All other conditions being equal, does a z or t value with larger magnitude have a larger or smaller corresponding P- value?

To determine whether a z or t value with a larger magnitude has a larger or smaller corresponding p-value, we need to understand the concept of statistical significance and how it is calculated.

A p-value is a measure of the evidence against a null hypothesis in a statistical test. It represents the probability of observing a test statistic as extreme as, or more extreme than, the one computed from your data, assuming the null hypothesis is true.

In general, when comparing two test statistics with larger magnitudes, the test statistic with the larger magnitude will have a smaller corresponding p-value. A smaller p-value indicates stronger evidence against the null hypothesis, suggesting that the observed result is unlikely to have occurred by chance.

For example, let's say we have two groups of data and we want to compare their means using a t-test. If one group has a larger mean difference from the null hypothesis (i.e., a higher t-value), then that group will have a smaller p-value. Similarly, in a z-test, a larger difference from the null hypothesis (i.e., a higher z-value) will correspond to a smaller p-value.

To calculate the p-value, you would need the test statistic (either z or t) and the degrees of freedom associated with the test. The p-value can be obtained from a statistical table or through software packages that perform hypothesis testing.

It's important to note that the p-value alone does not determine the practical significance of the result or the importance of the effect. It only provides evidence regarding the statistical significance of the observed data.