Experiments with Small Numbers of Observations

This is a report on part of an experiment that is under way having for its objective the determination of (a) the extent of divergence from theoretical values of probability in small samples, and (b) the extent of divergence from theoretical values of probability as computated by Student\u27s method if the sample is drawn from a non-normal distribution

Disproportionate subclass numbers in tables of multiple classification

Under the stimulus of some of the newer methods of experimentation there is a decided tendency toward the grouping of classes of data into smaller and more homogeneous sub-classes. The weights of swine, for example, may be simultaneously classified according to the sex as well as the litter of the individual animals. Corn yields may be entered in a three-way table by applying the criteria of variety, treatment and soil type. From the resulting tables of multiple classification can be derived information not only of the main effects, such as sex and litter, but also of the interactions between them. Analysis of variance is the most convenient and effective method of reducing such classified data to summary form and testing the significance of the various effects

Immediate effects of microclimate modification enhance native shrub encroachment

Shrubs have become more dense and expanded beyond their range all over the world for a variety of reasons including increased temperatures, overgrazing, and alteration of historical fire regime. Native shrubs have been encroaching on Virginia barrier island grasslands for over half a century for unknown reasons. Species composition, soil nutrients, leaf area index (LAI), and ground and air temperature were recorded across the shrub to grass transition and at free-standing shrubs in a coastal grassland in order to determine the effect of shrub encroachment on plant community and microclimate. Species richness was significantly lower inside shrub thickets. Soil water content, organic matter, nitrogen (N), carbon (C), and LAI were higher in shrub thickets and free-standing shrubs compared to grasslands. Summer and fall maximum temperatures were lower and more moderate where shrubs were present. Fall and winter minimum temperatures were highest inside shrub thickets. Native shrubs impact microclimate and species composition immediately upon encroachment. These shrubs lower overall species composition, increase soil nutrients and moisture, moderate summer temperature, and increase winter temperature, which has consequences on a larger scale. As barrier islands are critical for protecting marsh and mainland habitats, understanding this mechanism for shrub expansion is important to predict future encroachment of shrubs and displacement of grassland habitat

A Statistical Test of Experimental Technique

The phrase experimental technique is used in a largely inclusive sense in this paper. A more precise title would be A Statistical Test of Homogeneity. The reason for the more flexible phrase will be apparent, I trust, as the argument progresses

Statistical Control of a Grading System

Statistical Control is a phrase which is very popular in business circles. What does it mean? Let us examine two types, the statistical control of the quality of a manufactured product, and the statistical control of a purchasing department. In the former case, over a sufficient period of time, records are made of the number of defects per 1000 (say) found in the product manufactured. From these records statistical standards are set up consisting of the averages and distributions of the occurrence of defects. By comparing any subsequent sample with such standards, the statistician is able to assert that the occurrence of defects in this sample is within or without the ordinary limits of random sampling. If without, the manufacturing department is notified of the excess of defects and is expected to remedy the situation. In the case of the purchase of commodities, the standard (price to be paid) is ill defined or lacking. In this type of control, the distinguishing feature in the estimation of the proper price to be paid is the collection and use of a group of statistical facts concerning correlated, independent variables. Some such are (1) the trend of prices in the commodity itself with due attention to seasonal and cyclical fluctuations; (2) the level of general commodity prices, (3) the facility of credit, etc. From such data, the statistician fixes an average price to be paid for the commodity and a proper time for its purchase

Application of Volcano Plots in Analyses of mRNA Differential Expressions with Microarrays

Volcano plot displays unstandardized signal (e.g. log-fold-change) against noise-adjusted/standardized signal (e.g. t-statistic or -log10(p-value) from the t test). We review the basic and an interactive use of the volcano plot, and its crucial role in understanding the regularized t-statistic. The joint filtering gene selection criterion based on regularized statistics has a curved discriminant line in the volcano plot, as compared to the two perpendicular lines for the "double filtering" criterion. This review attempts to provide an unifying framework for discussions on alternative measures of differential expression, improved methods for estimating variance, and visual display of a microarray analysis result. We also discuss the possibility to apply volcano plots to other fields beyond microarray.Comment: 8 figure

Nitrogen and phosphorus loads to temperate seepage lakes associated with allochthonous dissolved organic carbon loads

Terrestrial loads of dissolved organic matter (DOM) have increased in recent years in many north temperate lakes. While much of the focus on the “browning” phenomena has been on its consequences for carbon cycling, much less is known about how it influences nutrient loading to lakes. We characterize potential loads of nitrogen and phosphorus to seepage lakes in northern Wisconsin, USA, based on a laboratory soil leaching experiment and a model that includes landscape cover and watershed area. In these seepage lakes, nutrient concentrations are positively correlated with dissolved organic carbon concentrations (nitrogen: r = 0.68, phosphorus: r = 0.54). Using long‐term records of browning, we found that dissolved organic matter‐associated nutrient loadings may have resulted in substantial increases in nitrogen and phosphorus in seepage lakes and could account for currently observed nutrient concentrations in the lake. “Silent” nutrient loadings to brown‐water lakes may lead to future water‐quality concerns. PLAIN LANGUAGE SUMMARY: The color of many temperate lakes is changing; some lakes are becoming more darkly stained brown. The tea‐colored stain is due to dissolved organic matter from the surrounding landscape. Much of the research related to the causes and consequences of increased staining, or “brownification,” relate to its connection to the carbon cycle. However, by examining long‐term lake chemical records, analyzing the properties of the organic compounds, and modeling potential flows of the compounds, we find that carbon is not the only element that is influenced by browning. Nitrogen and phosphorus, two nutrients important to growth of organisms at the base of the food web, may also be increasing in lakes due to brownification."Funding for this research was supported by the Northern Research Station and the Chequamegon-Nicolet National Forest (CNNF) of the United States Department of Agriculture (USDA) Forest Service and a National Science Foundation (NSF) grant to the University of Wisconsin-Madison to support the North Temperate Lakes Long-Term Ecological Research (NTLLTER) Site (DEB-#1440297)."https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2018GL07721

Stream biasing by different induction sequences: Evaluating stream capture as an account of the segregation-promoting effects of constant-frequency inducers

Stream segregation for a test sequence comprising high-frequency (H) and low-frequency (L) pure tones, presented in a galloping rhythm, is much greater when preceded by a constant-frequency induction sequence matching one subset than by an inducer configured like the test sequence; this difference persists for several seconds. It has been proposed that constant-frequency inducers promote stream segregation by capturing the matching subset of test-sequence tones into an on-going, pre-established stream. This explanation was evaluated using 2-s induction sequences followed by longer test sequences (12–20 s). Listeners reported the number of streams heard throughout the test sequence. Experiment 1 used LHL– sequences and one or other subset of inducer tones was attenuated (0–24 dB in 6-dB steps, and 1). Greater attenuation usually caused a progressive increase in segregation, towards that following the constant-frequency inducer. Experiment 2 used HLH– sequences and the L inducer tones were raised or lowered in frequency relative to their test-sequence counterparts (DfI¼ 0, 0.5, 1.0, or 1.5 DfT). Either change greatly increased segregation. These results are concordant with the notion of attention switching to new sounds but contradict the stream-capture hypothesis, unless a “proto-object” corresponding to the continuing subset is assumed to form during the induction sequence

The development of a space climatology: 1. solar-wind magnetosphere coupling as a function of timescale and the effect of data gaps

Different terrestrial space weather indicators (such as geomagnetic indices, transpolar voltage, and ring current particle content) depend on different “coupling functions” (combinations of near-Earth solar wind parameters) and previous studies also reported a dependence on the averaging timescale, {\tau}. We study the relationships of the am and SME geomagnetic indices to the power input into the magnetosphere P_{\alpha}, estimated using the optimum coupling exponent {\alpha} for a range of {\tau} between 1 min and 1 year. The effect of missing data is investigated by introducing synthetic gaps into near-continuous data and the best method for dealing with them when deriving the coupling function, is formally defined. Using P_{\alpha}, we show that gaps in data recorded before 1995 have introduced considerable errors into coupling functions. From the near-continuous solar wind data for 1996-2016, we find {\alpha} = 0.44 plus/minus 0.02 and no significant evidence that {\alpha} depends on {\tau}, yielding P_{\alpha} = B^0.88 Vsw^1.90 (mswNsw)^0.23 sin4({\theta}/2), where B is the Interplanetary Magnetic Field (IMF), Nsw the solar wind number density, msw its mean ion mass, Vsw its velocity and {\theta} is the IMF clock angle in the Geocentric Solar Magnetospheric reference frame. Values of P_{\alpha} that are accurate to within plus/minus 5% for 1996-2016 have an availability of 83.8% and the correlation between P_{\alpha} and am for these data is shown to be 0.990 (between 0.972 and 0.997 at the 2{\sigma} uncertainty level), 0.897 plus/minus 0.004, and 0.790 plus/minus 0.03, for {\tau} of 1 year, 1 day and 3 hours, respectively, and that between P_{alpha} and SME at {\tau} of 1 min. is 0.7046 plus/minus 0.0004