Alwina Hermann
2014-Apr-10 14:49 UTC
[R] Binom.test - hudge difference in p-value for little differences in PD forecast
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 ?
peter dalgaard
2014-Apr-10 20:40 UTC
[R] Binom.test - hudge difference in p-value for little differences in PD forecast
On 10 Apr 2014, at 16:49 , Alwina Hermann <alwina.hermann at 1plusi.de> wrote:> 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?Check the definition of the p value (you need to study the source for that, I suppose). It's the probability of getting an observation with a point probability less than or equal to that of the observed value. The crucial bit is whether the point probability p(1) is less than or bigger than p(3):> dbinom(0:4,101, 0.02403)[1] 0.08572022 0.21316798 0.26242746 0.21322618 0.12862456> dbinom(0:4,101, 0.02402)[1] 0.08580898 0.21329771 0.26247520 0.21317403 0.12853828 I.e., in the first case, X==3 is not counted into the p-value, whereas it is in the second case. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com