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Pearson correlation coefficient. Several sets of ( x , y) points, with the correlation coefficient of x and y for each set. The correlation reflects the strength and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom).
In mathematics, the logarithm is the inverse function to exponentiation. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 103, the logarithm base 10 {\displaystyle 10} of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is denoted as logb (x ...
- History
- Other Examples of Chi-Squared Tests
- Yates's Correction For Continuity
- Chi-Squared Test For Variance in A Normal Population
- Example Chi-Squared Test For Categorical Data
- Applications
- See Also
- Further Reading
In the 19th century, statistical analytical methods were mainly applied in biological data analysis and it was customary for researchers to assume that observations followed a normal distribution, such as Sir George Airy and Mansfield Merriman, whose works were criticized by Karl Pearsonin his 1900 paper. At the end of the 19th century, Pearson not...
One test statistic that follows a chi-squared distribution exactly is the test that the variance of a normally distributed population has a given value based on a sample variance. Such tests are uncommon in practice because the true variance of the population is usually unknown. However, there are several statistical tests where the chi-squared dis...
Using the chi-squared distribution to interpret Pearson's chi-squared statistic requires one to assume that the discrete probability of observed binomial frequencies in the table can be approximated by the continuous chi-squared distribution. This assumption is not quite correct and introduces some error. To reduce the error in approximation, Frank...
If a sample of size n is taken from a population having a normal distribution, then there is a result (see distribution of the sample variance) which allows a test to be made of whether the variance of the population has a pre-determined value. For example, a manufacturing process might have been in stable condition for a long period, allowing a va...
Suppose there is a city of 1,000,000 residents with four neighborhoods: A, B, C, and D. A random sample of 650 residents of the city is taken and their occupation is recorded as "white collar", "blue collar", or "no collar". The null hypothesis is that each person's neighborhood of residence is independent of the person's occupational classificatio...
In cryptanalysis, the chi-squared test is used to compare the distribution of plaintext and (possibly) decrypted ciphertext. The lowest value of the test means that the decryption was successful with high probability.This method can be generalized for solving modern cryptographic problems. In bioinformatics, the chi-squared test is used to compare ...
Weisstein, Eric W. "Chi-Squared Test". MathWorld.Corder, G. W.; Foreman, D. I. (2014), Nonparametric Statistics: A Step-by-Step Approach, New York: Wiley, ISBN 978-1118840313Greenwood, Cindy; Nikulin, M. S. (1996), A guide to chi-squared testing, New York: Wiley, ISBN 0-471-55779-XNikulin, M. S. (1973), "Chi-squared test for normality", Proceedings of the International Vilnius Conference on Probability Theory and Mathematical Statistics, vol. 2, pp. 119–122The Boundary Fire was a 2017 wildfire in Arizona that burned 17,788 acres (7,199 ha) of the Coconino and Kaibab National Forests. The fire was ignited on June 1 when lightning struck a spot on the northeast side of Kendrick Peak within the Coconino National Forest. The fire spread rapidly because of high temperatures, steep terrain, leftovers ...
In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci ...
This is a dynamic list and may never be able to satisfy particular standards for completeness. You can help by adding missing items with reliable sources. This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there ...
e. In economics, the Gini coefficient ( / ˈdʒiːni / JEE-nee ), also known as the Gini index or Gini ratio, is a measure of statistical dispersion intended to represent the income inequality, the wealth inequality, or the consumption inequality [3] within a nation or a social group. It was developed by Italian statistician and sociologist ...
