A logical analysis of type I and type II errors can be derived by assigning attributes to people and reality. For our purposes, reality contains either a 'T' (claim is true) or an 'F' (claim is false) value. People contain either an 'A' (accept claim) or an 'R' (reject claim) value.
Objective Truth:
T = claim is true
F = claim is false
Subjective Opinion:
A = accept claim
R = reject claim
Type 1 error = accepting a falsehood
= pair F with A
= false positive
= "the positiveness of the test is false"
= being deceived into thinking a false claim is true
Type 2 error = rejecting a truth
= pair T with R
= false negative
= "the negativeness of the test is false"
= being deceived into thinking a true claim is false
In a legal case, there is a claim of a crime.
A crime can have a T/F value and the jury can have a A/R value.
A legal system that favors "innocent until proven guilty" has a bias to reduce Type 1 errors at the cost of accepting Type 2 errors.
For example, a rape case.
TYPE 2 ERROR EXAMPLE - The claim of rape is true. But there is no evidence. So, the jury rejects a truth and fails to punish a guilty man. They created a type 2 error.
TYPE 1 ERROR EXAMPLE - The claim of rape is false. But a crazy ex-girlfriend is mad at her boyfriend for cheating, so she lies and claims he raped her. This is a falsehood. But she is tricky enough to string together former text messages in a way that seems like good evidence of intent to rape. The jury accepts her false claim, convicting an innocent man. They created a type 1 error.
So, the legal system must decide which type of error is more harmful. Legislatures can write into law a standard for how rigorous the evidence must be for convicting someone of a crime. Depending on what level of evidence is required in court will determine which type of error manifests more.
If we reduce the standard for evidence required to accept claims, then we can reduce type 1 errors. If we increase the standard for evidence required to accept claims, then we can reduce type 2 errors. Unfortunately, reducing one type of error increases the other type, so a complex analysis must be done in order to determine the right balance.
*For examples on type 1/2 errors, check this out - Examples of Type I/2 Errors | TranscendentPhilosop
*For a more in-depth discussion on how type 1/2 errors impact punishment, policy, conspiracy theories, and epistemologies, go here - Intent (transcendentphilos.wixsite.com)
Related Links:
The Evolution of Standards of Evidence - The most important boring idea in the universe - Big Think