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Table 3. Example of an interaction.

https://doi.org/10.1371/journal.pone.0132102.t003

Although gender and (dichotomized) age are perfectly balanced between T and C , the young woman has been allocated to the first group. Therefore a property of young women (e.g. pregnancy) may serve as an explanation for an observed effect, e.g. .

Given m factors, there are m ( m − 1)/2 possible interactions between just two of the factors, and possible interactions between ν of them. Thus, there is a high probability that some considerable imbalance occurs in at least one of these numerous interactions, in small groups in particular. For a striking early numerical study see [ Nunn Bush Chattanooga Shoe QbY5bkba
]. Detected or undetected, such imbalances provide excellent alternative explanations of an observed effect.

In the light of this, one can only hope for some ‘benign’ dependence structure among the factors, i.e., a reasonable balance in one factor improving the balance in (some of) the others. Given such a tendency, a larger number of nuisance factors may be controlled, since it suffices to focus on only a few. Independent variables possess a ‘neutral’ dependence structure in that the balance in one factor does not influence the balance in others. Yet, there may be a ‘malign’ dependence structure, such that balancing one factor tends to actuate imbalances in others. We will make this argument more precise in Section 4. However, a concrete example will illustrate the idea: Given a benign dependence structure, catching one cow (balancing one factor) makes it easier to catch others. Therefore it is easy to lead a herd into an enclosure: Grab some of the animals by their horns (balance some of the factors) and the others will follow. However, in the case of a malign dependence structure the same procedure tends to stir up the animals, i.e., the more cows are caught (the more factors are being balanced), the less controllable the remaining herd becomes.

3.2 Ordered random variables

In order to show that our conclusions do not depend on some specific model, let us next consider ordered random variables. To begin with, look at four units with ranks 1 to 4. If they are split into two groups of equal size, such that the best (1) and the worst (4) are in one group, and (2) and (3) are in the other, both groups have the same rank sum and are thus comparable. However, if the best and the second best constitute one group and the third and the fourth the other group, their rank sums (3 versus 7) differ by the maximum amount possible, and they do not seem to be comparable. If the units with ranks 1 and 3 are in the first group and the units with ranks 2 and 4 are in the second one, the difference in rank sums is ∣6 − 4∣ = 2 and it seems to be a matter of personal judgement whether or not one thinks of them as comparable.

Given two groups, each having members, the total sum of ranks is = 2(2+1)/2 = (2+1). If, in total analogy to the last section, and are the sum of the ranks in the first and the second group, respectively, = − . Therefore it suffices to consider , which is the test statistic of Wilcoxon’s test. Again, a natural way to measure the extent of imbalance between the groups is = − = 2 − . Like before = 0, and because () = (2+1)/12 we have

Moreover, (+1)/2 ≤ ≤ (3+1)/2 ( = 1,2) yields − ≤ ≤ . Thus, in this case, / ( ∈ {1, …, }) determines a proportion of the range of ∣∣ that may be used to define comparability. Given a fixed (< ), the quantity / is growing at a quadratic rate in , whereas is growing at a slower pace. Like before, there is a single point (, ), where / = (). Straightforward algebra gives, Again, we see that large numbers of observations are needed to ensure comparability:

As before, it is possible to work with the distribution of explicitly. That is, given and , one may calculate the probability = (, ) that two groups, constructed by randomization, are comparable. If ∣∣ ≤ / is considered comparable, it is possible to obtain, using the function pwilcox() in R:

These results for ordered random variables are perfectly in line with the conclusions drawn from the binary model. Moreover, the same argument as before shows that the situation becomes (considerably) worse if several factors may influence the final result.

3.3 A continuous model

Finally, we consider a continuous model. Suppose there is just one factor ∼ (, ). One may think of as a normally distributed personal ability, person having individual ability . As before, assume that 2 persons are randomized into two groups of equal size by a chance mechanism independent of the persons’ abilities.

Suppose that also in this model and measure the total amount of ability in the first and the second group respectively. Obviously, and are independent random variables, each having a normal distribution . A straightforward way to measure the extent of imbalance between the groups is (1) Due to independence, obviously .

Let the two groups be comparable if ∣∣ ≤ , i.e., if the difference between the abilities assembled in the two groups does not differ by more than standard deviations of the ability in a single unit. The larger , the more cases are classified as comparable. For every fixed , is a constant, whereas is growing slowly. Owing to continuity, there is yet another single point (), where . Straightforward algebra gives, In particular, we have: In other words, the two groups become non-comparable very quickly. It is almost impossible that two groups of 500 persons each, for example, could be close to one another with respect to total (absolute) ability.

However, one may doubt if this measure of non-comparability really makes sense. Given two teams with a hundred or more subjects, it does not seem to matter whether the total ability in the first one is within a few standard deviations of the other. Therefore it is reasonable to look at the advantage of group 1 with respect to group 2, i.e. = /. Why divide by and not by some other function of ? First, due to Eq (1) , exactly comparisons − have to be made. Second, since may be interpreted in a natural way, i.e., being the difference between the typical (mean) representative of group 1 (treatment) and the typical representative of group 2 (control). A straightforward calculation yields .

Let the two groups be comparable if ∣∣ ≤ . If one wants to be reasonably sure (three standard deviations of ) that comparability holds, we have . Thus, at least the following numbers of subjects are required per group: If one standard deviation is considered a large effect [ Sanuk Tbar sandals pink s2dvBLUO
], three dozen subjects are needed to ensure that such an effect will not be produced by chance. To avoid a small difference between the groups due to randomization (one quarter of a standard deviation, say), the number of subjects needed goes into the hundreds.

In general, if standard deviations of are desired, we have, Thus, for = 1,2 and 5, the following numbers of subjects are required in each group:

These are just the results for one factor. As before, the situation deteriorates considerably if one sets out to control several nuisance variables by means of randomization.

3.4 Intermediate conclusions

The above models have deliberately been kept as simple as possible. Their results are straightforward and they agree: If is small, it is almost impossible to control for a trait that occurs frequently at the individual level, or for a larger number of confounders, via randomization. It is of paramount importance to understand that random fluctuations lead to considerable differences between small or medium-sized groups, making them very often non-comparable, thus undermining the basic logic of experimentation. That is, ‘blind’ randomization does not create equivalent groups, but rather imbalances and subsequent artifacts. Even in larger samples one needs considerable luck to succeed in creating equivalent groups: close to 0 or 1, a small number of nuisance factors , or a favourable dependence structure that balances all factors, including their relevant interactions, if only some crucial factors are to be balanced by chance.

Had the trial not used random assignment, had it instead assigned patients one at a time to balance [some] covariates, then the balance might well have been better [for those covariates], but there would be no basis for expecting other unmeasured variables to be similarly balanced ([ 2 ], p. 21)

A commitment to local food production and consumption is seen more clearly in Melbourne, Victoria’s capital city. The city council recently released the City of Melbourne Food Policy and is preparing an accompanying food policy action plan (City of Melbourne Giuliano Galiano No Limits hi SMQQcCWDYn
). Already, the city council has made commitments to increase production, distribution, and consumption of locally (within 50km of the municipality) and regionally grown food to 30% of the total consumption (City of Melbourne 2008 ). The Food Policy plan includes explicit ambitions to increase food production within the City of Melbourne, advocating for the preservation of peri-urban agricultural lands along Melbourne’s fringe and supporting innovative forms of local agriculture (City of Melbourne Dior Patent Leather Mules CteiL
). But it is not clear how consumption is defined in the plan (limited to fruits and vegetables or inclusive of cereals and meats) nor how goals for increasing food production will be achieved and what their impact on other goals, such as biodiversity and open space preservation, will be. Also, the State’s agriculture department, the Department of Primary Industries, is notably absent from the plan and its development.

Water security is a continuing challenge worldwide, and Australia is not exempt, with recent droughts putting strain on both agricultural and urban water supplies (Radcliffe VERSACE Cloth Low Trainers POSl2
). As water is a critical resource for urban agriculture, continuous and reliable access to water of a high quality is important. Around the world, water supplies for urban agriculture vary, with most sources in developing nations being either raw or diluted wastewater (Hamilton et al. 2007 , 2013 ). The city of Melbourne provides a number of useful examples of centralized and decentralized wastewater irrigation options for urban agriculture. The two largest wastewater treatment plants in Melbourne underwent upgrades and now supply reclaimed water to neighboring market gardens on the peri-urban fringe. The Western Treatment Plant provides around 61ML per day of high-quality reclaimed water to around 170 customers, while the Eastern Treatment Plant supplies 30ML per day of high-quality water to approximately 80 customers (Barker et al. DORATEYMUR Sybil Leek over CmvwgK5dlE
). At the household scale, many residents responded to water restrictions by establishing informal (bucketing graywater onto gardens) or formal (fixed reuse systems) graywater reuse schemes for home vegetable gardens (Barker et al. Office Krown Suede Over The Knee Boots Zh4aaTw
, 2013 ). A recent study found that 67.6% (1,095/1,621, from 2007 to 2011) of surveyed respondents across Melbourne were graywater users (Sinclair et al. 2011 ). While there are no data to determine how much of this water was used in urban food production, it is reasonable to assume that a significant proportion was devoted to irrigating backyard vegetable plots and fruit trees. Untreated graywater reuse is not regulated by legislation, but EPA guidelines exist and recommend that graywater not be used on vegetables and crops that are eaten raw to reduce any risks of contamination from graywater irrigation (EPA Victoria 2008 ).

Other branches of linguistics, like Jasanoff’s research into the mutations languages underwent hundreds of years ago, have even less obvious applications. Why might that work matter? Jasanoff probably speaks for many linguists when he replies acerbically, “Because we’re human beings and we like to know stuff.” Knowledge of language represents another way of understanding human history and the human experience.

Another answer comes from Saussure, who famously wrote , “[O]f what use is linguistics? Very few people have clear ideas on this point…there is no other field in which so many absurd notions, prejudices, mirages and fictions have sprung up…the task of the linguist is, above all else, to condemn them and to dispel them as best he can.” The study of language has shown, for example, that there is no need to discriminate against people who use signed languages rather than spoken ones, because sign languages, too, offer the full range of human expression. Much as Saussure and the early linguists couldn’t have known the social contributions their field would make, today’s linguists can only imagine what social problems the study of language has yet to answer.

Sidebars:

“Social Justice in Linguistics”

Linguists have documented the ability of sign languages to do all the things spoken languages can do, using three-dimensional space instead of sound.

Marina N. Bolotnikova ’14 is an associate editor of this magazine.

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Fig 1. Nomenclature and taxonomy intersect objectively only at the type specimen, as designated through rules established by nomenclatural codes to anchor scientific names to the biological world.

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In addition, such a system raises many questions. Would it limit the kinds of characters used to assert taxonomically important distinctions, or be biased in favor of one class of characters (e.g., molecular versus morphological), when these cannot be equated across different taxa? How would new knowledge be incorporated? Would it favor one particular species concept for all organisms (and if so, which one)? Would newly discovered species automatically be acknowledged as legitimate new taxa or would they need to be approved before being considered valid? How often would the approved species lists be updated? Taking into account the vanishing taxonomic expertise, who would do this, and who would fund it? Can we afford to draw limited resources away from vital efforts to describe and catalogue biodiversity? There is already a scientific process to deal with updating taxonomy; “taxonomic revisions” carefully review all knowledge on a taxonomic group and may propose alternative classifications and relationships to accommodate new knowledge. These are peer-reviewed, published, and up to the community to accept or reject with further research. Furthermore, given that hundreds of thousands of species remain to be discovered, and that about 18,000 new species are described and named every year [ 26 ], adding layers of bureaucracy to this process would be both impractical and expensive. The governing structure proposed by Garnett and Christidis would need to include this peer review, consultation, and publication process regularly to reflect new knowledge. Therefore, it would add, and possibly duplicate, existing practice.

The products of taxonomic research underpin all biological research, but the proposal by Garnett and Christidis would regulate taxonomy primarily in the context of conservation. This has important potential ramifications because any supervisory body would implicitly have the power to direct, through its actions and judgments, the lumping or splitting of taxa according to conservation, economic significance, or political agendas to affect resource streams directed to those taxa. The process would also be vulnerable to conflicting pressures from advocacy groups in many areas, including conservation, trade, bioprospecting, and particularly politics. Even within birds, one of the groups that exemplify the problem that the proposal seeks to solve, taxonomic committees for managing taxa have had a mixed track record [ 27 ].

Certainly, there are many ways taxonomists can improve the value and impact of their research to conservation biology and other biological disciplines, such as explicitly citing the species concept employed in new taxonomic descriptions and including information on distributions, ecology, conservation status, and potential threats. Better and more modern approaches to organizing scientific names of organisms could also be expanded. In addition to overseeing the Codes of nomenclature, IUBS supports the International Committee on Bionomenclature (ICB) to promote harmony among the different Codes as nomenclature becomes increasingly digital. The development of online nomenclatural registration and indexing systems (e.g., the International Plant Names Index, ZooBank, various mycological registries, List of Prokaryotic Names with Standing in Nomenclature) offer improved access to nomenclatural information. These help avoid perpetuation of errors in the literature and thus increase stability and decrease ambiguity of taxon names.

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