1
$\begingroup$

I have $100$ coins and I want to test whether they are heterogeneous in their biases.

$H_O$: each coin have the same $p$ for heads
$H_1$: otherwise (heterogeneous $p$'s)

Each coin was tossed $20$ times and so i have the empirical $p$ for each coin ($p_j$) and the empirical $p$ for all $100\times20$ tosses ($p_{all}$).

I estimated for each coin separately, if it is significantly different than $p_{all}$ (using the pdf of a binomial distribution) and got that $\frac{X}{100}$ coins are significantly different from $p_{all}$.

Now I want to estimate the $p$.value of $\frac{X}{100}$, under the null hypothesis that for all coins: $p_j = p_{all}$. How should I do that?

I first thought of using the chi-square $\chi^2$ variance test, but my $p_j$'s are not normally distributed (and got a $p$.value of exactly zero).

$\endgroup$

1 Answer 1

0
$\begingroup$

If all $p$'s are the same, then you have one large sample (size $100 \times 20$) from the same binomial distribution, under the alternative hypothesis, not. So you could estimate the variance and see if that is consistent with a binomial variance of $n p (1-p)$ or is different. You could use a goodness of fit test for the binomial. Or, you could just use logistic regression and see if the model with a 100-levels factor fits better than the null model ...

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.