Related Research Articles
In statistics, the Kolmogorov–Smirnov test is a nonparametric test of the equality of continuous, one-dimensional probability distributions that can be used to compare a sample with a reference probability distribution, or to compare two samples. In essence, the test answers the question "How likely is it that we would see a collection of samples like this if they were drawn from that probability distribution?" or, in the second case, "How likely is it that we would see two sets of samples like this if they were drawn from the same probability distribution?". It is named after Andrey Kolmogorov and Nikolai Smirnov.
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.
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.
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made, based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy.
A permutation test is an exact statistical hypothesis test making use of the proof by contradiction. A permutation test involves two or more samples. The null hypothesis is that all samples come from the same distribution . Under the null hypothesis, the distribution of the test statistic is obtained by calculating all possible values of the test statistic under possible rearrangements of the observed data. Permutation tests are, therefore, a form of resampling.
In statistics, resampling is the creation of new samples based on one observed sample. Resampling methods are:
- Permutation tests
- Bootstrapping
- Cross validation
Terminal restriction fragment length polymorphism is a molecular biology technique for profiling of microbial communities based on the position of a restriction site closest to a labelled end of an amplified gene. The method is based on digesting a mixture of PCR amplified variants of a single gene using one or more restriction enzymes and detecting the size of each of the individual resulting terminal fragments using a DNA sequencer. The result is a graph image where the x-axis represents the sizes of the fragment and the y-axis represents their fluorescence intensity.
Microarray analysis techniques are used in interpreting the data generated from experiments on DNA, RNA, and protein microarrays, which allow researchers to investigate the expression state of a large number of genes - in many cases, an organism's entire genome - in a single experiment. Such experiments can generate very large amounts of data, allowing researchers to assess the overall state of a cell or organism. Data in such large quantities is difficult - if not impossible - to analyze without the help of computer programs.
In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed.
Mass spectrometry imaging (MSI) is a technique used in mass spectrometry to visualize the spatial distribution of molecules, as biomarkers, metabolites, peptides or proteins by their molecular masses. After collecting a mass spectrum at one spot, the sample is moved to reach another region, and so on, until the entire sample is scanned. By choosing a peak in the resulting spectra that corresponds to the compound of interest, the MS data is used to map its distribution across the sample. This results in pictures of the spatially resolved distribution of a compound pixel by pixel. Each data set contains a veritable gallery of pictures because any peak in each spectrum can be spatially mapped. Despite the fact that MSI has been generally considered a qualitative method, the signal generated by this technique is proportional to the relative abundance of the analyte. Therefore, quantification is possible, when its challenges are overcome. Although widely used traditional methodologies like radiochemistry and immunohistochemistry achieve the same goal as MSI, they are limited in their abilities to analyze multiple samples at once, and can prove to be lacking if researchers do not have prior knowledge of the samples being studied. Most common ionization technologies in the field of MSI are DESI imaging, MALDI imaging and secondary ion mass spectrometry imaging.
Mauchly's sphericity test or Mauchly's W is a statistical test used to validate a repeated measures analysis of variance (ANOVA). It was developed in 1940 by John Mauchly.
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.
Energy distance is a statistical distance between probability distributions. If X and Y are independent random vectors in Rd with cumulative distribution functions (cdf) F and G respectively, then the energy distance between the distributions F and G is defined to be the square root of
DNA barcoding is a method of species identification using a short section of DNA from a specific gene or genes. The premise of DNA barcoding is that by comparison with a reference library of such DNA sections, an individual sequence can be used to uniquely identify an organism to species, just as a supermarket scanner uses the familiar black stripes of the UPC barcode to identify an item in its stock against its reference database. These "barcodes" are sometimes used in an effort to identify unknown species or parts of an organism, simply to catalog as many taxa as possible, or to compare with traditional taxonomy in an effort to determine species boundaries.
In statistics, signal processing, and econometrics, an unevenlyspaced time series is a sequence of observation time and value pairs in which the spacing of observation times is not constant.
Analysis of similarities (ANOSIM) is a non-parametric statistical test widely used in the field of ecology. The test was first suggested by K. R. Clarke as an ANOVA-like test, where instead of operating on raw data, operates on a ranked dissimilarity matrix.
Permutational multivariate analysis of variance (PERMANOVA), is a non-parametric multivariate statistical permutation test. PERMANOVA is used to compare groups of objects and test the null hypothesis that the centroids and dispersion of the groups as defined by measure space are equivalent for all groups. A rejection of the null hypothesis means that either the centroid and/or the spread of the objects is different between the groups. Hence the test is based on the prior calculation of the distance between any two objects included in the experiment. PERMANOVA shares some resemblance to ANOVA where they both measure the sum-of-squares within and between group and make use of F test to compare within-group to between-group variance. However, while ANOVA bases the significance of the result on assumption of normality, PERMANOVA draws tests for significance by comparing the actual F test result to that gained from random permutations of the objects between the groups. Moreover, whilst PERMANOVA tests for similarity based on a chosen distance measure, ANOVA tests for similarity of the group averages.
Marti Jane Anderson is a New Zealand marine biology and statistics academic. She is currently a distinguished professor at the Massey University.
References
- ↑ Clarke, K.R.; Gorley, R.N. (2015). "PRIMER v7: User Manual/Tutorial". PRIMER-E.
{{cite journal}}: Cite journal requires|journal=(help) - ↑ Anderson, M.J.; Gorley, R.N.; Clarke, K.R. (2015). "PERMANOVA+ for PRIMER: Guide to Software and Statistical Methods". PRIMER-E.
{{cite journal}}: Cite journal requires|journal=(help)