# M.B.M.

 1d comment A reference for Pearson's chi-squared testingI have considered Pearson's original paper, but decided against it based on item (ii) in @Glen_b's comment. The dearth of references to the literature describing a chi-squared test is rather surprising that, considering that there is a myriad of chi-squared testing tutorials on the web. I am not a statistician, but is it something considered "common knowledge" in the stats community? (like you don't reference calculus books when claiming that the first derivative of location is the velocity) 1d asked A reference for Pearson's chi-squared testing Dec 15 accepted Trace distance between "weighted" Hermitian matrices Dec 15 asked Trace distance between "weighted" Hermitian matrices Nov 28 accepted How many ways can one "fit" $m$ non-overlapping sub-segments of length $k$ into a segment of length $n$? Nov 27 revised Random variable related to binomialcorrected the renaming of the random variable Nov 27 comment How many ways can one "fit" $m$ non-overlapping sub-segments of length $k$ into a segment of length $n$?Thanks for a nice answer! One follow-up question: you say that "we know how to count solutions of [diophantine equation $E_0+E_1+\ldots+E_m=x$]". Now this indeed looks like a very simple diophantine equation: a sum of $m+1$ non-negative variables and same constant (unity) multiplying each variable. It looks like, in general, there are $\binom{x+t-1}{t-1}$ solutions for $\sum_{i=1}^ta_i=x$. But could you please point me to a source of this statement or explain how one derives it? There must be a textbook that contains this... Nov 27 comment Random variable related to binomialBy @victorsouza's solution to my related question, shouldn't $\Pr(X=x)=\binom{n-x(k-1)}{x}p^x(1-p)^{n-xk}$? Nov 27 comment Random variable related to binomialPosted a related question. Nov 27 asked How many ways can one "fit" $m$ non-overlapping sub-segments of length $k$ into a segment of length $n$? Nov 27 revised Random variable related to binomialcorrected subquestion 2 ($k$ is constant) and renamed random variable to avoid confusion. Nov 27 comment Random variable related to binomial@GrahamKemp To obtain the p.m.f. I think the key is finding the expression for the number of ways one can "fit" $m$ non-overlapping sub-segments of length $k$ into a segment of length $n$. However, combinatorics isn't my strong suite and I can't figure that out. As for Gaussian approximation, for the binomial distribution it arises due to the Central Limit Theorem and the divisibility property of a binomial random variable (i.e. if $X\sim\text{Binomial}(n,p)$ and $Y\sim\text{Binomial}(m,p)$, then $X+Y\sim\text{Binomial}(n+m,p)$). The sums here won't be as nice, but maybe they aren't too bad. Nov 27 asked Random variable related to binomial Nov 26 comment Is there a test for independence in a Bernoulli process?@whuber Thanks! I think I won't apply the continuity correction since the values in my tables are large (on the order of hundreds). Nov 25 comment Is there a test for independence in a Bernoulli process?@whuber Aha! So R applies Yate's correction for continuity because there are small values in your table (like 2 and 3). If the table contained large values, then continuity correction is not necessary. Is that correct? Nov 25 comment Is there a test for independence in a Bernoulli process?@whuber Your test makes sense. The reason I asked my question is because the $\chi^2$ statistic 1.8947 that you calculated with R doesn't match the $\chi^2$ statistic I calculated by hand using the formula on the page you cite: $\frac{(3-5*6/23)^2}{5*6/23}+\frac{(2-5*17/23)^2}{5*17/23}+\frac{(3-18*6/23)^2}{18*6/23}+\frac{(15-18*17/23)^2}{18*17/23}=3.8101$. What am I doing wrong? (I don't use R, though I'm quite familiar with MATLAB.) Nov 13 comment Is there a test for independence in a Bernoulli process?@whuber I am confused by this test. Could you elaborate how your calculate the chi-square test statistic from the table of counts in your example? Nov 4 asked Is there a test of pair-wise independence for a sequence of non-identical Bernoulli random variables? Nov 3 comment Testing for samples being drawn from identical Bernoulli r.v.'sI've given my problem a lot of thought, and I think that what I need is simply testing the null defined in $H_0$ against an alternate that $s_j$'s come from a different distribution. I think that I can use chi-square test for this, but still not completely sure how (though I should be able to figure it out after a night of sleep). One issue is that $p$ is unknown. Since the chi-squared test seems to testing the goodness of fit to a specific binomial, can I estimate $p$ from the data? And should I re-write my original question to reflect my thoughts? Thanks for all your help! Nov 1 comment Testing for samples being drawn from identical Bernoulli r.v.'sHmmm.... I may have made things more complicated with the update. Basically, I am interested in finding out whether a substantial number of subsequences is not identical (I can tolerate a few non-identical subsequences, but not too many). I think your pointer to the chi-square test is what I need -- I gotta figure out how it works...