![]() ![]() ![]() ![]() For a hypothesis test, it guarantees protection from type I error at the nominal significance level. A conservative interval guarantees that the actual coverage level is at least as large as the nominal confidence level, though it can be much larger. When using the true distribution, due to the discreteness of the distribution, the p-value and confidence intervals are conservative. For small sample sizes or sparse data, the exact and asymptotic p-values can be quite different and can lead to different conclusions about the hypothesis of interest. For large sample sizes, the exact and asymptotic p-values are very similar. A p-value calculated using the true distribution is called an exact p-value. Approximations assume the sample size is large enough so that the test statistic converges to an appropriate limiting normal orĪ p-value that is calculated using an approximation to the true distribution is called an asymptotic p-value. Instead, many statistical tests use an approximation to the true distribution. It can be computationally difficult and time intensive even for a powerful computer. However, hand calculation of the true probability distributions of many test statistics is too tedious except for small samples. Many test statistics follow a discrete probability distribution. Asymptotic p-values are useful for large sample sizes when the calculation of an exact p-value is too computer-intensive. ![]()
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