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I read terms binary data and binomial data in a textbook. What's the difference between them?

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    $\begingroup$ binomial data is an ambiguous word. Sometimes it means "numbers coming from binomial distribution" and sometimes it means =binary data (or dichotomous data). Tim has given a good distinction. $\endgroup$
    – ttnphns
    Commented Jul 29, 2017 at 8:29

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Possibly what is meant is that binary data consists only of 0's and 1's for "failures" and "successes" (notice that what you consider as a "success" is arbitrary) and follows a Bernoulli distribution. Binomial data is data that emerged after observing $n$ Bernoulli trials, i.e. it is a sum of Bernoulli random variables and it consists of non-negative integers, it follows a binomial distribution. I say "possibly" because this should be defined in your textbook and it is the only reference that tells you what the author meant.

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    $\begingroup$ @WhiteGirl what are a and b? If you can consider one of them as "success" (1) and second as "failure" (0) then yes. See stats.stackexchange.com/a/204007/35989 $\endgroup$
    – Tim
    Commented Jul 29, 2017 at 6:55

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