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Point-biserial Correlation Coefficient
The point biserial correlation coefficient (''rpb'') is a correlation coefficient used when one variable (e.g. ''Y'') is dichotomous; ''Y'' can either be "naturally" dichotomous, like whether a coin lands heads or tails, or an artificially dichotomized variable. In most situations it is not advisable to dichotomize variables artificially. When a new variable is artificially dichotomized the new dichotomous variable may be conceptualized as having an underlying continuity. If this is the case, a biserial correlation would be the more appropriate calculation. The point-biserial correlation is mathematically equivalent to the Pearson (product moment) correlation coefficient; that is, if we have one continuously measured variable ''X'' and a dichotomous variable ''Y'', ''rXY'' = ''rpb''. This can be shown by assigning two distinct numerical values to the dichotomous variable. __TOC__ Calculation To calculate ''rpb'', assume that the dichotomous variable ''Y'' has the two values 0 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation Coefficient
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution. Several types of correlation coefficient exist, each with their own definition and own range of usability and characteristics. They all assume values in the range from −1 to +1, where ±1 indicates the strongest possible correlation and 0 indicates no correlation. As tools of analysis, correlation coefficients present certain problems, including the propensity of some types to be distorted by outliers and the possibility of incorrectly being used to infer a causal relationship between the variables (for more, see Correlation does not imply causation). Types There are several different measures for the degree of correlation in data, depending on the kind of data: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dichotomy
A dichotomy () is a partition of a set, partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be * jointly exhaustive: everything must belong to one part or the other, and * mutually exclusive: nothing can belong simultaneously to both parts. If there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice versa, and they are jointly exhaustive, since they cover all of A, and together again give A. Such a partition is also frequently called a bipartition. The two parts thus formed are Complement (set theory), complements. In logic, the partitions are dual (category theory), opposites if there exists a proposition such that it holds over one and not the other. Treating continuous variables or multicategorical variables as binary variables is called discretization, dichotomization. The discretization error inherent in dichoto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biserial Correlation
The point biserial correlation coefficient (''rpb'') is a correlation coefficient used when one variable (e.g. ''Y'') is dichotomous; ''Y'' can either be "naturally" dichotomous, like whether a coin lands heads or tails, or an artificially dichotomized variable. In most situations it is not advisable to dichotomize variables artificially. When a new variable is artificially dichotomized the new dichotomous variable may be conceptualized as having an underlying continuity. If this is the case, a biserial correlation would be the more appropriate calculation. The point-biserial correlation is mathematically equivalent to the Pearson (product moment) correlation coefficient; that is, if we have one continuously measured variable ''X'' and a dichotomous variable ''Y'', ''rXY'' = ''rpb''. This can be shown by assigning two distinct numerical values to the dichotomous variable. __TOC__ Calculation To calculate ''rpb'', assume that the dichotomous variable ''Y'' has the two values 0 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pearson Correlation Coefficient
In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of children from a school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation). Naming and history It was developed by Karl Pearson from a related idea introduced by Francis Galton in the 1880s, and for which the mathematical formula was derived and published by Auguste Bravais in 1844. The nami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Set
A data set (or dataset) is a collection of data. In the case of tabular data, a data set corresponds to one or more table (database), database tables, where every column (database), column of a table represents a particular Variable (computer science), variable, and each row (database), row corresponds to a given Record (computer science), record of the data set in question. The data set lists values for each of the variables, such as for example height and weight of an object, for each member of the data set. Data sets can also consist of a collection of documents or files. In the open data discipline, a dataset is a unit used to measure the amount of information released in a public open data repository. The European data.europa.eu portal aggregates more than a million data sets. Properties Several characteristics define a data set's structure and properties. These include the number and types of the attributes or variables, and various statistical measures applicable to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek alphabet, Greek letter Sigma, σ (sigma), for the population standard deviation, or the Latin script, Latin letter ''s'', for the sample standard deviation. The standard deviation of a random variable, Sample (statistics), sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Allyn & Bacon
Allyn & Bacon, founded in 1868, is a higher education textbook publisher in the areas of education, humanities and social sciences. It is an imprint of Pearson Education, the world's largest education publishing and technology company, which is part of Pearson PLC. Allyn & Bacon was an independent company until it was purchased by Esquire, Inc., the former publishers of the magazine of the same name, in 1981. Esquire, Inc. was sold to Gulf+Western in 1983, and Allyn & Bacon became part of Simon & Schuster Simon & Schuster LLC (, ) is an American publishing house owned by Kohlberg Kravis Roberts since 2023. It was founded in New York City in 1924, by Richard L. Simon and M. Lincoln Schuster. Along with Penguin Random House, Hachette Book Group US ...'s education division. Pearson purchased the education and reference divisions of Simon & Schuster in 1998. In 2007, Allyn & Bacon merged with Merrill, also a Pearson company. As a result of the merge, the company's website ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Null Hypothesis
The null hypothesis (often denoted ''H''0) is the claim in scientific research that the effect being studied does not exist. The null hypothesis can also be described as the hypothesis in which no relationship exists between two sets of data or variables being analyzed. If the null hypothesis is true, any experimentally observed effect is due to chance alone, hence the term "null". In contrast with the null hypothesis, an alternative hypothesis (often denoted ''H''A or ''H''1) is developed, which claims that a relationship does exist between two variables. Basic definitions The null hypothesis and the ''alternative hypothesis'' are types of conjectures used in statistical tests to make statistical inferences, which are formal methods of reaching conclusions and separating scientific claims from statistical noise. The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the e ... [...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] |
Probability Density Function
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a Function (mathematics), function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a ''relative likelihood'' that the value of the random variable would be equal to that sample. Probability density is the probability per unit length, in other words, while the ''absolute likelihood'' for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample. More precisely, the PDF is used to specify the probability of the random variable falling ''within ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma^2 is the variance. The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
