|
Chi-squared Test
A chi-squared test (also chi-square or test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical variables (''two dimensions of the contingency table'') are independent in influencing the test statistic (''values within the table''). The test is valid when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof. Pearson's chi-squared test is used to determine whether there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table. For contingency tables with smaller sample sizes, a Fisher's exact test is used instead. In the standard applications of this test, the observations are classified into mutually exclusive classes. If the null hypothesis that there are no di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chi-square DistributionCDF-English
The term chi-square, chi-squared, or \chi^2 has various uses in statistics: *chi-square distribution, a continuous probability distribution *chi-square test A chi-squared test (also chi-square or test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical variabl ..., name given to some tests using chi-square distribution * chi-square target models, a mathematical model used in radar cross-section {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mansfield Merriman
Mansfield Merriman (March 27, 1848 June 7, 1925) was an American civil engineer, born in Southington, Connecticut. He graduated from Yale's Sheffield Scientific School in 1871, was an assistant in the United States Corps of Engineers in 187273, and was an instructor in civil engineering at Sheffield from 1875 to 1878. He was professor of civil engineering at Lehigh University from 1878 to 1907 and, thereafter, a consulting civil and hydraulic engineer. From 1880 to 1885, Merriman was also an assistant on the United States Coast and Geodetic Survey. His researches in hydraulics, bridges, strength of materials, and pure mathematics are important. He was elected as a member to the American Philosophical Society The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ... in 1881. Merriman's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Likelihood-ratio Test
In statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models based on the ratio of their likelihoods, specifically one found by maximization over the entire parameter space and another found after imposing some constraint. If the constraint (i.e., the null hypothesis) is supported by the observed data, the two likelihoods should not differ by more than sampling error. Thus the likelihood-ratio test tests whether this ratio is significantly different from one, or equivalently whether its natural logarithm is significantly different from zero. The likelihood-ratio test, also known as Wilks test, is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent. In the case of comparing two models each of which has no unknown parameters, use o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autocorrelation
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals. Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with autocovariance. Unit root processes, trend-stationary processes, autoregressive processes, and moving average processes are specific forms of processes with autocorrelation. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time-series Analysis
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. Time series ''analysis'' comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series ''forecasting'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Portmanteau Test
A portmanteau test is a type of statistical hypothesis test in which the null hypothesis is well specified, but the alternative hypothesis is more loosely specified. Tests constructed in this context can have the property of being at least moderately powerful against a wide range of departures from the null hypothesis. Thus, in applied statistics, a portmanteau test provides a reasonable way of proceeding as a general check of a model's match to a dataset where there are many different ways in which the model may depart from the underlying data generating process. Use of such tests avoids having to be very specific about the particular type of departure being tested. Examples In time series analysis, two well-known versions of a portmanteau test are available for testing for autocorrelation in the residuals of a model: it tests whether any of a group of autocorrelations of the residual time series are different from zero. This test is the Ljung–Box test, which is an improved ... [...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] |
McNemar's Test
In statistics, McNemar's test is a statistical test used on paired nominal data. It is applied to 2 × 2 contingency tables with a dichotomous trait, with matched pairs of subjects, to determine whether the row and column marginal frequencies are equal (that is, whether there is "marginal homogeneity"). It is named after Quinn McNemar, who introduced it in 1947. An application of the test in genetics is the transmission disequilibrium test for detecting linkage disequilibrium. The commonly used parameters to assess a diagnostic test in medical sciences are sensitivity and specificity. Sensitivity (or recall) is the ability of a test to correctly identify the people with disease. Specificity is the ability of the test to correctly identify those without the disease. Now presume two tests are performed on the same group of patients. And also presume that these tests have identical sensitivity and specificity. In this situation one is carried away by these findings ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cochran–Mantel–Haenszel Statistics
In statistics, the Cochran–Mantel–Haenszel test (CMH) is a test used in the analysis of stratified or matched categorical data. It allows an investigator to test the association between a binary predictor or treatment and a binary outcome such as case or control status while taking into account the stratification. Unlike the McNemar test which can only handle pairs, the CMH test handles arbitrary strata size. It is named after William G. Cochran, Nathan Mantel and William Haenszel. Extensions of this test to a categorical response and/or to several groups are commonly called Cochran–Mantel–Haenszel statistics. It is often used in observational studies where random assignment of subjects to different treatments cannot be controlled, but confounding covariates can be measured. Definition We consider a binary outcome variable such as case status (e.g. lung cancer) and a binary predictor such as treatment status (e.g. smoking). The observations are grouped in strata. The strat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Test
In statistics, the binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories using sample data. Usage The binomial test is useful to test hypotheses about the probability (\pi) of success: : H_0:\pi=\pi_0 where \pi_0 is a user-defined value between 0 and 1. If in a sample of size n there are k successes, while we expect n\pi_0, the formula of the binomial distribution gives the probability of finding this value: : \Pr(X=k)=\binomp^k(1-p)^ If the null hypothesis H_0 were correct, then the expected number of successes would be n\pi_0. We find our p-value for this test by considering the probability of seeing an outcome as, or more, extreme. For a one-tailed test, this is straightforward to compute. Suppose that we want to test if \pi\pi_0 using the summation of the range from k to n instead. Calculating a p-value for a two-tailed test is slightly more complicated, since a bin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \sigma^2, s^2, \operatorname(X), V(X), or \mathbb(X). An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Test Statistic
A test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing.Berger, R. L.; Casella, G. (2001). ''Statistical Inference'', Duxbury Press, Second Edition (p.374) A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test. In general, a test statistic is selected or defined in such a way as to quantify, within observed data, behaviours that would distinguish the null from the alternative hypothesis, where such an alternative is prescribed, or that would characterize the null hypothesis if there is no explicitly stated alternative hypothesis. An important property of a test statistic is that its sampling distribution under the null hypothesis must be calculable, either exactly or approximately, which allows ''p''-values to be calculated. A ''test statistic'' shares some of the same qualities o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
