[R] Binom.test - hudge difference in p-value for little differences in PD forecast

[Alwina Hermann]

Dear R team,
 
I'm not sure if I use the right distribution list, but I hope in case if
not, you will forward it to the reference person.
 
Following problem occured:
I used R to calculate the p-value for the two sided binomial test (exact -
Pearson).
For a very little difference for my forecast I get a very big difference in
my p-value
 
 >  binom.test(1,101, 0.02402)

        Exact binomial test

data:  1 and 101
number of successes = 1, number of trials = 101, p-value = 0.7375
alternative hypothesis: true probability of success is not equal to 0.02402
95 percent confidence interval:
0.00025064 0.05393235
sample estimates:
probability of success 
            0.00990099

> binom.test(1,101, 0.02403)

        Exact binomial test

data:  1 and 101
number of successes = 1, number of trials = 101, p-value = 0.5243
alternative hypothesis: true probability of success is not equal to 0.02403
95 percent confidence interval:
0.00025064 0.05393235
sample estimates:
probability of success 
            0.00990099


Can you please explain where this huge difference come from?
Which mathematical explanation is given for this topic?

Please help.

I hope for your soon feedback.

Kind Regards,
Alwina