF/2010/20103160490.pdf

http://www.iasri.res.in/iasriwebsite/DESIGNOFEXPAPPLICATION/Electronic-Book/Module%202/4LATTICE%20Designs.pdf

http://www.stat.ncsu.edu/people/dickey/courses/st711/notes/Notes_pdf/Alpha%20Lattice%20designs.pdf

http://www2.hawaii.edu/~halina/603/IncBlock.pdf

Good luck!

You can use the full array block design to reduce experimental error caused by the spatial distribution of soil