Why does a larger sample size produce a smaller p-value?

[Alycat]

Hi, I need help with this problem...

The obtained p value for a correlation analysis is .036, for a sample size is 50. If the analysis had been undertaken with n = 90, and the same sample correlation value was again observed, what would be the relative size of the p value for the second hypothesis test compared to the original p value obtained when n = 50?

I think: the larger sample size would be more statistically significant and thus have a p-value which was relatively smaller

But how can I explain why this is?

Any help would be most appreciated!

 

[Englund]

The standard error converge to zero in probability as n ---> infinity.

 

[Alycat]

Thanks Englund. This is what I wrote... does it sound right? Would you add anything to it?:

Larger sample sizes result in smaller standard errors due to the following relationship: standard error = standard deviation / the square root of n. That is, as n increases, the standard error of the sample statistic gets smaller. And a smaller standard error means that the width of the confidence interval will be narrower for the same critical test statistic value used in calculating a confidence interval. As the p-value is a function of the standard error, the smaller standard error (all other things constant) means a smaller p-value. In summary, larger sample sizes lead to more significant p-values.

Thanks for your help!