F-testAn F-test is a statistical test that compares variances. It is used to determine if the variances of two samples, or if the ratios of variances among multiple samples, are significantly different. The test calculates a statistic, represented by the random variable F, and checks if it follows an F-distribution. This check is valid if the null hypothesis is true and standard assumptions about the errors (ε) in the data hold.
VarianceIn probability theory and statistics, variance is a measure of dispersion, meaning it is a measure of how far a set of numbers are spread out from their average value. It is defined as the expected value of the squared deviation from the mean of a random variable. The standard deviation is the square root of the variance.
Law of total varianceThe law of total variance is a fundamental result in probability theory that expresses the variance of a random variable Y in terms of its conditional variances and conditional means given another random variable X. Informally, it states that the overall variability of Y can be split into an “unexplained” component (the average of within-group variances) and an “explained” component (the variance of group means).
Ronald FisherSir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was an English polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. He has been described as "a genius who almost single-handedly created the foundations for modern statistical science" and "the single most important figure in 20th century statistics".
Pierre-Simon LaplacePierre-Simon, Marquis de Laplace (; French: [pjɛʁ simɔ̃ laplas]; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summarized and extended the work of his predecessors in his five-volume Mécanique céleste (Celestial Mechanics) (1799–1825).
Carl Friedrich GaussGerman polymath and scholar (1777–1855)Johann Carl Friedrich Gauss ( ; German: Gauß; 30 April 1777 – 23 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. His mathematical contributions spanned the branches of number theory, algebra, analysis, geometry, statistics, and probability.
Student's t-testStatistical hypothesis testStudent'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.
Stephen StiglerStephen Mack Stigler (born August 10, 1941) is the Ernest DeWitt BurtonDistinguished Service Professor at the Department of Statistics of the University of Chicago. He has authored several books on the history of statistics; he is the son of the economist George Stigler. Stigler is also known for Stigler's law of eponymy which states that no scientific discovery is named after its original discoverer – whose first formulation he credits to sociologist Robert K. Merton.
StatisticsStudy of collection and analysis of dataThe normal distribution, a very common probability density, is used extensively in inferential statistics.Scatter plots and line charts are used in descriptive statistics to show the observed relationships between different variables, here using the Iris flower data set.Statistics (from German: Statistik, orig.
StatisticianA statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, and statisticians may work as employees or as statistical consultants. OverviewAccording to the United States Bureau of Labor Statistics, as of 2014, 26,970 jobs were classified as statistician in the United States.
AverageNumber taken as representative of a list of numbersIn mathematics, an average of a collection or group is a value that is most central, common, or typical in some sense, and represents its overall position. In mathematics, it most commonly refers to the arithmetic mean, but may also refer to other measures such as other types of mean, the median, or the mode.Statistical hypothesis testA statistical hypothesis test is a method of statistical inference used to decide whether the data provides 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.*As an Amazon Associate I earn from qualifying purchases.