Contents
What is the relationship between p-value and probability?
A p-value is a measure of the probability that an observed difference could have occurred just by random chance. The lower the p-value, the greater the statistical significance of the observed difference. P-value can be used as an alternative to or in addition to pre-selected confidence levels for hypothesis testing.
What does a p-value tell us about the results of a statistical analysis?
A p-value, or probability value, is a number describing how likely it is that your data would have occurred by random chance (i.e. that the null hypothesis is true). A p-value higher than 0.05 (> 0.05) is not statistically significant and indicates strong evidence for the null hypothesis.
What does P value 0.1 mean?
The significance level for a given hypothesis test is a value for which a P-value less than or equal to is considered statistically significant. Typical values for are 0.1, 0.05, and 0.01. These values correspond to the probability of observing such an extreme value by chance.
What is a posterior p value in Bayesian theory?
In Gelmans words: “From a Bayesian context, a posterior p-value is the probability, given the data, that a future observation is more extreme (as measured by some test variable) than the data”
What is the posterior value of a probability statement?
posterior predictive p-value is such a probability statement, conditional on the model and data, about what might be expected in future replications. The p-value is to the u-value as the posterior interval is to the con dence
How is the prior predictive p-value defined?
Then, one can define the prior predictive p-value or tail area under the predictive distribution through the expression is the prior predictive density. Notice that this approach may be influenced by the choice of the prior (for an example, see pg.180 of [1]). For this reason, the posterior predictive p-value was introduced.
What are the two schools of statistical inference?
We have now learned about two schools of statistical inference: Bayesian and frequentist. Both approaches allow one to evaluate evidence about competing hypotheses. In these notes we will review and compare the two approaches, starting from Bayes’ formula. 3 Bayes’ formula as touchstone