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The concept of predictive power, the power of a scientific theory to generate testable predictions, differs from explanatory power and descriptive power (where phenomena that are already known are retrospectively explained or described by a given theory) in that it allows a prospective test of theoretical understanding.
Both frequentist power and Bayesian power use statistical significance as the success criterion. However, statistical significance is often not enough to define success. To address this issue, the power concept can be extended to the concept of predictive probability of success (PPOS).
The positive predictive value (PPV), or precision, is defined as = + = where a "true positive" is the event that the test makes a positive prediction, and the subject has a positive result under the gold standard, and a "false positive" is the event that the test makes a positive prediction, and the subject has a negative result under the gold standard.
Predictive power is a Bayesian power. A parameter in Bayesian setting is a random variable. Predictive power is a function of a parameter(s), therefore predictive power is also a variable. Both conditional power and predictive power use statistical significance as success criteria. However statistical significance is often not enough to define ...
Predictive power can also be calculated in a frequentist setting. No matter how it is calculated, predictive power is a random variable since it is a conditional probability conditioned on randomly observed data. Both conditional power and predictive power use statistical significance as the success criterion. However, statistical significance ...
Although the original C method has negative predictive power, simply reversing its decisions leads to a new predictive method C′ which has positive predictive power. When the C method predicts p or n, the C′ method would predict n or p, respectively. In this manner, the C′ test would perform the best. The closer a result from a ...
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To use regressions for prediction or to infer causal relationships, respectively, a researcher must carefully justify why existing relationships have predictive power for a new context or why a relationship between two variables has a causal interpretation.