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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.
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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
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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.
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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.
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It is the value of a random variable which has a chi-square distribution with the appropriate number of degrees of freedom.
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Um... how am i supposed to know
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A chi-squared test is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true.
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Not sure if you want properties of chi-square distribution or the characteristic function. If it is the latter, see the last cell of the table with the equations labeled cf.
See related link.
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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.
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The Chi-square test is a statistical test that is usually used to test how well a data set fits some hypothesised distribution.
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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.
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Chi-Square Goodness-of-fit Test is used when you want to test if the sample observed follows an assumed theoretical distribution.
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It can be thought of as a generalization of the Chi-square distribution. See the link to a related WikiAnswer question below.
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You could calculate it by integrating the chi-square probability distribution function but you are likely to be much better off using a table in a book or on the web.
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1. It is a probability distribution function and so the area under the curve must be 1.
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It can be, but it is also a statistical distribution in its own right - on which the test is based.
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Chi-square is mainly used for a goodness of fit test. This is a test designed to assess how well a set of observations agree with what might be expected from some hypothesised distribution.
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Given Z~N(0,1), Z^2 follows
χ_1^2 Chi-square Probability Distribution with one degree of freedom
Given Z_i~N(0,1), ∑_(i=1)^ν▒Z_i^2 follows
χ_ν^2 Chi-square Probability Distribution with ν degree of freedom
Given E_ij=n×p_ij=(r_i×c_j)/n, U=∑_(∀i,j)▒(O_ij-E_ij )^2/E_ij follows
χ_((r-1)(c-1))^2 Chi-square Probability Distribution with ν=(r-1)(c-1) degree of freedom
Given E_i=n×p_i, U=∑_(i=1)^m▒(O_i-E_j )^2/E_i follows
χ_(m-1)^2 Chi-square Probability Distribution with ν=m-1 degree of freedom
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Answer 1) Look up Gamma distribution in say Wikipedia or an on-line encyclopedia. This is not a simple subject.
Answer 2) The Gamma distribution is essentially a generalization of the Chi-square distribution. Multiplying a Chi-square random variable by a positive constant you get a Gamma random variable. See also the introduction to the Gamma random variable on statlect.com (see link below).
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No, but the approximation is better for normally distributed variables.
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- 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 a
distribution.
The sum of 2 independent Chi-square random variables with
υ
1
, υ
2
degrees of freedom respectively, has a Chi-square distribution with
υ = υ
1
+ υ
2
degrees of freedom.
E(
) = υ
and V(
) = 2 υ.
If {X
1
, X
2
, …, 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 =
~
.
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Yes, the chi-square test can be used to test how well a binomial fits, provided the observations are independent of one another and all from the same (or identical) binomial distribution.
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The most common use for a chi-square test is a "goodness of fit" test.
Suppose you have a set of observations. These may be classified according to one or more characteristics. You also have a hypothesis about what the distribution should be. The chi-square statistic is an indicator of how well the observed values agree with the values that you might expect if your hypothesis were true.
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what is chi-square test of 2X2 table,what we choose for yates correction formula
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As the value of k, the degrees of freedom increases, the (chisq - k)/sqrt(2k) approaches the standard normal distribution.
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A Chi-square table is used in a Chi-square test in statistics. A Chi-square test is used to compare observed data with the expected hypothetical data.
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For a chi-square test there is a null hypothesis which describes some distribution for the variable that is being tested. The expected frequency for a particular cell is the number of observations that would be expected in that cell if the null hypothesis were true.
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To test how well observations agree with some expected distribution. The latter is often non-parametric so that tests based on the Gaussian (Normal) distribution are not appropriate.
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The F-distribution is either zero or positive, so there are no negative values for F. This feature of the F-distribution is similar to the chi-square distribution. The F-distribution is skewed to the right. Thus this probability distribution is nonsymmetrical.
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The Pearson chi-square test will tell you how well a given set of observations fit some hypothesised distribution. That is, you have some idea as to what the distribution should be and the test will show how closely (or not) the observations agree with that.
Another use is to test the independence betwen two (or more) matched observation on a set of subjects.
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You seem to be referring to the Pearson chi-square test-of-fit statistic. To do this you need not only the observed values in a frequency table (which you have) but the expected (or theoretical) values for that table.
In practical situations the expected values are obtained by making some educated guess about what distribution the observed values came from, estimating the parameters of that distribution and then using the estimated distribution to obtain the required expected values to calculate the chi-square.
In short, you need more information.
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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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The value specified is usually the maximum value that the test statistic can take for a given level of statistical significance when the null hypothesis is true. This value will depend on the parameter of the chi-square distribution which is also known as its degrees of freedom.
The value specified is usually the maximum value that the test statistic can take for a given level of statistical significance when the null hypothesis is true. This value will depend on the parameter of the chi-square distribution which is also known as its degrees of freedom.
The value specified is usually the maximum value that the test statistic can take for a given level of statistical significance when the null hypothesis is true. This value will depend on the parameter of the chi-square distribution which is also known as its degrees of freedom.
The value specified is usually the maximum value that the test statistic can take for a given level of statistical significance when the null hypothesis is true. This value will depend on the parameter of the chi-square distribution which is also known as its degrees of freedom.
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According to the Central Limit Theorem if the sample size is large enough then the means will tend towards a normal distribution regardless of the distribution of the actual sample.
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A chi-square statistic which is near zero suggests that the observations are exceptionally consistent with the hypothesis.
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A probability sampling method is any method of sampling that utilizes some form of random selection. See: http://www.socialresearchmethods.net/kb/sampprob.php The simple random sample is an assumption when the chi-square distribution is used as the sampling distribution of the calculated variance (s^2). The second assumption is that the particular variable is normally distributed. It may not be in the sample, but it is assumed that the variable is normally distributed in the population. For a very good discussion of the chi-square test, see: http://en.wikipedia.org/wiki/Pearson%27s_chi-square_test
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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.
See link.
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No- skewness parameter declines with increased degrees of freedom. skewness = sqrt(8/k) see link
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If your chi square test has a probability of 0.05 or less it is likely, but not certain, that your hypothesis is not correct.
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