The phrase "a true hypothesis" is correct and usable in written English.
It can be used when discussing scientific or logical propositions that are considered valid or accurate based on evidence or reasoning.
Example: "After conducting several experiments, we concluded that our initial assumption was indeed a true hypothesis."
Alternatives: "a valid hypothesis" or "an accurate hypothesis".
We can also mistake a true hypothesis for a mere opportunity.
The result of this will be that a true hypothesis will be rejected.
Thus, false competitors of a true hypothesis will effectively be eliminated by increasing evidence.
Analogous considerations are presented for the power function when testing a hypothesis concerning the expectation both under the assumption of a true hypothesis and under a local alternative.
For Bayesians, the Likelihood Ratio Convergence Theorem further implies the likely convergence to agreement near 0 of the posterior probabilities of false competitors of a true hypothesis.
Introducing the distinction between the error of rejecting a true hypothesis (type I error) and accepting a false hypothesis (type II error), they argued that it depends on the consequences of the error to decide whether it is more important to avoid rejecting a true hypothesis or accepting a false one.
In multiple testing, FWER refers to the probability of rejection of any true hypothesis.
Tests gave error-prone results, i.e. occasionally failed to provide a positive result for the true hypothesis (false negative) or provided positive evidence for a false hypothesis (false positive).
So, it does not show that these converging support functions converge on strong support for the true hypothesis, as a CoA result is supposed to do.
We assess the relation between the profit and the information received by a participant based on two quantities, namely the support that a test provides for the true hypothesis, and its informativity.
This threshold is appropriate for samples' size in the range of this study (22 units) because of the risk of rejecting the true hypothesis with a p-value threshold of 5% [ 40, 41].
