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Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
A chart showing a uniform distribution. In probability theory and statistics, a collection of random variables is independent and identically distributed (i.i.d., iid, or IID) if each random variable has the same probability distribution as the others and all are mutually independent. [1]
For an exact test used in place of the 2 × 2 chi-squared test for independence when all the row and column totals were fixed by design, see Fisher's exact test. When the row or column margins (or both) are random variables (as in most common research designs) this tends to be overly conservative and underpowered [10].
Shanks was born in 1812 in Corsenside.He may have been a student of William Rutherford as a young boy in the 1820s, and he dedicated a book on π published in 1853 to Rutherford.
In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. [1] Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter is called the degrees ...
In probability theory and statistics, the chi-squared distribution (also chi-square or -distribution) with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables.
Under the null hypothesis, the number of runs in a sequence of N elements [note 1] is a random variable whose conditional distribution given the observation of N + positive values [note 2] and N − negative values (N = N + + N −) is approximately normal, with: [1] [2]
= the number of cells in the table. The chi-squared statistic can then be used to calculate a p-value by comparing the value of the statistic to a chi-squared distribution. The number of degrees of freedom is equal to the number of cells , minus the reduction in degrees of freedom, .