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Topic: Chi-square distribution


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In the News (Mon 19 Aug 19)

  
 Chi-square distribution - Wikipedia, the free encyclopedia
The best-known situations in which the chi-square distribution is used are the common chi-square tests for goodness of fit of an observed distribution to a theoretical one, and of the independence of two criteria of classification of qualitative data.
It enters all analysis of variance problems via its role in the F-distribution, which is the distribution of the ratio of two independent chi-squared random variables divided by their respective degrees of freedom.
The chi-square distribution has numerous applications in inferential statistics, for instance in chi-square tests and in estimating variances.
en.wikipedia.org /wiki/Chi-square_distribution   (500 words)

  
 Pearson's chi-square test - Wikipedia, the free encyclopedia
Consultation of the chi-square distribution for 1 degree of freedom shows that the probability of observing this difference (or a more extreme difference than this) if men and women are equally numerous in the population is approximately 0.3.
By the normal approximation to a binomial this is the square of one standard normal variate, and hence is distributed as chi-square with 1 degree of freedom.
It is commonly stated that the degrees of freedom for the chi-square distribution of the statistic are then k − 1 − r, where r is the number of unknown parameters.
en.wikipedia.org /wiki/Chi-square_statistic   (971 words)

  
 Chi Square Distribution
The Chi Square distribution is a mathematical distribution that is used directly or indirectly in many tests of significance.
The most common use of the chi square distribution is to test differences between proportions.
The chi square distribution has one parameter, its degrees of freedom (df).
davidmlane.com /hyperstat/A100557.html   (110 words)

  
 1.3.6.6.6. Chi-Square Distribution
Since the chi-square distribution is typically used to develop hypothesis tests and confidence intervals and rarely for modeling applications, we omit the formulas and plots for the hazard, cumulative hazard, survival, and inverse survival probability functions.
The chi-square distribution is used in many cases for the critical regions for hypothesis tests and in determining confidence intervals.
Since the chi-square distribution is typically used to develop hypothesis tests and confidence intervals and rarely for modeling applications, we omit any discussion of parameter estimation.
www.itl.nist.gov /div898/handbook/eda/section3/eda3666.htm   (288 words)

  
 Stats: Chi-Square Distribution
Since the chi-square distribution isn't symmetric, the method for looking up left-tail values is different from the method for looking up right tail values.
) distribution is obtained from the values of the ratio of the sample variance and population variance multiplied by the degrees of freedom.
This occurs when the population is normally distributed with population variance sigma^2.
www.richland.edu /james/lecture/m170/ch12-int.html   (358 words)

  
 Chi-Square Distribution
distribution is equal to the number of degrees of freedom n-1, the variance is twice the degrees of freedom.
distribution is used to test differences between population and sample variances, and between theoretical and observed distributions.
distribution with n-1 degrees of freedom for a random sample of size n.
www.statistics4u.info /fundstat_eng/cc_distri_chisqr.html   (166 words)

  
 Talk:Chi-square distribution - Wikipedia, the free encyclopedia
Further, there is what Wolfram calls the "chi distribution" (but which is more or less absent elsewhere on the Web) which is what you get if you take the square root of a chi-square.
It's possible that one could express this distribution in terms of some sort of "noncentral chi distribution" whose pdf we could actually calculate; then a maximum likelihood estimator would be a reasonable thing to obtain.
Remember that this statistic is only asymptotically chi-squared.
en.wikipedia.org /wiki/Talk:Chi-square_distribution   (1877 words)

  
 Distribution Tables
The F distribution is a ratio of two Chi-square distributions, and a specific F distribution is denoted by the degrees of freedom for the numerator Chi-square and the degrees of freedom for the denominator Chi-square.
For examples of tests of hypothesis which use the Chi-square distribution, see Statistics in crosstabulation tables in the Basic Statistics and Tables chapter as well as the Nonlinear Estimation chapter.
The F distribution is a right-skewed distribution used most commonly in Analysis of Variance (see ANOVA/MANOVA).
www.statsoft.com /textbook/sttable.html   (676 words)

  
 Samples and Chi Squares
Comparing this value to the Chi Square distribution with 1 Degree of Freedom it can be found that the probability of getting a Chi Square value this large or larger, just due to chance, is.00389.
In Excel, the Chi Square statistic can be obtained by entering a rather lengthy formula in one cell or creating a table of (O - E) / E values and then summing these contribution to obtain the Chi Square value.
The sum of these values is the Chi Square value of 8.33.
www.perseusdevelopment.com /customersupp/WebHelpv4/surveysolutions/samples_and_chi_squares.htm   (389 words)

  
 Random Numbers Generator - Chi-Square Distribution
The most common use of the chi-square distribution is to test the difference between proportions.
The mean of a chi-square distribution is its degree of freedom.
The skew decreases when degree of freedom increases as the distribution approaches normal.
www.anthony-vba.kefra.com /vba/vbar1.htm   (147 words)

  
 IFA Services: Statistics, Chi-square distribution
The importance of the Chi-square distribution stems from the fact that it describes the distribution of the Variance of a sample taken from a Normal distributed population.
The Chi-square distribution, is derived from the Normal distribution.
It is the distribution of a sum of squared Normal distributed variables.
www.fon.hum.uva.nl /Service/Statistics/ChiSquare_distribution.html   (263 words)

  
 Probability Distributions (Statistics Toolbox)
distribution is actually a simple special case of the noncentral chi-square distribution.
The noncentral chi-square distribution requires two parameters; the degrees of freedom and the noncentrality parameter.
There are many equivalent formulas for the noncentral chi-square distribution function.
www-rohan.sdsu.edu /doc/matlab/toolbox/stats/prob_d12.html   (212 words)

  
 The Chi-Square Distribution
The mean, variance, moments, and moment generating function of the chi-square distribution can be obtained easily from general results for the gamma distribution.
Sums of squares of independent normal variables occur frequently in statistics.
In particular, this distribution will arise in the study of the sample variance when the underlying distribution is normal and in a goodness of fit test.
www.ds.unifi.it /VL/VL_EN/special/special4.html   (594 words)

  
 glosc.html
The entropic approach corresponds to maximum likelihood optimization, assuming that the data is drawn from the exponential family of distributions.
A common starting point is to use the squared multiple correlation of an item with all other items as an estimate of the communality (refer to Multiple Regression for details about multiple regression).
This is the square of the product-moment correlation between two variables (r
www.statsoft.com /textbook/glosc.html   (7574 words)

  
 1.3.6.7.4. Critical Values of the Chi-Square Distribution
Because of the lack of symmetry of the chi-square distribution, separate tables are provided for the upper and lower tails of the distribution.
This table contains the critical values of the chi-square distribution.
For two-sided tests, the test statistic is compared with values from both the table for the upper critical value and the table for the lower critical value.
www.itl.nist.gov /div898/handbook/eda/section3/eda3674.htm   (262 words)

  
 Chi-square distribution
A variable from a chi-square distribution with n degrees of freedom is the sum of the squares of
A chi-square variable with one degree of freedom is equal to the square of the standard normal variable.
The distribution function F(x) of a chi-square random variable x with
www.statsdirect.com /help/distributions/chi_square_distribution.htm   (241 words)

  
 Term: Chi-square Distribution
The chi-square distribution is a skewed right distribution.
It is used with the chi-square test to draw conclusions about the shape of a population variable or the relationship between two population variables.
www.public.coe.edu /~gcross/toolkit/glossary/glsry-49.html   (32 words)

  
 Probability distribution - Wikipedia, the free encyclopedia
The rectangular distribution is a uniform distribution on [-1/2,1/2].
A probability distribution is a special case of the more general notion of a probability measure, which is a function that assigns probabilities satisfying the Kolmogorov axioms to the measurable sets of a measurable space.
The probability distribution of the sum of two random variables is the convolution of each of their distributions.
www.wikipedia.org /wiki/Probability_distribution   (32 words)

  
 Chi-square distribution - Wikipedia, the free encyclopedia
The best-known situations in which the chi-square distribution is used are the common chi-square tests for goodness of fit of an observed distribution to a theoretical one, and of the independence of two criteria of classification of qualitative data.
The expected value of a random variable having chi-square distribution with k degrees of freedom is k and the variance is 2 k.
The chi-square distribution is a special case of the gamma distribution.
en.wikipedia.org /wiki/Chi-square_distribution   (32 words)

  
 Chi Square Calculator
To Find tail probabilities (or p-values), enter the chi square value in the "Area right of" box and hit "Compute!".
To find chi square critical values, enter a probabilitiy in the "=" box and hit "Compute!".
The answer is displayed in the "Area right of" box.
www.stat.sc.edu /~west/applets/chisqdemo.html   (99 words)

  
 Chi-Square Table
The table below contains the area under the right-hand tail of the Chi-square distribution curve for a particular value of chi-squared.
The number of degrees of freedom (df) is listed in the table.
physics.ubishops.ca /phy101/chi_table.htm   (33 words)

  
 Glossary of research economics
are drawn from a standard normal distribution, squared, and summed, the resulting statistic is said to have a chi-squared distribution with n degrees of freedom: z
Is the distribution of sums of squares of r standard normal variables.
This is a one-parameter family of distributions, and the parameter, n, is conventionally labeled the degrees of freedom of the distribution.
www.econterms.com /econtent.html   (14590 words)

  
 Freeware Home - Education ... Research
Normal Distribution and Invers Normal Distribution - Chi Square Distribution and Invers Chi Square Distribution - t Distribution and Invers t Distribution - F Distribution and Invers F Distribution - Binomial Distribution - Poisson Distribution - Hypergeometric Distribution - Factorial Function - Binomial Coefficent.
SLGallery, a unique probability distribution calculation toolbox featuring 11 continuous and 4 discrete functions to plot graph and find values for probability density, cumulative distribution (CDF), survival and Hazard functions.
Its purpose is to create and distribute a free international encyclopedia in as many languages as possible.
www.freewarehome.com /Education/Research_t.html   (389 words)

  
 cdfchi: ----- cumulative distribution function chi-square distribution
Calculates any one parameter of the chi-square distribution given values for the others.
P,Q (Q=1-P) : The integral from 0 to X of the chi-square distribution.
2.16.3 cdfchi: ----- cumulative distribution function chi-square distribution
www.snv.jussieu.fr /~wensgen/Doc/scilab-2.6/manual/Docu-html1043.html   (136 words)

  
 Chi square
Like the Poisson distribution mentioned before, Chi-square is a type of probability distribution.
  The important take-home message is that under certain assumptions, -2 ln (ratio) tends to a chi-square distribution with the degrees of freedom = difference in the number of parameters estimated in the 2 models.
  Different from Poisson being a discrete distribution, Chi-square is continuous.
www.genetics.wustl.edu /bio5488/lecture_notes_2004/chi.html   (722 words)

  
 Intro to Chi-Square Distribution
What assumptions must be made to use the chi-squared distribution?
Test the claim that the distribution of crashes conforms to the distribution of ages.
If all ages have the same crash rate, we would expected (because of the age distribution of licensed drivers) the given categories to have 16%, 44%, 27% and 13% of the subjects, respectively.
www.lhs.logan.k12.ut.us /~jsmart/chi-intro.htm   (649 words)

  
 chi-squared tests
Never fear: most counts are distributed according to the Poisson distribution, and as such the standard deviation equals the square root of the expected count.
Finally it should be noted that the technical differences between a Poisson distribution and a normal distribution cause problems for small E
(This formula says: find how each x deviates from the mean µ, square each difference, add up all the squared-differences and divide by the standard deviation squared.) More general versions of this formula would allow different means and standard deviations for each measurement.
www.physics.csbsju.edu /stats/chi-square.html   (414 words)

  
 Inverse-chi-square distribution - Wikipedia, the free encyclopedia
That is, if X has the chi-square distribution with ν degrees of freedom, then according to the first definition, 1 / X has the inverse-chi-square distribution with ν degrees of freedom; while according to the second definition, ν / X has the inverse-chi-square distribution with ν degrees of freedom.
In probability and statistics, the inverse-chi-square distribution is the probability distribution of a random variable whose inverse has a chi-square distribution.
It is also often defined as the distribution of a random variable whose inverse divided by its degrees of freedom is a chi-square distribution.
en.wikipedia.org /wiki/Inverse-chi-square_distribution   (414 words)

  
 Probability distribution - Wikipedia, the free encyclopedia
The Voigt distribution, or Voigt profile, is the convolution of a normal distribution and a Cauchy distribution.
A probability distribution is a special case of the more general notion of a probability measure, which is a function that assigns probabilities satisfying the Kolmogorov axioms to the measurable sets of a measurable space.
The Weibull distribution, of which the exponential distribution is a special case, is used to model the lifetime of technical devices.
en.wikipedia.org /wiki/Probability_distribution   (414 words)

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