Type I and Type II Errors of the First Amendment
How a Simple Variable, Such as the Definition of Religion Can Radically Change Our Lives
Arnold Kling’s post from this morning was so good that I decided to write a brief summary of it - painted somewhat heavily with my own signature. In that post, he teaches us to use and avoid certain types of statistical jargon. For example to:
Use Type I and Type II error terminology in decision-making that involves trade-offs;
Avoid the inverse probability faux paus;
Avoid “statistically-significant dogmatism.”
Lesson #1: Trade-offs Expressed in Terms of Type I and Type II Errors
Arnold Kling writes
Economist Thomas Sowell is known for saying “There are no solutions, only trade-offs.” That should be known as Sowell’s Law.
When we are faced with a set of binary decisions of a given sort, Sowell’s Law can be described as the trade-off between making two types of mistakes. In classical statistics, a Type I error means claiming that the evidence for a hypothesis is strong when it isn’t. And a Type II error means failing to recognize that the evidence for a hypothesis actually is strong.
But Type I and Type II errors can be used to describe many more situations. For instance, in a court case, the jury must find the defendant guilty or not. One mistake would be to convict an innocent defendant. Call that a Type I error. The opposite mistake would be to fail to convict a guilty defendant. That is a Type II error. By setting a standard of “innocent unless guilty beyond a reasonable doubt,” our legal tradition is saying that we should try to minimize Type I errors, at the risk of committing Type II errors.
You can apply this jargon to the decision to get married. Maybe young people today want to be really sure before they get married. They want to avoid Type I error of getting married and regretting it. But they will make more Type II errors, in which they postpone marriage and regret that.
In mortgage lending, a Type I error is approving a loan that subsequently defaults. A Type II error is failing to approve a loan that would have worked out.
In the early 2000s, politicians accused lenders of making too many Type II errors. They put pressure on lenders to approve more borrowers, including borrowers with poor credit histories. There was a bipartisan consensus, reinforced by industry lobbyists, that there was an “underserved” market for buying homes on credit. Under intense pressure, lenders loosened their standards.
Then the housing market tanked, defaults skyrocketed, and the politicians turned around and blamed the lenders for making Type I errors. Accusations of “predatory lending” flew. So after the crisis, pressured by the political scapegoating and the Dodd-Frank legislation that passed in response to the 2008 crisis, lenders adopted very strict standards.
In a situation with Type I and Type II errors, if you want to make fewer errors of one type, your decision criteria will cause you to make more errors of the other type. The closer you drive the instances of one type of error toward zero, the more you will suffer many errors of the other type.
If you want perfectly safe streets, then police will probably have to stop and frisk some innocent people. If you want the police to never harass an innocent person, then street crime will become more prevalent.
If you understand the trade-off between Type I and Type II errors, then you have a pretty decent grasp of Sowell’s Law.
Let’s summarize that.
Type I Error Definition: claiming that the evidence for a hypothesis is strong when it isn’t
Type I Error Examples:
Convicting an innocent person
Marrying the wrong person
Approving a loan that defaults
(Police) stopping and frisking innocent people
Type II Error Definition: failing to recognize that the evidence for a hypothesis actually is strong
Type II Error Examples:
Failure to convict a guilty person
Passing up on good marriage opportunities
Failing to approve a loan that would have worked out
(Police) never harassing an innocent person
Arnold Kling’s Conclusion
Sowell’s Law - If you want to make fewer errors of one type, your decision criteria will cause you to make more errors of the other type.
Trim to Truth Signature Addition to Lesson #1
I’ve added another example. Let’s call it Type I and Type II Errors of the First Amendment.
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof;
Type I Error of the First Amendment:
Defining religion to include all acts of learning, acting, believing, and expressing including supernatural, non-supernatural, secular and non-secular
Defining religion in this way (broadly) as: “all the ways that we learn, act, believe and express ourselves” leads to the elimination of all state-funded religions. This sounds like a good thing right?
Type II Error of the First Amendment
Defining religion as supernatural religions only (excluding both non-supernatural and secular religions)
Defining in this way religion (narrowly) as: “supernatural-only” leads to a proliferation of state-funded religions. See below for examples of state-funded religions. This supernatural-only definition of religion is one that defines religion as “actions, beliefs, and expressions that utilize supernatural explanations of phenomenon.”
Type II Errors of the First Amendment have damaging implications. For example, here are examples of state-funded religions.
Failure to define secular religion as religion leads to state-funded secular religions
Failure to define secular dogma as religion leads to state-funded secular dogmas
Failure to define censorship as religion leads to state-funded censorship
Failure to define propaganda as religion leads to state-funded propaganda
Failure to define education as religion leads to state-funded education
Failure to define DEI as religion leads to state-funded DEI
Failure to define climate alarmism as religion leads to state-funded climate alarmism
Failure to define racism as religion leads to state-funded racism (e.g. Jim Crow and the Fugitive Slave Acts)
Failure to define discrimination as religion leads to state-funded discrimination (e.g., DEI, Jim Crow, Japanese-American Internment, Chinese Exclusion Act)
Failure to define social justice as religion leads to state-funded social justice (e.g. DEI, affirmative action)
Failure to define paternalism as religion leads to state-funded paternalism (e.g. Obamacare, Social Security, and Medicare)
Failure to define socialism as religion leads to state-funded socialism
Failure to define anti-communism as religion leads to state-funded anti-communism (e.g. McCarthyism)
Failure to define science as religion leads to state-funded science, propaganda and censorship (e.g., Anthony Fauci, Wuhan Lab cover-up, and climate alarmism)
Failure to define The Church of Jesus Christ of Latter-Day Saints as a legitimate religion leads to state-funded persecution of Latter-Day Saints (see here)
What others can you think of?
A supernatural-only definition of religion is one that views religion only as those ways learning, acting, believing and viewing the world that utilize supernatural explanations of phenomenon (God, Satan, magic, or any explanations that defy the laws of physics). In the context of the First Amendment this is a big mistake.
Type I Errors of the First Amendment
An all-encompassing definition of religion that includes all the ways that we learn, act, believe and express ourselves might lead to the elimination of all state-funded religions. What might this look like? It might cure us of many ills, but it might also lead to more:
Child abuse;
DUI drivers,
Drug addicted parents;
Religious fanaticism;
Suicide cults;
Loss of national identity;
Lack of patriotism;
Weak national defense.
How plausible are these Type I consequences? Are these problems avoidable through character education and justice? I would say so.
Lesson #2 Summary: Understanding Inverse Probability
(a) The turnstile jumpers are almost all black.
(b) Almost all black young men jump over the turnstile.
Conclusion - When you tell your audience (a) is realistic, but people hear (b) and call you a racist, don’t say Arnold Kling didn’t warn you.
Lesson #3 Summary: Statistically-Significant Dogmatism
When someone says that a cancer drug produced a statistically significant result, what you want it to mean is that it had a big effect in shrinking a tumor and that the method for testing and measuring that effect was reliable. But “statistically significant” does not mean that.
When Scott Alexander or Emily Oster looks into a question, they look at all of the relevant studies they can find. They decide which studies employed the most credible methods. They look for the consistency, or lack thereof, in the results of different studies. Then they give you their judgment. I highly respect that sort of approach.