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One-tailed 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernoulli Trial
In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted. It is named after Jacob Bernoulli, a 17th-century Swiss mathematician, who analyzed them in his ' (1713). The mathematical formalization and advanced formulation of the Bernoulli trial is known as the Bernoulli process. Since a Bernoulli trial has only two possible outcomes, it can be framed as a "yes or no" question. For example: *Is the top card of a shuffled deck an ace? *Was the newborn child a girl? (See human sex ratio.) Success and failure are in this context labels for the two outcomes, and should not be construed literally or as value judgments. More generally, given any probability space, for any event (set of outcomes), one can define a Bernoulli trial according to whether the event occurred or not (event or c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Critical Value (statistics)
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 or equivalently by evaluating a ''p''-value computed from the test statistic. Roughly 100 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 theory, a more precise experiment will be a more severe test of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantile Function
In probability and statistics, the quantile function is a function Q: ,1\mapsto \mathbb which maps some probability x \in ,1/math> of a random variable v to the value of the variable y such that P(v\leq y) = x according to its probability distribution. In other words, the function returns the value of the variable below which the specified cumulative probability is contained. For example, if the distribution is a standard normal distribution then Q(0.5) will return 0 as 0.5 of the probability mass is contained below 0. The quantile function is also called the percentile function (after the percentile), percent-point function, inverse cumulative distribution function (after the cumulative distribution function or c.d.f.) or inverse distribution function. Definition Strictly increasing distribution function With reference to a continuous and strictly increasing cumulative distribution function (c.d.f.) F_X\colon \mathbb \to ,1/math> of a random variable , the quantile function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Z-test
A ''Z''-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution. ''Z''-test tests the mean of a distribution. For each statistical significance, significance level in the Confidence intervals, confidence interval, the ''Z''-test has a single critical value (for example, 1.96 for 5% two-tailed), which makes it more convenient than the Student's t-test, Student's ''t''-test whose critical values are defined by the sample size (through the corresponding degrees of freedom (statistics), degrees of freedom). Both the ''Z''-test and Student's ''t''-test have similarities in that they both help determine the significance of a set of data. However, the ''Z''-test is rarely used in practice because the population deviation is difficult to determine. Applicability Because of the central limit theorem, many test statistics are approximately normally distributed for large samples. Therefore, many s ... [...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] |
Student's T-distribution
In probability theory and statistics, Student's distribution (or simply the distribution) t_\nu is a continuous probability distribution that generalizes the Normal distribution#Standard normal distribution, standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However, t_\nu has Heavy-tailed distribution, heavier tails, and the amount of probability mass in the tails is controlled by the parameter \nu. For \nu = 1 the Student's distribution t_\nu becomes the standard Cauchy distribution, which has very fat-tailed distribution, "fat" tails; whereas for \nu \to \infty it becomes the standard normal distribution \mathcal(0, 1), which has very "thin" tails. The name "Student" is a pseudonym used by William Sealy Gosset in his scientific paper publications during his work at the Guinness Brewery in Dublin, Ireland. The Student's distribution plays a role in a number of widely used statistical analyses, including Student's t- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Design Of Experiments
''The Design of Experiments'' is a 1935 book by the English statistician Ronald Fisher about the design of experiments and is considered a foundational work in experimental design. Among other contributions, the book introduced the concept of the null hypothesis in the context of the lady tasting tea experiment.OED, "null hypothesis," first usage: 1935 R. A. Fisher, ''The Design of Experiments'' ii. 19, "We may speak of this hypothesis as the 'null hypothesis'...the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation." A chapter is devoted to the Latin square. Chapters # Introduction # The principles of experimentation, illustrated by a psycho-physical experiment # A historical experiment on growth rate # An agricultural experiment in randomized blocks # The Latin square # The factorial design in experimentation # Confounding # Special cases of partial confounding # The increase of precision by concomitant measurements. Sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Methods For Research Workers
''Statistical Methods for Research Workers'' is a classic book on statistics, written by the statistician R. A. Fisher. It is considered by some to be one of the 20th century's most influential books on statistical methods, together with his '' The Design of Experiments'' (1935). It was originally published in 1925, by Oliver & Boyd (Edinburgh); the final and posthumous 14th edition was published in 1970. The impulse to write a book on the statistical methodology he had developed came not from Fisher himself but from D. Ward Cutler, one of the two editors of a series of "Biological Monographs and Manuals" being published by Oliver and Boyd. Reviews According to Denis Conniffe: Ronald A. Fisher was "interested in application and in the popularization of statistical methods and his early book ''Statistical Methods for Research Workers'', published in 1925, went through many editions and motivated and influenced the practical use of statistics in many fields of study. His ''Design ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation Diagram
Standard may refer to: Symbols * Colours, standards and guidons, kinds of military signs * Heraldic flag, Standard (emblem), a type of a large symbol or emblem used for identification Norms, conventions or requirements * Standard (metrology), an object that bears a defined relationship to a unit of measure used for calibration of measuring devices * Standard (timber unit), an obsolete measure of timber used in trade * Breed standard (also called bench standard), in animal fancy and animal husbandry * BioCompute Object, BioCompute Standard, a standard for next generation sequencing * De facto standard, ''De facto'' standard, product or system with market dominance * Gold standard, a monetary system based on gold; also used metaphorically for the best of several options, against which the others are measured * Internet Standard, a specification ratified as an open standard by the Internet Engineering Task Force * Learning standards, standards applied to education content * Stand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goodness Of Fit
The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measures can be used in statistical hypothesis testing, e.g. to test for normality of residuals, to test whether two samples are drawn from identical distributions (see Kolmogorov–Smirnov test), or whether outcome frequencies follow a specified distribution (see Pearson's chi-square test). In the analysis of variance, one of the components into which the variance is partitioned may be a lack-of-fit sum of squares. Fit of distributions In assessing whether a given distribution is suited to a data-set, the following tests and their underlying measures of fit can be used: * Bayesian information criterion * Kolmogorov–Smirnov test * Cramér–von Mises criterion * Anderson–Darling test * Berk-Jones tests * Shapiro–Wilk test * Chi-s ... [...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] |
