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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 means. ANOVA was developed by the statistician Ronald Fisher. 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. In other words, the ANOVA is used to test the difference between two or more means.
A meta-analysis is a statistical analysis that combines the results of multiple scientific studies. Meta-analyses 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. Meta-analytic results are considered the most trustworthy source of evidence by the evidence-based medicine literature.
A randomized controlled trial is a form of scientific experiment used to control factors not under direct experimental control. Examples of RCTs are clinical trials that compare the effects of drugs, surgical techniques, medical devices, diagnostic procedures or other medical treatments.
In scientific research, the null hypothesis is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative relationship does not exist, hence the term "null". In addition to the null hypothesis, an alternative hypothesis is also developed, which claims that a relationship does exist between two variables.
In statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis when a specific alternative hypothesis is true. It is commonly denoted by , and represents the chances of a true positive detection conditional on the actual existence of an effect to detect. Statistical power ranges from 0 to 1, and as the power of a test increases, the probability of making a type II error by wrongly failing to reject the null hypothesis decreases.
Validity is the main extent to which a concept, conclusion or measurement is well-founded and likely corresponds accurately to the real world. The word "valid" is derived from the Latin validus, meaning strong. The validity of a measurement tool is the degree to which the tool measures what it claims to measure. Validity is based on the strength of a collection of different types of evidence described in greater detail below.
An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. It is most often used when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled. Exact "F-tests" mainly arise when the models have been fitted to the data using least squares. The name was coined by George W. Snedecor, in honour of Ronald Fisher. Fisher initially developed the statistic as the variance ratio in the 1920s.
Data dredging 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. This is done by performing many statistical tests on the data and only reporting those that come back with significant results.
The Friedman test is a non-parametric statistical test developed by Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to detect differences in treatments across multiple test attempts. The procedure involves ranking each row together, then considering the values of ranks by columns. Applicable to complete block designs, it is thus a special case of the Durbin test.
In a scientific study, post hoc analysis 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 by critics because the statistical associations that it finds are often spurious.
In statistics, particularly in analysis of variance and linear regression, a contrast is a linear combination of variables whose coefficients add up to zero, allowing comparison of different treatments.
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 logrank test, or log-rank test, is a hypothesis test to compare the survival distributions of two samples. It is a nonparametric test and appropriate to use when the data are right skewed and censored. It is widely used in clinical trials to establish the efficacy of a new treatment in comparison with a control treatment when the measurement is the time to event. The test is sometimes called the Mantel–Cox test. The logrank test can also be viewed as a time-stratified Cochran–Mantel–Haenszel test.
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.
A glossary of terms used in clinical research.
In statistics, a paired difference test is a type of location test that is used when comparing two sets of measurements to assess whether their population means differ. A paired difference test uses additional information about the sample that is not present in an ordinary unpaired testing situation, either to increase the statistical power, or to reduce the effects of confounders.
In medicine and psychology, clinical significance is the practical importance of a treatment effect—whether it has a real genuine, palpable, noticeable effect on daily life.
Peter Björn Nemenyi was an American mathematician, who worked in statistics and probability theory. He taught mathematics at a number of American colleges and universities, including Hunter College, Tougaloo College, Oberlin College, University of North Carolina at Chapel Hill, Virginia State College and the University of Wisconsin–Madison. Several statistical tests, for example the Nemenyi test, bear his name. He was also a prominent civil-rights activist. He was the son of Paul Nemenyi an eminent fluid and engineering mechanics expert of the twentieth century. His mother was Aranka Heller, poet and scholar, daughter of Bernat Heller, a renowned 'Aggadist, Islamic scholar and folklorist.
In statistics, Dunnett's test is a multiple comparison procedure developed by Canadian statistician Charles Dunnett to compare each of a number of treatments with a single control. Multiple comparisons to a control are also referred to as many-to-one comparisons.
Ajit C. Tamhane is a professor in the Department of Industrial Engineering and Management Sciences (IEMS) at Northwestern University and also holds a courtesy appointment in the Department of Statistics.
References
- ↑ Nemenyi, P.B. (1963) Distribution-free Multiple Comparisons. PhD thesis, Princeton University.
- ↑ Hollander; Wolfe, Douglas A. (1999). Nonparametric Statistical Methods (2nd ed.). ISBN 0-471-19045-4.
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