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Analysis Of Similarities
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 dissimilaritmatrix Given a matrix of rank dissimilarities between a set of samples, each belonging to a single site (e.g. a single treatment group), the ANOSIM tests whether we can reject the null hypothesis that the similarity between sites is greater than or equal to the similarity within each site. The test statistic ''R'' is calculated in the following way: : R = \frac where B is the average of rank similarities of pairs of samples (or replicates) originating from different sites, W is the average of rank similarity of pairs among replicates within sites, and ''M'' = ''n''(''n'' − 1)/2 where ''n'' is the number of samples. The test statistic ''R'' is constrained between the values −1 to 1, where positive numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonparametric Statistics
Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric statistics. Nonparametric statistics can be used for descriptive statistics or statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated. Definitions The term "nonparametric statistics" has been defined imprecisely in the following two ways, among others: The first meaning of ''nonparametric'' involves techniques that do not rely on data belonging to any particular parametric family of probability distributions. These include, among others: * Methods which are ''distribution-free'', which do not rely on assumptions that the data are drawn from a given parametric family of probability distributions. * Statistics defined to be a function on a sample, without dependency on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ecology
Ecology () is the natural science of the relationships among living organisms and their Natural environment, environment. Ecology considers organisms at the individual, population, community (ecology), community, ecosystem, and biosphere levels. Ecology overlaps with the closely related sciences of biogeography, evolutionary biology, genetics, ethology, and natural history. Ecology is a branch of biology, and is the study of abundance (ecology), abundance, biomass (ecology), biomass, and distribution of organisms in the context of the environment. It encompasses life processes, interactions, and adaptations; movement of materials and energy through living communities; ecological succession, successional development of ecosystems; cooperation, competition, and predation within and between species; and patterns of biodiversity and its effect on ecosystem processes. Ecology has practical applications in fields such as conservation biology, wetland management, natural resource m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analysis Of Variance
Analysis of variance (ANOVA) is a family of statistical methods used to compare the Mean, means of two or more groups by analyzing variance. Specifically, ANOVA compares the amount of variation ''between'' the group means to the amount of variation ''within'' each group. If the between-group variation is substantially larger than the within-group variation, it suggests that the group means are likely different. This comparison is done using an F-test. The underlying principle of ANOVA is based on the law of total variance, which states that the total variance in a dataset can be broken down into components attributable to different sources. In the case of ANOVA, these sources are the variation between groups and the variation within groups. ANOVA was developed by the statistician Ronald Fisher. In its simplest form, it provides a statistical test of whether two or more population means are equal, and therefore generalizes the Student's t-test#Independent two-sample t-test, ''t''- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raw Data
Raw data, also known as primary data, are ''data'' (e.g., numbers, instrument readings, figures, etc.) collected from a source. In the context of examinations, the raw data might be described as a raw score (after test scores). If a scientist sets up a computerized thermometer which records the temperature of a chemical mixture in a test tube every minute, the list of temperature readings for every minute, as printed out on a spreadsheet or viewed on a computer screen are "raw data". Raw data have not been subjected to processing, "cleaning" by researchers to remove outliers, obvious instrument reading errors or data entry errors, or any analysis (e.g., determining central tendency aspects such as the average or median result). As well, raw data have not been subject to any other manipulation by a software program or a human researcher, analyst or technician. They are also referred to as ''primary'' data. Raw data is a relative term (see data), because even once raw data have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). The term is also frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between string (computer science), strings of text) or a degree of separation (as exemplified by distance (graph theory), distance between people in a social network). Most such notions of distance, both physical and metaphorical, are formalized in mathematics using the notion of a metric space. In the social sciences, distance can refer to a qualitative measurement of separation, such as social distance or psychological distance. Distances in physics and geometry The distance between physical locations can be defined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Treatment And Control Groups
In the design of experiments, hypotheses are applied to experimental units in a treatment group. In comparative experiments, members of a control group receive a standard treatment, a placebo, or no treatment at all. There may be more than one treatment group, more than one control group, or both. A placebo control group can be used to support a double-blind study, in which some subjects are given an ineffective treatment (in medical studies typically a sugar pill) to minimize differences in the experiences of subjects in the different groups; this is done in a way that ensures no participant in the experiment (subject or experimenter) knows to which group each subject belongs. In such cases, a third, non-treatment control group can be used to measure the placebo effect directly, as the difference between the responses of placebo subjects and untreated subjects, perhaps paired by age group or other factors (such as being twins). For the conclusions drawn from the results of an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Null Hypothesis
The null hypothesis (often denoted ''H''0) is the claim in scientific research that the effect being studied does not exist. The null hypothesis can also be described as the hypothesis in which no relationship exists between two sets of data or variables being analyzed. If the null hypothesis is true, any experimentally observed effect is due to chance alone, hence the term "null". In contrast with the null hypothesis, an alternative hypothesis (often denoted ''H''A or ''H''1) is developed, which claims that a relationship does exist between two variables. Basic definitions The null hypothesis and the ''alternative hypothesis'' are types of conjectures used in statistical tests to make statistical inferences, which are formal methods of reaching conclusions and separating scientific claims from statistical noise. The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Similarity Measure
In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such measures are in some sense the inverse of distance metrics: they take on large values for similar objects and either zero or a negative value for very dissimilar objects. Though, in more broad terms, a similarity function may also satisfy metric axioms. Cosine similarity is a commonly used similarity measure for real-valued vectors, used in (among other fields) information retrieval to score the similarity of documents in the vector space model. In machine learning, common kernel functions such as the RBF kernel can be viewed as similarity functions. Use of different similarity measure formulas Different types of similarity measures exist for various types of objects, depending on the objects being compared. For each type of object there ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Replicate (statistics)
In engineering, science, and statistics, replication is the process of repeating a study or experiment under the same or similar conditions. It is a crucial step to test the original claim and confirm or reject the accuracy of results as well as for identifying and correcting the flaws in the original experiment. ASTM, in standard E1847, defines replication as "... the repetition of the set of all the treatment combinations to be compared in an experiment. Each of the repetitions is called a ''replicate''." For a full factorial design, replicates are multiple experimental runs with the same factor levels. You can replicate combinations of factor levels, groups of factor level combinations, or even entire designs. For instance, consider a scenario with three factors, each having two levels, and an experiment that tests every possible combination of these levels (a full factorial design). One complete replication of this design would comprise 8 runs (2^3). The design can be executed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sign (mathematics)
In mathematics, the sign of a real number is its property of being either positive, negative, or 0. Depending on local conventions, zero may be considered as having its own unique sign, having no sign, or having both positive and negative sign. In some contexts, it makes sense to distinguish between a positive and a negative zero. In mathematics and physics, the phrase "change of sign" is associated with exchanging an object for its additive inverse (multiplication with −1, negation), an operation which is not restricted to real numbers. It applies among other objects to vectors, matrices, and complex numbers, which are not prescribed to be only either positive, negative, or zero. The word "sign" is also often used to indicate binary aspects of mathematical or scientific objects, such as odd and even ( sign of a permutation), sense of orientation or rotation ( cw/ccw), one sided limits, and other concepts described in below. Sign of a number Numbers from various number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypothesis
A hypothesis (: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or thought. If a hypothesis is repeatedly independently demonstrated by experiment to be true, it becomes a scientific theory. In colloquial usage, the words "hypothesis" and "theory" are often used interchangeably, but this is incorrect in the context of science. A working hypothesis is a provisionally-accepted hypothesis used for the purpose of pursuing further progress in research. Working hypotheses are frequently discarded, and often proposed with knowledge (and warning) that they are incomplete and thus false, with the intent of moving research in at least somewhat the right direction, especially when scientists are stuck on an issue and brainstorming ideas. A different meaning of the term ''hypothesis'' is used in formal l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation
In mathematics, a permutation of a set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first meaning is the six permutations (orderings) of the set : written as tuples, they are (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). Anagrams of a word whose letters are all different are also permutations: the letters are already ordered in the original word, and the anagram reorders them. The study of permutations of finite sets is an important topic in combinatorics and group theory. Permutations are used in almost every branch of mathematics and in many other fields of science. In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences. The number of permutations of distinct objects is factorial, us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
