# Compare one distribution with multiple other distribution

I've a distribution of numeric scores computed using real data ( my reference distribution ). After that I generated 100000 random distributions of numeric scores computed using points picked at random in a space of possible points. So now I want to compare my reference distribtuion with these random distributions and to test whether the reference distribution is significantly different from random distributions.

Thanks

I think you are concerning about level of significance or more precisely p-value. I don't know this answers your question or not, lets try with a hypothetical example.

Let us consider you are to test the probability of success of a coin. For reference distribution you are considering to be unbiased that is the probability of success=$.5$. $\hat{p}=.65$ calculated from the sample

The hypothesis to be tested

$H_0 : p=.5 \\ H_1 : p>.5$

To evaluate the problem you randomly generate 100 or 1000 data points and calculate the $\hat{p}$ under $H_0$. Calculate the p-value as follows

p-value= $P(\hat{p} > .65|H_0)$

If you are familiar with R, try the following codes

#Testing unbiasness of a coin
#H0: p = .5
#H1: p > .5 (p_hat calculated from sample=13/20)
estimate<-13/20
p_hat<-NULL
for(i in 1:5000){
p_hat<-c(p_hat,mean(rbinom(20,1,.5)))
}
pvalue<-mean(p_hat > 13/20)