ANOVA

Method categorization
Quantitative	Qualitative
Inductive	Deductive
Individual	System	Global
Past	Present	Future

In short: The Analysis of Variance is a statistical method that allows to test differences of the mean values of groups within a sample.

• • 0) visualisation of a typical result**

MAKE BOXPLOT OF YIELDS DATASET

• • 1) background:**

With a rise in knowledge during the enlightenment, it became apparent that the controlled setting of a laboratory was not enough for experiments, as more knowledge as out to be discovered in the real world. First in astronomy, but then also in agriculture and other fields the notion became apparent that our reproducible settings may sometimes be hard to achieve within real world settings. Observations can be unreliable, and error of measurements in astronomy was a prevalent problem in the 18th and 19th century. Fisher equally recognised the mess - or variance - that nature forces onto a systematic experimenter. The demand for more food due to the rise in population, and the availability of potent seed varieties and fertiliser - both made possible thanks to scientific experimentation - raised the question how to conduct experiments under field conditions. Build on the previous development of the t-test, Fisher proposed the Analysis of Variance, which allowed fro experimental setting where several categories could be compared in an experimental settings, comparing how a continuous variable fared under different experimental settings. Making experiments in the laboratory reached its outer borders, as plant growth experiments were hard to conduct in the small confined spaces of a laboratory, and it was questioned whether the results were actually applicable in the real world. Hence experiments literally shifted into fields, with a dramatic effect on their design, conduct and outcome. While laboratory conditions aimed to minimise variance - ideally conducting experiments with a high confidence -, the new field experiments increased sample size to tame the variability - or messiness - of factors that could not be controlled, such as subtle changes in the soil or microclimate. Fisher and his Analysis of Variance became the forefront of a new development of scientifically designed experiments, which allowed for a systematic testing of hypothesis under field conditions, taming variance through replicates. The power of repeated samples allowed to account for the variance under field conditions, and thus compare differences in mean values between different treatments, comparing for instance different levels of fertiliser to optimise plant growth. Establishing the field experiment became thus a step in the scientific development, but also in the industrial capabilities associated to it. Science contributed directly to the efficiency of production, for better or worse. Equally did the such systematic experiments translate into other domains of science such as psychology and medicine.

• • 2) What the method does**

The analysis of variance allow to compare how a continuous variable differs under different treatments in a designed experiment.

• • categorization:**

- inductive - **deductive** - qualitative - **quantitative** -** individual - system** - global - **present**-past-future

• • how it works (description of the *how* and *why)***

The analysis of variance eis one of the most important statistical models, and allow for an analysis of data gathered from designed experiments. In an Anova designed experiment several categories are thus compared in terms of their menu value regarding a continuous variable. A classical example would be how a certain type of barley grows on different soil types, with the three soil types loamy, sandy and clay. If the majority of the data from one soil type differs from the majority of the data from the other soil type, then these two types differ, which can be tested by a t-test. The Anova extends this test and can compare more than two group levels, hence allowing to compare overall in more complex designed experiments. Such data can be ideally visualised in boxplots, which allows for an initial visualisation of the data distribution, since the classical Anova builds on the regression model, and thus demands data that is normally distributed. In addition is the original Anova build on balanced designs, thus all categories are represented by an equal sample size. Extension have been developed later on, and the type three Anova allows for the testing of unbalanced designs, where sample sizes differ between different categories levels. The analysis of variance is implemented into all stan hard statistical software, such as R and SPSS, however differences in the calculation may occur when it comes to the calculation of unbalanced designs. - position in the research process: data gathering - analysis - interpretation - type of data - how and where do you gather the data? - which software / hardware does the method require? - What is necessary to know about the method?

• • 3) Strengths & challenges**

The Anova can be a powerful tool to tame the variance in field experiment or more complex laboratory experiments, as it allows to account for variance in repeated experimental measures of experiments that are build around replicates. Anova is thus the most robust method when it comes to the design of deductive experiments, yet with the availability of more and more data, also inductive data is increasingly analysed by the Anova. This was certainly quite alien to the original idea of Fisher who believed in clear robust designs and rigid testing of hypothesis. The reproducibility crisis has proven that there are limits to deductive approaches, or at least to the knowledge these experiments produce. The 20th century was certainly fuelled in its development by experimental designs that were at their heart analysed by the analysis of variance. However, we have to acknowledge that there are limits to the knowledge that can be produced, and more complex analysis methods evolved with the wider availability of computers. In addition is the Anova equally limited like the regression, as both build on the normal distribution. Extensions of the Anova translated this analysis into the logic of generalised linear models, thus implementing other distributions as well into Anova analysis schemes. What unites all different approaches is the demand that the Anova has in terms of data, and with increasing complexity are equally increased demands necessary when it comes to the sample sizes. Within experimental settings, this can be quite demanding, and thus the Anova allows only to test very constructed settings of the world. All categories that are implemented as predictors in an Anova design represent a constructed worldview, which can be very robust, but is always a compromise. The Anova thus tries to approximate causality by creating more rigid designs. However we have to acknowledge that experimental designs are always compromises, and more knowledge may become available later. Within clinical trials, most of which have an Anova design at their heart, great care is taken into account in terms of robustness and documentation, and clinical trial stages are build on increasing sample sizes to minimise the harm on humans in these experiments. Taken together, the Anova is one of the statistical models that is indirectly most relevant as the calculation tool to fuel the exponential growth that characterises the 20th century. Agricultural experiments and medical trials widely build on the Anova, yet we also increasingly recognise the limitations of this statistical model. Around the millennium new models emerged, such as mixed effect models, yet at its core, the Anova is the basis of modern deductive statistical analysis.

• • 4) Normativity**

Designing an Anova based design demands experience, and building on the previous literature. The deductive approach of an Anova is thus typically embedded into an incremental development in the literature, associating Anova based designs more often than not part of the continuous development in normal science. However, especially since the millennium did other more advanced approaches such as mixed effect models, information theoretical approaches and structural equation model gain momentum. The rigid root of the normal distribution and the basis of p-values is increasingly recognised as rigid if not flawed, and model reduction in more complex Anova designs is far from coherent between different branches of sciences. Some areas of science reject p-driven statistics altogether, while other branches of science are still publishing full models without any model reduction whatsoever. In addition is the Anova today often also used to analyse inductive datasets, which is technically ok, but can represents several problems from a statistical standpoint, as well as based on a critical perspective rooted in a coherent theory of science. Hence the Anova became a swiss army of group comparison for a continuous variable, and whenever different category levels need to be compared across a dependend variable, the Anova is being pursued. Whether there is an actual question of dependency is often ignored, let alone model assumptions and necessary preconditions. Science evolved, and with it did our questions become ever more complex, as are the problems that we face in the world, or want to test. Complexity reigns, and simple designs are more often than not questioned. The Anova remains as one of the two fundamental models of deductive statistics, with regression being the other important line of thinking. As soon as rigid questions of dependence were conveniently ignored, statisticians of the researchers that applied statistics basically dug the grave for these rigid yet robust approaches. There are still many cases where the Anova represents the most parsimonious and even adequate model. However, as long as positivist scientists share a room with a view in their ivory tower and fail to clearly indicate the limitations of their Anova based designs, they undermine their credibility, and with it the trust between science and society. The Anova is a testimony of hw much statsicsi can serve society, for better or worse. In a bist case, the Anova may serve as a sound approximations of knowledge, yet at its worst it speaks of the arrogance of researchers how imply causally into mere patterns that can and will change once more knowledge becomes available.

• • 5) Outlook**

Analysis of variance was one of the most relevant contributions of statistics to the developments of the 20th century. By allowing for the systematic testing of hypothesis, not only did a whole line of thinking of the theory of science evolve, but whole disciplines were literally emerging. Lately, frequentist statistics was increasingly critizised for its relying on p-values, and the reproducibility crisis highlights the limitations of Anova based designs, which are more often than not reproducible. Psychological research faces this challenge for instance by pre-registering studies, and other branches of science are also attempting to do more justice to the limitations of the knowledge of experiments. In addition, new ways of experimentation of science evolve, introducing a systematic approach to case studies and solution oriented approaches. This may open a more systematic approach to inductive experiments, making documentation a key process in the creation of a canonised knowledge. Scientific experiments were at the forefront of developments that are seen more critical regarding their limitations. Taking more complexities into account, Anovas become more of a basis for more advanced statistics, but they can serve as a robust basis if the limitations are clearly indicated, and Anova designs add to parts of a larger picture of knowledge.

• • 6) Key publications**

Theoretical

Empirical

• • 7) References**

• • 8) any further information,** (e.g. external videos, documents, websites, tools etc. that explain the method in more detail) can be noted, but does not go on the wiki immediately

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The author of this entry is Henrik von Wehrden.