5

Suppose you have a set of data (eg. [a, b, a, a, b, b, etc.]), and you have the suspicion that the set of data follows the binomial distribution.

Your Null Hypothesis is: The probability of success p=0.6.

You run a binomial test on the data with a probability of success p=0.6, and the resulting P-value of the test is 0.55.

Is this result evidence that your data set follows the binomial distribution with probability of success p=0.6? I ask because the thought that the data follows a binomial distribution was not known for certain from the start, but the results of the binomial test seem to confirm it. Or do they?

You could also use a chi-squared test to test if the data fits a binomial distribution with probability of success p=0.6. But if the results of the initial binomial test were as described (p-value = 0.55), is there any reason to do this?

Thanks!

Stuart
  • 51
  • 1
    (1) Where did this null hypothesis come from? (2) By definition, data that can have just two values are Binomial. If you assume the values are independent, the counts (either of "a" or "b") must have a Binomial distribution. There's nothing to test. – whuber Aug 18 '16 at 17:57
  • Right, so allow me to clarify the situation:

    The data is indeed composed of two values (either "a" or "b"), much like an unfair coin flip. However, it is possible that the probability for the fairness of the coin is changing over time. My goal is to use a binomial test to test the data can be explained by a binomial distribution with fixed probability of success p=0.6.

     – Stuart Aug 18 '16 at 21:28
  • It is impossible to test whether the probability changes over time when all you have is a "set of data"! If indeed there is a time associated with each value, or even if they simply are ordered, then you have much more information to work with. You can, for instance, study how the frequencies change from beginning to end. BTW, your question begins to sound similar to the one at http://stats.stackexchange.com/questions/230087--take a look. – whuber Aug 18 '16 at 23:24
  • You still need to test exchangeability of the values to ensure it is a binomial distribution. To do this you would use a runs test. – Ben Mar 25 '18 at 23:11

0 Answers0