• ###### cumulative
• They find the critical values using a chart and then confirm the area between the critical values and in each tail using the cumulative Chi-Square command. (ti.com)
• Johnson and Kotz give a comprehensive review on the approximations to the cumulative distribution function (cdf) of the F distribution. (scirp.org)
• Computer code for evaluating the cumulative distribution function of the generalized chi-squared distribution has been published, but some preliminary manipulation of the parameters of the distribution is usually necessary. (wikipedia.org)
• ###### goodness
• The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. (wikipedia.org)
• ###### gamma
• There are several other such variants for which the same term is sometimes used, or which clearly are generalizations of the chi-squared distribution, and which are treated elsewhere: some are special cases of the family discussed here, for example the noncentral chi-squared distribution and the gamma distribution, while the generalized gamma distribution is outside this family. (wikipedia.org)
• ###### differences
• Whereas group differences indicate differing score distributions on Y, DIF explicitly involves conditioning on θ. (wikipedia.org)
• ###### contingency
• So, we construct a contingency table that shows the distribution of one variable at each level of the other variable. (symynet.com)
• ###### value
• The Chi-Square distribution is based on a sum of squares, therefore the value of X^2 will always be larger than (or equal to) zero. (uva.nl)
• If we wish to reject H o at the .05 level, we will determine if our value of chi square is greater than the critical value of chi square that cuts off the upper 5% of the distribution at our particular degrees of freedom value. (symynet.com)
• If our value of chi square from the formula is greater than the critical value of chi square, we reject H o and conclude that the obtained frequencies differ from the expected frequencies more than would be predicted by chance. (symynet.com)
• Define a new random variable Q. To generate a random sample from Q, take a sample from Z and square the value. (wikipedia.org)
• The expected value of a chi-square random variable with 8 degrees of freedom is 8. (wikipedia.org)
• ###### population
• The oldest of these tests are used to detect whether two or more population distributions differ from one another. (biology-online.org)
• ###### standard
• Some important special cases relating to this particular form either omit the additional standard normal term and/or have central rather than non-central chi-squared distributions for the components of the summation. (wikipedia.org)
• ###### sample
• If the number of deaths at each hospital is large (say, five or more), then the usual chi-square distribution or other large-sample approach may be used, avoiding the need for simulations that would require a large amount of computer time. (thefreedictionary.com)
• ###### mean
• In practice it is rare - if not impossible - for an increase of X in a group mean to occur via an increase of each member's score by X.) This will shift the distribution X units in the positive direction, but will not have any impact on the variability within the group. (wikipedia.org)
• The most general form of generalized chi-squared distribution is obtained by extending the above consideration in two ways: firstly, to allow z to have a non-zero mean and, secondly, to include an additional linear combination of z in the definition of X. Note that, in the above formulation, A and B need not be positive definite. (wikipedia.org)
• ###### parameters
• distribution, where r is the degrees of freedom, which is the difference in the number of unconstrained parameters being estimated and the number of constrained parameters being estimated. (scirp.org)