Sample (material)

Abstract: When a crystal deforms plastically, phenomena such as dislocation storage, multiplication, motion, pinning, and nucleation occur over the submicron-to-nanometer scale. Here we report measurements of plastic yielding for single crystals of micrometer-sized dimensions for three different types of metals. We find that within the tests, the overall sample dimensions artificially limit the length scales available for plastic processes. The results show dramatic size effects at surprisingly large sample dimensions. These results emphasize that at the micrometer scale, one must define both the external geometry and internal structure to characterize the strength of a material.

Abstract: The purpose of this paper is to deduce, from a number of examples and from theoretical considerations, some plausible general law as to how abundance or commonness is distributed among species. Experimentally, this could be done by making a complete census of every species, but, with rare exceptions, this procedure is quite impractical. We therefore attempt to deduce the "universe" from a sample. Commonness, as understood by ecologists, has several rather different meanings: we are here concerned with (1) the total number of living individuals of a given species, which might be called its global abundance, (2) the total number of individuals living at any instant on a given area, such as on an acre or a square mile, which might be called its local abundance, (3) the ratio which the number of individuals or one species bears to that of another species, i.e., its relative abundance, and (4) the number of individuals observed, for example, the number of a moth species counted in a sample from a light trap, its "observed," "apparent," or "sample" abundance. There will not usually be any difficulty in deciding which phase of the subject is under discussion at any time. The Raunkiaer "Index of Frequency" is a measure of ubiquity rather than of commonness as above defined: its relation to our other concepts is discussed later. As a rule, we are interested in a sample only in so far as it throws light upon the "universe" that is being sampled. The sample will be a sufficiently accurate replica of the universe provided (1) it is a perfectly "random" sample, and (2) no species is represented in the sample by less than 20 or 30 individuals. In most ecological work condition (2) will never obtain, and much of the present paper will center on this difficulty. Condition (1) will not usually obtain in the broadest sense, and needs a moment's consideration. A geologist sampling an ore-body, whose boundaries have been delimited accurately by previous exploration, has a known "universe" and merely needs information on composition. His universe is permanent. But in ecological work, the "universe" changes rapidly. The moths flying tonight are not those that flew a month ago, or will fly a month hence. Those flying this year are a vastly different association from those that flew last year in the same area. The same thing is true of rodent populations, of birds, and of plants. We are dealing with a fleeting and fluctuating assemblage, a "universe" continually expanding, contracting, and changing in composition. Thus it is important to recognize at the outset that, for the purposes of our present investigation, the "universe" from which the sample is drawn is that universe declared to us by the sample itself, and not our preconceived notion of what the universe ought to be. Further, it is important to recognize that the randomness we seek is merely randomness with respect to commonness or rarity. A light trap is satisfactory in this respect and samples its own universe appropriately. It is definitely selective in respect of phototropism, but it is random in respect of commonness, i.e., it does not care which of two moths, equally phototropic, it catches, though one may be a great rarity and the other of a very common species. On the other hand, an entomologist, or even an intelligent boy, with a net, is not a satisfactory collector, for he will go after the rarity. For this reason we have to reject Corbet's ('41)

Abstract: I challenge (1) the assumption that habitat patches are natural units of measurement for species richness, and (2) the assumption of distinct effects of habitat patch size and isolation on species richness. I propose a simpler view of the relationship between habitat distribution and species richness, the ‘habitat amount hypothesis’, and I suggest ways of testing it. The habitat amount hypothesis posits that, for habitat patches in a matrix of non-habitat, the patch size effect and the patch isolation effect are driven mainly by a single underlying process, the sample area effect. The hypothesis predicts that species richness in equal-sized sample sites should increase with the total amount of habitat in the ‘local landscape’ of the sample site, where the local landscape is the area within an appropriate distance of the sample site. It also predicts that species richness in a sample site is independent of the area of the particular patch in which the sample site is located (its ‘local patch’), except insofar as the area of that patch contributes to the amount of habitat in the local landscape of the sample site. The habitat amount hypothesis replaces two predictor variables, patch size and isolation, with a single predictor variable, habitat amount, when species richness is analysed for equal-sized sample sites rather than for unequal-sized habitat patches. Studies to test the hypothesis should ensure that ‘habitat’ is correctly defined, and the spatial extent of the local landscape is appropriate, for the species group under consideration. If supported, the habitat amount hypothesis would mean that to predict the relationship between habitat distribution and species richness: (1) distinguishing between patch-scale and landscape-scale habitat effects is unnecessary; (2) distinguishing between patch size effects and patch isolation effects is unnecessary; (3) considering habitat configuration independent of habitat amount is unnecessary; and (4) delineating discrete habitat patches is unnecessary.

Abstract: An important step when designing an empirical study is to justify the sample size that will be collected. The key aim of a sample size justification for such studies is to explain how the collected data is expected to provide valuable information given the inferential goals of the researcher. In this overview article six approaches are discussed to justify the sample size in a quantitative empirical study: 1) collecting data from (almost) the entire population, 2) choosing a sample size based on resource constraints, 3) performing an a-priori power analysis, 4) planning for a desired accuracy, 5) using heuristics, or 6) explicitly acknowledging the absence of a justification. An important question to consider when justifying sample sizes is which effect sizes are deemed interesting, and the extent to which the data that is collected informs inferences about these effect sizes. Depending on the sample size justification chosen, researchers could consider 1) what the smallest effect size of interest is, 2) which minimal effect size will be statistically significant, 3) which effect sizes they expect (and what they base these expectations on), 4) which effect sizes would be rejected based on a confidence interval around the effect size, 5) which ranges of effects a study has sufficient power to detect based on a sensitivity power analysis, and 6) which effect sizes are expected in a specific research area. Researchers can use the guidelines presented in this article, for example by using the interactive form in the accompanying online Shiny app, to improve their sample size justification, and hopefully, align the informational value of a study with their inferential goals.