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Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures used to analyze the differences among group means in a sample. ANOVA was developed by the statistician Ronald Fisher. The ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means.
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. The application of multivariate statistics is multivariate analysis.
A meta-analysis is a statistical analysis that combines the results of multiple scientific studies. Meta-analysis can be performed when there are multiple scientific studies addressing the same question, with each individual study reporting measurements that are expected to have some degree of error. The aim then is to use approaches from statistics to derive a pooled estimate closest to the unknown common truth based on how this error is perceived.
Chemometrics is the science of extracting information from chemical systems by data-driven means. Chemometrics is inherently interdisciplinary, using methods frequently employed in core data-analytic disciplines such as multivariate statistics, applied mathematics, and computer science, in order to address problems in chemistry, biochemistry, medicine, biology and chemical engineering. In this way, it mirrors other interdisciplinary fields, such as psychometrics and econometrics.
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem.
Partial least squares regression is a statistical method that bears some relation to principal components regression; instead of finding hyperplanes of maximum variance between the response and independent variables, it finds a linear regression model by projecting the predicted variables and the observable variables to a new space. Because both the X and Y data are projected to new spaces, the PLS family of methods are known as bilinear factor models. Partial least squares discriminant analysis (PLS-DA) is a variant used when the Y is categorical.
Morphometrics or morphometry refers to the quantitative analysis of form, a concept that encompasses size and shape. Morphometric analyses are commonly performed on organisms, and are useful in analyzing their fossil record, the impact of mutations on shape, developmental changes in form, covariances between ecological factors and shape, as well for estimating quantitative-genetic parameters of shape. Morphometrics can be used to quantify a trait of evolutionary significance, and by detecting changes in the shape, deduce something of their ontogeny, function or evolutionary relationships. A major objective of morphometrics is to statistically test hypotheses about the factors that affect shape.
A phase response curve (PRC) illustrates the transient change in the cycle period of an oscillation induced by a perturbation as a function of the phase at which it is received. PRCs are used in various fields; examples of biological oscillations are the heartbeat, circadian rhythms, and the regular, repetitive firing observed in some neurons in the absence of noise.
Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis. Ordination orders objects that are characterized by values on multiple variables so that similar objects are near each other and dissimilar objects are farther from each other. Such relationships between the objects, on each of several axes, are then characterized numerically and/or graphically. Many ordination techniques exist, including principal components analysis (PCA), non-metric multidimensional scaling (NMDS), correspondence analysis (CA) and its derivatives, Bray–Curtis ordination, and redundancy analysis (RDA), among others.
Phytosociology is the branch of science which deals with plant communities, their composition and development, and the relationships between the species within them. A phytosociological system is a system for classifying these communities.
The dose–response relationship, or exposure–response relationship, describes the magnitude of the response of an organism, as a function of exposure to a stimulus or stressor after a certain exposure time. Dose–response relationships can be described by dose–response curves. This is explained further in the following sections. A stimulus response function or stimulus response curve is defined more broadly as the response from any type of stimulus, not limited to chemicals.
Analysis of variance – simultaneous component analysis is a method that partitions variation and enables interpretation of these partitions by SCA, a method that is similar to principal components analysis (PCA). This method is a multivariate or even megavariate extension of analysis of variance (ANOVA). The variation partitioning is similar to ANOVA. Each partition matches all variation induced by an effect or factor, usually a treatment regime or experimental condition. The calculated effect partitions are called effect estimates. Because even the effect estimates are multivariate, interpretation of these effects estimates is not intuitive. By applying SCA on the effect estimates one gets a simple interpretable result. In case of more than one effect this method estimates the effects in such a way that the different effects are not correlated.
Biplots are a type of exploratory graph used in statistics, a generalization of the simple two-variable scatterplot. A biplot allows information on both samples and variables of a data matrix to be displayed graphically. Samples are displayed as points while variables are displayed either as vectors, linear axes or nonlinear trajectories. In the case of categorical variables, category level points may be used to represent the levels of a categorical variable. A generalised biplot displays information on both continuous and categorical variables.
Repeated measures design is a research design that involves multiple measures of the same variable taken on the same or matched subjects either under different conditions or over two or more time periods. For instance, repeated measurements are collected in a longitudinal study in which change over time is assessed.
Detrended correspondence analysis (DCA) is a multivariate statistical technique widely used by ecologists to find the main factors or gradients in large, species-rich but usually sparse data matrices that typify ecological community data. DCA is frequently used to suppress artifacts inherent in most other multivariate analyses when applied to gradient data.
The Unscrambler X is a commercial software product for multivariate data analysis, used for calibration of multivariate data which is often in the application of analytical data such as near infrared spectroscopy and Raman spectroscopy, and development of predictive models for use in real-time spectroscopic analysis of materials. The software was originally developed in 1986 by Harald Martens and later by CAMO Software.
In randomized statistical experiments, generalized randomized block designs (GRBDs) are used to study the interaction between blocks and treatments. For a GRBD, each treatment is replicated at least two times in each block; this replication allows the estimation and testing of an interaction term in the linear model.
The growth curve model in statistics is a specific multivariate linear model, also known as GMANOVA. It generalizes MANOVA by allowing post-matrices, as seen in the definition.
In statistics, linear regression is a linear approach to modeling the relationship between a scalar response and one or more explanatory variables. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.
Patrick James Curran is an American statistician and professor of quantitative psychology at the University of North Carolina, where he is also a faculty member at the Center for Developmental Science.
References
- ↑ ter Braak, Cajo J.F. & Šmilauer, Petr (2012). Canoco reference manual and user´s guide: software for ordination (version 5.0), p 292. Microcomputer Power, Ithaca, NY.
- ↑ van den Brink, Paul J.; ter Braak, Cajo J.F. (1999). "Principal response curves: analysis of time-dependent multivariate responses of biological community to stress". Environmental Toxicology and Chemistry. 18 (2): 138–148. doi:10.1002/etc.5620180207.
- ↑ Pardal, M.A.; Cardoso, P.G.; Sousa, J. P.; Marques, J. C.; Raffaelli, D. (2004). "Assessing environmental quality: a novel approach". Marine Ecology Progress Series. 267: 1–8. Bibcode:2004MEPS..267....1P. doi: 10.3354/meps267001 .
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