Final answer:
The biggest contributor to having different p-values can be differences in sample size, variance, effect size, and the degree of deviation from the null hypothesis. Understanding how these factors affect the computation of test statistics is crucial for interpreting p-values correctly.
Step-by-step explanation:
The p-value in statistics represents the probability that the observed data could have occurred under the assumption that the null hypothesis is true. Different p-values can result from a variety of factors, including differences in the sample size, variance, and the effect size.
The computations required for obtaining p-values incorporate these factors into the formula for the test statistic, which is then used to find the p-value from the relevant distribution. In simple terms, when comparing two different p-values, the biggest contributor to the differences could be the underlying differences in these parameters or how extreme the observed results are compared to what we would expect if the null hypothesis were true.
For example, a larger sample size generally provides a smaller p-value if there is a true effect, because larger samples provide more precise estimates of the population parameters.
Similarly, a smaller standard deviation makes it less likely that the sample mean will differ from the population mean by chance, leading to a lower p-value when there is a true effect. Larger effect sizes also contribute to smaller p-values because the observed statistic is more likely to fall in the tails of the distribution if the null hypothesis is false.