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For a Bernoulli variable $Ber(p)$, $p$ is the mean and sd $\sqrt{p(1-p)}$ If you have i.i.d. Bernoulli variable $X_1, \cdots, X_n \sim Ber(p)$, you can sum them up: the random variable $X_1 + \cdots + X_n$ has mean $np$ and sd $\sqrt{np(1-p)}$ (which I suppose is what you heard) - this is the binomial distribution $B(n, p)$. But your data your showed very ...


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With enough data, the tests you mention are all the same. At sample sizes this large, the binomial is very well approximated by a normal distribution with the same mean and variance. But more to your question, you could use any of those tests. Here are some results in R. results = c(5000, 500000, 6000, 499000) m = matrix(results, nrow = 2) #Chisquare ...


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Don't use thresholds in assessing models. (See here for some of the problems with them.) Instead, find out which of your models yield well-calibrated and sharp probabilistic predictions, using proper scoring rules. We have a scoring-rules tag. (Consider combining models, this often improves predictions.) Once you have a well-performing model, consider using ...


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To quote a source on this topic of correlation relating to dummy variables: A popular approach for dichotomous variables (i.e. variables with only two categories) is built on the chi-squared distribution. We are not interested in testing the statistical significance however, we are more interested in effect size and specifically in the strength of ...


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Random thoughts: In the following I'm assuming that your logistic regression provides as good enough fit that $\hat{p}$ from the logistic regression is a good approximation of the true success probability $p$. (1) Definitely $Z = (Y-p)/\sqrt{np(1-p)}$ won't converge in distribution to a normal distribution, because $Y$ is a single, Bernoulli random ...


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