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Given "n" random variables, normally distributed, and the squared values of these RV are summed, the resultant random variable is chi-squared distributed, with degrees of freedom, k = n-1. As k goes to infinity, the resulant RV becomes normally distributed.
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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
What happens to the shape of the chi-square distribution as the df value increases?
As the value of k, the degrees of freedom increases, the (chisq - k)/sqrt(2k) approaches the standard normal distribution.
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.
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.
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.
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
What is the underlying principle of a chi square test?
The underlying principle is that the square of an independent Normal variable has a chi-square distribution with one degree of freedom (df). A second principle is that the sum of k independent chi-squares variables is a chi-squared variable with k df.
What are the characteristics of chi-square distribution?
Chi-square density curves are right-skewed. Each Chi-square random variable is associated with a degree of freedom (υ), .As υ increase, Chi-square curves become more symmetric.Z2, the square of a normal[0,1] random variable, follows adistribution.The sum of 2 independent Chi-square random variables withυ1, υ2degrees of freedom respectively, has a Chi-square distribution withυ = υ1+ υ2degrees of freedom.E() = υand V() = 2 υ.If {X1, X2, …, Xn} is a random sample of size n drawn from normal population with mean μ and standard deviation σ (i.e., X ~ normal[μ,σ]), then {(n-1)S2 }/ σ2 =~.
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.
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.
What happens to the shape of the chi-square distribution as the df value increases?
As the value of k, the degrees of freedom increases, the (chisq - k)/sqrt(2k) approaches the standard normal distribution.
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.
