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Two-sample Test
In statistical hypothesis testing, a two-sample test is a test performed on the data of two random samples, each independently obtained from a different given population. The purpose of the test is to determine whether the difference between these two populations is statistically significant. There are a large number of statistical tests that can be used in a two-sample test. Which one(s) are appropriate depend on a variety of factors, such as: * Which assumptions (if any) may be made ''a priori'' about the distributions from which the data have been sampled? For example, in many situations it may be assumed that the underlying distributions are normal distributions. In other cases the data are categorical, coming from a discrete distribution over a nominal scale, such as which entry was selected from a menu. * Does the hypothesis being tested apply to the distributions as a whole, or just some population parameter, for example the mean or the variance? * Is the hypothesis being ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Hypothesis Testing
A statistical hypothesis test is a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a Critical value (statistics), critical value or equivalently by evaluating a p-value, ''p''-value computed from the test statistic. Roughly 100 list of statistical tests, specialized statistical tests are in use and noteworthy. History While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see . Choice of null hypothesis Paul Meehl has argued that the epistemological importance of the choice of null hypothesis has gone largely unacknowledged. When the null hypothesis is predicted by the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
One-sided Test
In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of scores. This method is used for null hypothesis testing and if the estimated value exists in the critical areas, the alternative hypothesis is accepted over the null hypothesis. A one-tailed test is appropriate if the estimated value may depart from the reference value in only one direction, left or right, but not both. An example can be whether a machine produces more than one-percent defective products. In this situation, if the estimated value exists in one of the one-sided critical areas, depending on the direction of interest (greater than or less than), the alternative hypothesis is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-proportion Z-test
The Two-proportion Z-test (or, Two-sample proportion Z-test) is a statistical method used to determine whether the difference between the proportions of two groups, coming from a binomial distribution is statistically significant. This approach relies on the assumption that the sample proportions follow a normal distribution under the Central Limit Theorem, allowing the construction of a z-test for hypothesis testing and confidence interval estimation. It is used in various fields to compare success rates, response rates, or other proportions across different groups. Hypothesis test The z-test for comparing two proportions is a Statistical hypothesis test for evaluating whether the proportion of a certain characteristic differs significantly between two independent samples. This test leverages the property that the sample proportions (which is the average of observations coming from a Bernoulli distribution) are asymptotically normal under the Central Limit Theorem, enabling th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mann–Whitney U Test
The Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric statistical test of the null hypothesis that randomly selected values ''X'' and ''Y'' from two populations have the same distribution. Nonparametric tests used on two ''dependent'' samples are the sign test and the Wilcoxon signed-rank test. Assumptions and formal statement of hypotheses Although Henry Mann and Donald Ransom Whitney developed the Mann–Whitney ''U'' test under the assumption of continuous responses with the alternative hypothesis being that one distribution is stochastically greater than the other, there are many other ways to formulate the null and alternative hypotheses such that the Mann–Whitney ''U'' test will give a valid test. A very general formulation is to assume that: # All the observations from both groups are independent of each other, # The responses are at least ordinal (i.e., one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tukey–Duckworth Test
In statistics, the Tukey–Duckworth test is a two-sample location test – a statistical test of whether one of two samples was significantly greater than the other. It was introduced by John Tukey John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distributi ..., who aimed to answer a request by W. E. Duckworth for a test simple enough to be remembered and applied in the field without recourse to tables, let alone computers. Given two groups of measurements of roughly the same size, where one group contains the highest value and the other the lowest value, then (i) count the number of values in the one group exceeding all values in the other, (ii) count the number of values in the other group falling below all those in the one, and (iii) sum these two counts (we require that neither cou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Welch's T-test
In statistics, Welch's ''t''-test, or unequal variances ''t''-test, is a two-sample location test which is used to test the (null) hypothesis that two populations have equal means. It is named for its creator, Bernard Lewis Welch, and is an adaptation of Student's ''t''-test, and is more reliable when the two samples have unequal variances and possibly unequal sample sizes. These tests are often referred to as "unpaired" or "independent samples" ''t''-tests, as they are typically applied when the statistical units underlying the two samples being compared are non-overlapping. Given that Welch's ''t''-test has been less popular than Student's ''t''-test and may be less familiar to readers, a more informative name is "Welch's unequal variances ''t''-test" — or "unequal variances ''t''-test" for brevity. Sometimes, it is referred as Satterthwaite or Welch–Satterthwaite test. Assumptions Student's ''t''-test assumes that the sample means being compared for two populations are no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Student's T-test
Student's ''t''-test is a statistical test used to test whether the difference between the response of two groups is statistically significant or not. It is any statistical hypothesis test in which the test statistic follows a Student's ''t''-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known (typically, the scaling term is unknown and is therefore a nuisance parameter). When the scaling term is estimated based on the data, the test statistic—under certain conditions—follows a Student's ''t'' distribution. The ''t''-test's most common application is to test whether the means of two populations are significantly different. In many cases, a ''Z''-test will yield very similar results to a ''t''-test because the latter converges to the former as the size of the dataset increases. History The term "''t''-statistic" is abbreviated from " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pearson's Chi-squared Test
Pearson's chi-squared test or Pearson's \chi^2 test is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g., Yates, likelihood ratio, portmanteau test in time series, etc.) – statistical procedures whose results are evaluated by reference to the chi-squared distribution. Its properties were first investigated by Karl Pearson in 1900. In contexts where it is important to improve a distinction between the test statistic and its distribution, names similar to ''Pearson χ-squared'' test or statistic are used. It is a p-value test. The setup is as follows: * Before the experiment, the experimenter fixes a certain number N of samples to take. * The observed data is (O_1, O_2, ..., O_n), the count number of samples from a finite set of given categories. They satisfy \sum_i O_i = N. * The null hypothesis is that the count numbers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Median Test
The median test (also Mood’s median-test, Westenberg-Mood median test or Brown-Mood median test) is a special case of Pearson's chi-squared test. It is a nonparametric test that tests the null hypothesis that the medians of the populations from which two or more samples are drawn are identical. The data in each sample are assigned to two groups, one consisting of data whose values are higher than the median value in the two groups combined, and the other consisting of data whose values are at the median or below. A Pearson's chi-squared test is then used to determine whether the observed frequencies in each sample differ from expected frequencies derived from a distribution combining the two groups. Relation to other tests The test has low power (efficiency) for moderate to large sample sizes. The Wilcoxon– Mann–Whitney U two-sample test or its generalisation for more samples, the Kruskal–Wallis test, can often be considered instead. The relevant aspect of the median tes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kuiper's Test
Kuiper's test is used in statistics to test whether a data sample comes from a given distribution (one-sample Kuiper test), or whether two data samples came from the same unknown distribution (two-sample Kuiper test). It is named after Dutch mathematician Nicolaas Kuiper. Kuiper's test is closely related to the better-known Kolmogorov–Smirnov test (or K-S test as it is often called). As with the K-S test, the discrepancy statistics ''D''+ and ''D''− represent the absolute sizes of the most positive and most negative differences between the two cumulative distribution functions that are being compared. The trick with Kuiper's test is to use the quantity ''D''+ + ''D''− as the test statistic. This small change makes Kuiper's test as sensitive in the tails as at the median and also makes it invariant under cyclic transformations of the independent variable. The Anderson–Darling test is another test that provides equal sensitivity at the tails as the medi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kolmogorov–Smirnov Test
In statistics, the Kolmogorov–Smirnov test (also K–S test or KS test) is a nonparametric statistics, nonparametric test of the equality of continuous (or discontinuous, see #Discrete and mixed null distribution, Section 2.2), one-dimensional probability distributions. It can be used to test whether a random sample, sample came from a given reference probability distribution (one-sample K–S test), or to test whether two samples came from the same distribution (two-sample K–S test). Intuitively, it provides a method to qualitatively answer 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 (but unknown) probability distribution?". It is named after Andrey Kolmogorov and Nikolai Smirnov (mathematician), Nikolai Smirnov. The Kolmogorov–Smirnov statistic quantifies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kernel Embedding Of Distributions
In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which a probability distribution is represented as an element of a reproducing kernel Hilbert space (RKHS).A. Smola, A. Gretton, L. Song, B. Schölkopf. (2007)A Hilbert Space Embedding for Distributions. ''Algorithmic Learning Theory: 18th International Conference''. Springer: 13–31. A generalization of the individual data-point feature mapping done in classical kernel methods, the embedding of distributions into infinite-dimensional feature spaces can preserve all of the statistical features of arbitrary distributions, while allowing one to compare and manipulate distributions using Hilbert space operations such as inner products, distances, projections, linear transformations, and spectral analysis.L. Song, K. Fukumizu, F. Dinuzzo, A. Gretton (2013)Kernel Embeddings of Conditional Distributions: A unified kernel framework for n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
