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Results tagged with chi-squared-test
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user 8402
A test (typically of distribution, independence, or goodness of fit), for the family of distributions use [chi-squared-distribution].
1
vote
Chi square statistic and contingency coefficients
About the contingency coefficient, I want to take the opportunity to leave a remark.
Consider the "theoretical chi-square statistic"
$$
v= \sum_{i,j}\frac{(p_{i,j}-p_ip_j)^2}{p_ip_j}
$$
and the theo …
- 19.7k
33
votes
Accepted
Why is a likelihood-ratio test distributed chi-squared?
As mentioned by @Nick this is a consequence of Wilks' theorem. But note that the test statistic is asymptotically $\chi^2$-distributed, not $\chi^2$-distributed.
I am very impressed by this theorem b …
- 19.7k
7
votes
Accepted
Expectation of inverse non central chi-squared
I can give the expectation but I don't know for the monotonicity.
Let $C \sim \chi^2(d,\theta)$ (where $d$ degrees of freedom, and $\theta$ non-centrality parameter).
If $d > 2$, then
$$
\mathbb{E} …
- 19.7k
12
votes
Accepted
What distribution does Fisher's exact test assume?
In the $2\times 2$ case the distributional assumption is given by two independent binomial random variables $X_1 \sim Bin(n_1, \theta_1)$ and $X_2 \sim Bin(n_2, \theta_2)$. The null hypothesis is the …
- 19.7k