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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).
It was formed approximately 4.5 billion years ago, is a terrestrial planet and is the second smallest of the Solar System 's planets with a diameter of 6,779 km (4,212 mi). A Martian solar day ( sol) is 24.5 hours and a Martian solar year is 1.88 Earth years (687 Earth days). Mars has two small and irregular natural satellites: Phobos and Deimos.
Fibonacci sequence. A tiling with squares whose side lengths are successive Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13 and 21. 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 .
- 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. 119–122In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. [1] .
Example of samples from two populations with the same mean but different variances. The red population has mean 100 and variance 100 (SD=10) while the blue population has mean 100 and variance 2500 (SD=50) where SD stands for Standard Deviation. In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable.
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 ...
