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Ratios and effect size.

ABSTRACT: Responding to a related pair of measurements is often expressed as a single discrimination ratio. Authors have used various discrimination ratios; yet, little information exists to guide their choice. A second use of ratios is to correct for the influence of a nuisance variable on the measurement of interest. I examine 4 discrimination ratios using simulated data sets. Three ratios, of the form a/(a + b), b/(a + b), and (a - b)/(a + b), introduced distortions to their raw data. The fourth ratio, (b - a)/b largely avoided such distortions and was the most sensitive at detecting statistical differences. Effect size statistics were also often improved with a correction ratio. Gustatory sensory preconditioning experiments involved measurement of rats' sucrose and saline consumption; these flavors served as either a target flavor or a control flavor and were counterbalanced across rats. However, sensory preconditioning was often masked by a bias for sucrose over saline. Sucrose and saline consumption scores were multiplied by the ratio of the overall consumption to the consumption of that flavor alone, which corrected the bias. The general utility of discrimination and correction ratios for data treatment is discussed. (PsycINFO Database Record

SUBMITTER: Robinson J

PROVIDER: S-EPMC5628573 | biostudies-literature | 2017 Oct

REPOSITORIES: biostudies-literature

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Ratios and effect size.

Robinson Jasper J

Journal of experimental psychology. Animal learning and cognition 20170814 4

Responding to a related pair of measurements is often expressed as a single discrimination ratio. Authors have used various discrimination ratios; yet, little information exists to guide their choice. A second use of ratios is to correct for the influence of a nuisance variable on the measurement of interest. I examine 4 discrimination ratios using simulated data sets. Three ratios, of the form a/(a + b), b/(a + b), and (a - b)/(a + b), introduced distortions to their raw data. The fourth ratio, ...[more]

PMID: 28805439

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Project description:Mammalian molar crowns form a module in which measurements of size for individual teeth within a tooth row covary with one another. Molar crown size covariation is proposed to fit the inhibitory cascade model (ICM) or its variant the molar module component (MMC) model, but the inability of the former model to fit across biological scales is a concern in the few cases where it has been tested in Primates. The ICM has thus far failed to explain patterns of intraspecific variation, an intermediate biological scale, even though it explains patterns at both smaller organ-level and larger between-species biological scales. Studies of this topic in a much broader range of taxa are needed, but the properties of a sample appropriate for testing the ICM at the intraspecific level are unclear. Here, we assess intraspecific variation in relative molar sizes of the cotton mouse, Peromyscus gossypinus, to further test the ICM and to develop recommendations for appropriate sampling protocols in future intraspecific studies of molar size variation across Mammalia. To develop these recommendations, we model the sensitivity of estimates of molar ratios to sample size and simulate the use of composite molar rows when complete ones are unavailable. Similar to past studies on primates, our results show that intraspecific variance structure of molar ratios within the rodent P. gossypinus does not meet predictions of the ICM or MMC. When we extend these analyses to include the MMC, one model does not fit observed patterns of variation better than the other. Standing variation in molar size ratios is relatively constant across mammalian samples containing all three molars. In future studies, analyzing average ratio values will require relatively small minimum sample sizes of two or more complete molar rows. Even composite-based estimates from four or more specimens per tooth position can accurately estimate mean molar ratios. Analyzing variance structure will require relatively large sample sizes of at least 40-50 complete specimens, and composite molar rows cannot accurately reconstruct variance structure of ratios in a sample. Based on these results, we propose guidelines for intraspecific studies of molar size covariation. In particular, we note that the suitability of composite specimens for averaging mean molar ratios is promising for the inclusion of isolated molars and incomplete molar rows from the fossil record in future studies of the evolution of molar modules, as long as variance structure is not a key component of such studies.

Project description:Food web structure and dynamics depend on relationships between body sizes of predators and their prey. Species-based and community-wide estimates of preferred and realized predator-prey mass ratios (PPMR) are required inputs to size-based size spectrum models of marine communities, food webs, and ecosystems. Here, we clarify differences between PPMR definitions in different size spectrum models, in particular differences between PPMR measurements weighting prey abundance in individual predators by biomass (r bio) and numbers (r num). We argue that the former weighting generates PPMR as usually conceptualized in equilibrium (static) size spectrum models while the latter usually applies to dynamic models. We use diet information from 170,689 individuals of 34 species of fish in Alaskan marine ecosystems to calculate both PPMR metrics. Using hierarchical models, we examine how explained variance in these metrics changed with predator body size, predator taxonomic resolution, and spatial resolution. In the hierarchical analysis, variance in both metrics emerged primarily at the species level and substantially less variance was associated with other (higher) taxonomic levels or with spatial resolution. This suggests that changes in species composition are the main drivers of community-wide mean PPMR. At all levels of analysis, relationships between weighted mean r bio or weighted mean r num and predator mass tended to be dome-shaped. Weighted mean r num values, for species and community-wide, were approximately an order of magnitude higher than weighted mean r bio, reflecting the consistent numeric dominance of small prey in predator diets. As well as increasing understanding of the drivers of variation in PPMR and providing estimates of PPMR in the north Pacific Ocean, our results demonstrate that that r bio or r num, as well as their corresponding weighted means for any defined group of predators, are not directly substitutable. When developing equilibrium size-based models based on bulk energy flux or comparing PPMR estimates derived from the relationship between body mass and trophic level with those based on diet analysis, weighted mean r bio is a more appropriate measure of PPMR. When calibrating preference PPMR in dynamic size spectrum models then weighted mean r num will be a more appropriate measure of PPMR.

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Ratios and effect size.

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Ratios and effect size.

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