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A quick answer: F is the ratio of two Chi squared divided by their degrees of freedom respectively. Where: * (X1)2 & (X2)2 are the Chi squared for the variables 1 & 2 respectively (formatting issues prevented proper use of Greek letters for Chi sq) * v1 & V2 are the degrees of freedom (also refered to as df) respective to the variables 1 & 2
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Why use chi-square?
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 among proportions
Does use of chi-square demand a random sample?
Well, sort of. The Chi-square distribution is the sampling distribution of the variance. It is derived based on a random sample. A perfect random sample is where any value in the sample has any relationship to any other value. I would say that if the Chi-square distribution is used, then every effort should be made to make the sample as random as possible. I would also say that if the Chi-square distribution is used and the sample is clearly not a random sample, then improper conclusions may be reached.
What was the motivation for introducing the Gamma distribution?
It can be thought of as a generalization of the Chi-square distribution. See the link to a related WikiAnswer question below.
What is the area underneath curve for chi-square distribution?
1. It is a probability distribution function and so the area under the curve must be 1.
Does a population have to be normally distributed in order to use the chi-square distribution?
No, but the approximation is better for normally distributed variables.
Can you get a negative chi square statistic?
The characteristics of the chi-square distribution are: A. The value of chi-square is never negative. B. The chi-square distribution is positively skewed. C. There is a family of chi-square distributions.
What is the difference between a chi-square and t-distribution?
Chi-square is a distribution used to analyze the standard deviation of two samples. A t-distribution on the other hand, is used to compare the means of two samples.
Why use chi-square?
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 among proportions
Is chi square distribution is continuous distribution?
Yes
The properties of chi-square distribution?
it has reproductive property
Are the mean and median equal in a chi-square distribution?
No.
Is chi-square distribution symmetrical about mean value?
No.
Properties of Chi-square distribution?
It is a continuous distribution. Its domain is the positive real numbers. It is a member of the exponential family of distributions. It is characterised by one parameter. It has additive properties in terms of the defining parameter. Finally, although this is a property of the standard normal distribution, not the chi-square, it explains the importance of the chi-square distribution in hypothesis testing: If Z1, Z2, ..., Zn are n independent standard Normal variables, then the sum of their squares has a chi-square distribution with n degrees of freedom.
What does the number that Chi-Square produces represent?
It is the value of a random variable which has a chi-square distribution with the appropriate number of degrees of freedom.
What is the posterior distribution when sampling from a poisson distribution with a chi square prior?
Um... how am i supposed to know
Chi-square distribution assumes only positive value?
1
Is the shape of the chi-square distribution bsed on the degrees of freedom?
Yes.
