ANOVA in agronomy: When can you rely on it ?
Have you never wondered: “How on earth can I explain the results of this field experiment?” I’m sure you have already heard of the ANOVA. You may even use it to analyze your data, but this statistical tool can be tricky, notably with few repetitions, missing data. Let’s see when this test can help you and how to make the most of it.
Interpreting the results of an agronomic experiment is a complex task because of the variability of the living material studied. Many factors such as the environment, culture protocol and genetics have deeply intricated consequences on the findings of studies. The Analysis Of Variance - ANOVA - makes it easier for you to analyze datasets and assess the validity of your results. However, it is crucial to avoid a few common mistakes to guarantee the reliability of ANOVA and its interpretation. And we are here to help you doing that ;-).
“Before ANOVA and its applications for designing field experiments, agronomic research was a patchwork of field trials that produced treatment differences that were unrepeatable and biased.” Marla S. McIntosh¹
When is ANOVA worthy for agronomic research?
ANOVA allows you to find out if experiment results are significant, by comparing groups of data. It is used in testing to study the differences between several treatments, for example phytosanitary spraying, variety or location. It is also useful in plant breeding to evaluate the heritability of a trait. Sounds good? Let’s see how to use it !
“Agriculturalists seek general explanations for the variations in agricultural yields in response to a treatment. An increasingly popular solution is the powerful statistical technique one-way ANOVA.”²
Choose a design that meets your experiment goals
When designing your experiment, beware of the quality and the number of replicates you produce: They affect the accuracy of your results – and therefore, your conclusions.
ANOVA works well with true replicates. What does it mean? Applying a treatment to various independent units. For example, if you grow plants in a same plot, where you spray herbicide before scoring each plants separately, you are making pseudo-replicates. However, if you use several plots, you are making useful replicates, and you can use ANOVA. Yey!
Generally, 4 to 6 replicates are enough in agronomy. Still, depending on your design - and your passion for replicates - you might want to use more. Let’s stick with the example of herbicide: if you apply scant amounts of thinned herbicide on a few plots, you will record only small differences between the treatments. Using more replicates would help you to get more precise results. Looking at the results of similar studies can help you calculate the optimum number of replicates and elect the right sampling size for your experiment.
Now you have the perfect design, let’s play with statistics to analyze your data. Why are you laughing? Yes, statistics are fun!
“Better experimental design and statistical analysis make for more robust science”³
One-Way or Two-Way ANOVA depending on your needs
One-Way ANOVA compares the means of several data groups. Hum, that is theory, let’s apply it to an example: You are testing two different phytosanitary products. ANOVA will tell you whether there is a significant difference in the means, and therefore if your plant is more sensitive to one of the herbicides. Isn’t that wonderful?
Two-Way ANOVA is useful for studying the interrelationship of 2 factors. In the previous example, you were only testing the response of one variety of plant to several herbicides. But what if you are comparing several varieties? You can use a Two-Way ANOVA which tells you if each variety is as sensitive to herbicides as the other and if one herbicide is more efficient than the other. It also assesses the interaction between the factors - here variety and herbicide.
In a nutshell, One-Way ANOVA is useful to studying the effect of one factor - herbicide in the example. If you are working on the effect of two different factors, you can use Two-Way ANOVA. You see? I told you it was simple. Now let’s see the 3 conditions to meet for a significant ANOVA.
“The statistical validity of ANOVA hinges on comprehensive statistical analyses appropriate for the populations and hypotheses tested.”4
Make sure the test’s assumptions are met
ANOVA has three key assumptions: homogeneity, independent errors, and normality. Keep calm, let me explain!
To confirm homogeneity of data, make sure that groups of units receiving a same treatment have similar variances. Don’t worry, it is the case most of the time. Otherwise, you can just transform your data with a logarithm or square root to correct it. Easy peasy.
Now what is it with independent errors? It means you can’t apply the same treatment to experimental units that are very close. Why? Because their results may be similar due to a shared environment. What can you do? Simple: You work with a randomized design and proper replicates. Lucky you, replicate lover!
Last but not least, errors should be normally distributed. It means that you can just check that most values are close to the group mean – or that few of them are extreme. Don’t panic, ANOVA is only sensitive to normality for small amounts of data (less than ~30): In many cases in agronomy you have more data! Otherwise you can use a logarithm or square root to correct it.
“Surveys of biological and agricultural journals indicate that at the end of last century, 70 % of research papers involved incorrect use or interpretation of statistics.”5
Agronomy research software helping you with ANOVA
Now you see what the ANOVA represents for your agronomical trials. But how to proceed? You can find various software programs to do the test for you.
RnDExperience™ has been designed especially for agronomists. When your data is stored in the database, you can launch a standard statistical report in one click, including an ANOVA. Even if you are not fully at ease with statistics, you are able to analyze the results yourself in real time. Your data analyst or colleague who used to deal with your raw data will thank you !
Now if it’s your thing, open the statistical wizard included in RnDExperience™ research software: You will find the most advanced options to optimize the study of trial variation factors. And since your colleagues are autonomous with their trials, you have time to focus on your own experimentations, or go further with advanced analysis.
“Elaborate statistics are not substitute for meticulous experimentation.”6 G.W. Snedecor
From our 30 years of experience in IT for plant breeding and testing departments, at Doriane we have seen the benefits to let a secured analysis tool in the hands of researchers. Statistics are the cornerstone of vegetal experimentation, and R&D departments have much to gain in facilitating and automating the whole procedure.
1- Can Analysis of Variance Be More Significant?, Agronomy Journal, 2015, Marla S. McIntosh
2- One Way ANOVA: Concepts and Application in Agricultural System, Hussaini Adamu Federal Polytechnic Kazaure, Jigawa, Nigeria, 2018, Abubakar et al.
3- Applied Statistics in Agricultural, Biological, and Environmental Sciences, American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Madisson, 2018, Burgueño et al.
4- Can Analysis of Variance Be More Significant?, Agronomy Journal, 2015, Marla S. McIntosh
5- Application of statistics in plant and crop research: important issues, Zemdirbyste-Agriculture, 2017, Steponas Raudionus
6- Statistical Methods Applied To Experiments In Agriculture And Biology, The Iowa State College Press, 1938, George W. Snedecor
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3.left : https://www.indiamart.com/proddetail/agricultural-greenhouses-21123575588.html
3.right: The Intermountain (site internet)
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