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Post Hoc Analysis
In a scientific study, post hoc analysis (from Latin '' post hoc'', "after this") consists of statistical analyses that were specified after the data were seen. They are usually used to uncover specific differences between three or more group means when an analysis of variance (ANOVA) test is significant. This typically creates a multiple testing problem because each potential analysis is effectively a statistical test. Multiple testing procedures are sometimes used to compensate, but that is often difficult or impossible to do precisely. Post hoc analysis that is conducted and interpreted without adequate consideration of this problem is sometimes called ''data dredging Data dredging (also known as data snooping or ''p''-hacking) is the misuse of data analysis to find patterns in data that can be presented as statistically significant, thus dramatically increasing and understating the risk of false positives. T ...'' by critics because the statistical associations that it fin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin Language
Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the Roman Republic it became the dominant language in the Italy (geographical region), Italian region and subsequently throughout the Roman Empire. Even after the Fall of the Western Roman Empire, fall of Western Rome, Latin remained the common language of international communication, science, scholarship and academia in Europe until well into the 18th century, when other regional vernaculars (including its own descendants, the Romance languages) supplanted it in common academic and political usage, and it eventually became a dead language in the modern linguistic definition. Latin is a fusional language, highly inflected language, with three distinct grammatical gender, genders (masculine, feminine, and neuter), six or seven ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scheffé's Method
In statistics, Scheffé's method, named after the American statistician Henry Scheffé, is a method for adjusting significance levels in a linear regression analysis to account for multiple comparisons. It is particularly useful in analysis of variance (a special case of regression analysis), and in constructing simultaneous confidence bands for regressions involving basis functions. Scheffé's method is a single-step multiple comparison procedure which applies to the set of estimates of all possible contrasts among the factor level means, not just the pairwise differences considered by the Tukey–Kramer method. It works on similar principles as the Working–Hotelling procedure for estimating mean responses in regression, which applies to the set of all possible factor levels. The method Let ''μ''1, ..., ''μ''''r'' be the means of some variable in ''r'' disjoint populations. An arbitrary contrast is defined by :C = \sum_^r c_i\mu_i where :\sum_^r c_i = 0. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiple Comparisons
In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously or infers a subset of parameters selected based on the observed values. The more inferences are made, the more likely erroneous inferences become. Several statistical techniques have been developed to address that problem, typically by requiring a stricter significance threshold for individual comparisons, so as to compensate for the number of inferences being made. History The problem of multiple comparisons received increased attention in the 1950s with the work of statisticians such as Tukey and Scheffé. Over the ensuing decades, many procedures were developed to address the problem. In 1996, the first international conference on multiple comparison procedures took place in Israel. Definition Multiple comparisons arise when a statistical analysis involves multiple simultaneous statistical tests, each of which has a potent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Analysis
Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, and is used in different business, science, and social science domains. In today's business world, data analysis plays a role in making decisions more scientific and helping businesses operate more effectively. Data mining is a particular data analysis technique that focuses on statistical modeling and knowledge discovery for predictive rather than purely descriptive purposes, while business intelligence covers data analysis that relies heavily on aggregation, focusing mainly on business information. In statistical applications, data analysis can be divided into descriptive statistics, exploratory data analysis (EDA), and confirmatory data analysis (CDA). EDA focuses on discovering ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nemenyi Test
In statistics, the Nemenyi test is a post-hoc test intended to find the groups of data that differ after a global statistical test (such as the Friedman test) has rejected the null hypothesis that the performance of the comparisons on the groups of data is similar. The test makes pair-wise tests of performance. The test is named after Peter Nemenyi. The test is sometimes referred to as the "Nemenyi–Damico–Wolfe test", when regarding one-sided multiple comparisons of "treatments" versus "control", but it can also be referred to as the "Wilcoxon–Nemenyi–McDonald–Thompson test", when regarding two-sided multiple comparisons of "treatments" versus "treatments". See also * Tukey's range test Tukey's range test, also known as Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD (honestly significant difference) test, Also occasionally as "honestly," see e.g. is a single-step multiple comparison procedure and ... References Statistical test ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Testing Hypotheses Suggested By The Data
In statistics, hypotheses suggested by a given dataset, when tested with the same dataset that suggested them, are likely to be accepted even when they are not true. This is because circular reasoning (double dipping) would be involved: something seems true in the limited data set; therefore we hypothesize that it is true in general; therefore we wrongly test it on the same, limited data set, which seems to confirm that it is true. Generating hypotheses based on data already observed, in the absence of testing them on new data, is referred to as post hoc theorizing (from Latin '' post hoc'', "after this"). The correct procedure is to test any hypothesis on a data set that was not used to generate the hypothesis. The general problem Testing a hypothesis suggested by the data can very easily result in false positives (type I errors). If one looks long enough and in enough different places, eventually data can be found to support any hypothesis. Yet, these positive data do not by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HARKing
HARKing (hypothesizing after the results are known) is an acronym coined by social psychologist Norbert Kerr that refers to the questionable research practice of “presenting a post hoc hypothesis in the introduction of a research report as if it were an a priori hypothesis”. Hence, a key characteristic of HARKing is that post hoc hypothesizing is falsely portrayed as a priori hypothesizing. HARKing may occur when a researcher tests an a priori hypothesis but then omits that hypothesis from their research report after they find out the results of their test; inappropriate forms of post hoc analysis and/or post hoc theorizing then may lead to a post hoc hypothesis. Types Several types of HARKing have been distinguished, including: ;THARKing: Transparently hypothesizing after the results are known, rather than the secretive, undisclosed, HARKing that was first proposed by Kerr (1998). In this case, researchers openly declare that they developed their hypotheses after they observe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tukey's Test Of Additivity
In statistics, Tukey's test of additivity, named for John Tukey, is an approach used in two-way ANOVA (regression analysis involving two qualitative factors) to assess whether the factor variables ( categorical variables) are additively related to the expected value of the response variable. It can be applied when there are no replicated values in the data set, a situation in which it is impossible to directly estimate a fully general non-additive regression structure and still have information left to estimate the error variance. The test statistic proposed by Tukey has one degree of freedom under the null hypothesis, hence this is often called "Tukey's one-degree-of-freedom test." Introduction The most common setting for Tukey's test of additivity is a two-way factorial analysis of variance (ANOVA) with one observation per cell. The response variable ''Y''''ij'' is observed in a table of cells with the rows indexed by ''i'' = 1,..., ''m'' and the columns indexe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rodger's Method
Rodger's method is a statistical procedure for examining research data post hoc following an 'omnibus' analysis (e.g., after an analysis of variance Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician ... – anova). The various components of this methodology were fully worked out by R. S. Rodger in the 1960s and 70s, and seven of his articles about it were published in the British Journal of Mathematical and Statistical Psychology between 1967 and 1978. Statistical procedures for finding differences between groups, along with interactions between the groups that were included in an experiment or study, can be classified along two dimensions: 1) were the statistical contrasts that will be evaluated decided upon prior to collecting the data (planned) or while trying to figure out ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newman–Keuls Method
The Newman–Keuls or Student–Newman–Keuls (SNK) method is a stepwise multiple comparisons procedure used to identify sample means that are significantly different from each other. It was named after Student (1927), D. Newman, and M. Keuls. This procedure is often used as a post-hoc test whenever a significant difference between three or more sample means has been revealed by an analysis of variance (ANOVA). The Newman–Keuls method is similar to Tukey's range test as both procedures use studentized range statistics. Unlike Tukey's range test, the Newman–Keuls method uses different critical values for different pairs of mean comparisons. Thus, the procedure is more likely to reveal significant differences between group means and to commit type I errors by incorrectly rejecting a null hypothesis when it is true. In other words, the Neuman-Keuls procedure is more powerful but less conservative than Tukey's range test. History and type I error rate control The Newman–Keul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holm–Bonferroni Method
In statistics, the Holm–Bonferroni method, also called the Holm method or Bonferroni–Holm method, is used to counteract the problem of multiple comparisons. It is intended to control the family-wise error rate (FWER) and offers a simple test uniformly more powerful than the Bonferroni correction. It is named after Sture Holm, who codified the method, and Carlo Emilio Bonferroni. Motivation When considering several hypotheses, the problem of multiplicity arises: the more hypotheses are checked, the higher the probability of obtaining Type I errors (false positives). The Holm–Bonferroni method is one of many approaches for controlling the FWER, i.e., the probability that one or more Type I errors will occur, by adjusting the rejection criteria for each of the individual hypotheses. Formulation The method is as follows: * Suppose you have m p-values, sorted into order lowest-to-highest P_1,\ldots,P_m, and their corresponding hypotheses H_1,\ldots,H_m（null hypotheses). You ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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