Why does large sample size lead to smaller P-value?
When we increase the sample size, decrease the standard error, or increase the difference between the sample statistic and hypothesized parameter, the p value decreases, thus making it more likely that we reject the null hypothesis.
Does a large test statistic mean a small P-value?
A small p (≤ 0.05), reject the null hypothesis. This is strong evidence that the null hypothesis is invalid. A large p (> 0.05) means the alternate hypothesis is weak, so you do not reject the null.
How does sample size affect the p-value?
Commenting on the P-value of 0.059 obtained in the example, Moore & McCabe say, “Sample size strongly influences the P-value of a test. An effect that fails to be significant at a specified level alpha in a small sample can be significant in a larger sample.
When to use larger alpha or smaller p-value?
Increasing the sample size will tend to result in a smaller P-value only if the null hypothesis is false, which is the point at issue. However, it is possible to justify using a larger alpha when the sample size is small by considering the probabilities of both type I and type II errors.
Is there a problem with a large sample?
There are many advantages to large samples, but researchers using statistical inference must be aware of the p-value problem associated with them. In very large samples, p-values go quickly to zero, and solely relying on p- values can lead the researcher to claim support for results of no practical significance.
What happens when sample size is too big for statistical significance?
People often make the mistaken assumption that statistical significance always implies something practically meaningful. In large samples, it may not. As sample sizes get very large even very tiny differences from the situation specified in the null may become detectable. This is not a failure of the test, that’s how it’s supposed to work!