Regression Can’t Prove Discrimination


Anybody out there a lawyer, or do you know one, who is involved on the side of angels in these so-called discrimination lawsuits? Have them contact me.

The argument that complainers (usually our government) are using to “prove” discrimination are statistical nonsense. This is easy to prove. Problem is, those who are defending against these charges also appear to believe statistics can prove discrimination, and instead of arguing that it doesn’t, they instead attack the data or say different statistics can prove lack of discrimination. All this is wrong.

Two recent examples: “Obama bullied bank to pay racial settlement without proof: report“.

So CFPB applied the screws to Ally, saying it had “statistical evidence” showing its participating dealers were “marking up” loan prices for blacks and Hispanics vs. whites (by an average of $3 a month). Ally fought back, insisting non-discriminatory factors, such as credit history, down payments, trade-ins, promotions and rate-shopping, explained differences in loan pricing. After conducting a preliminary regression analysis, the bank found these factors alone accounted for at least 70 percent of the “racial disparities” the government was claiming.

Second: “Obama’s new equal pay executive action distorts the definition of equality“.

On Friday, the Obama administration announced executive action that would require companies with 100 employees or more to report to the federal government how much they pay their employees broken down by race, gender, and ethnicity. The proposed regulation is being jointly published by the U.S. Equal Employment Opportunity Commission and the Department of Labor. It is hoped that this transparency will help to root out discrimination and reduce the gender pay gap..

You have a sample of incomes, or loans, or whatever, given or measured on people of two races, J and K. You run a regression with incomes (or whatever) on race, which gives a wee p-value on race. What has been proved?

Nothing. Or, rather, it proves that given this data and the ad hoc, crude assumption of a normal to quantify income, and assuming the spread parameter of this normal for both races is equal, if the central parameter for race (or race difference) was certainly equal to 0, then the probability of seeing a p-value in the test used on the parameter larger than the one seen if the experiment which gave rise to the data could be embedded in an infinite sequence of such experiments is wee.

And that is all that is proved. (That mouth-numbing sentence is the definition of a p-value.)

Does the wee p-value prove that racism exists? No. Does it prove that race J makes more than race K? No. What does the regression say about what caused the observed “discrepancy”? Nothing. Not. One. Thing. As in nothing. Zero. Nada. Nothing.

How do I know this? Because of the Banana Test. Every person in the sample, because they are human, have a mind-boggling number of things we could have measured on them, besides their race. Something like this will therefore almost surely be true: the folks in race J will have eaten over their entire lives at least one banana more than did the folks in K. Therefore in the regression we need not have labeled the groups by the two races, J and K, but instead by the equally true High Bananas and Low Bananas.

It may not be bananas, but number of Lego blocks owned, or has breathed in more air downstream from Cleveland, or number of bubbles blown, or on and on and on and on some more.

It could even be ability to do a task! Like a job for which one receives an income.

Anyway, the wee p-value applies just as equally and logically as to High/Low Bananas as races J/K. It must because the Bananas are just as true of the people in the sample as their race.

“C’mon Briggs, that’s absurd. Eating one more banana can’t cause discrimination in income.”

That’s probably true. But so what? Statistical models are silent on cause.

“No way. Everybody knows race is cause of discrimination. That p-value proved it.”

Everybody knows?

“They do.”

So why run the statistical model to “prove” what you already know? You’re arguing circularly. If statistical models show what-causes-what the wee p-value also proved that eating bananas causes income disparities.

Or, if you already knew race was a cause, then it is a cause regardless what the statistical model showed. If the p-value wasn’t wee, and race is a cause of income “disparity”, then race is still a cause of income “disparity.”

Using statistical models to “prove” discrimination is always cheap, lazy, and wrong. To really prove discrimination you have to do the hard work of investigating each person in the sample and discover what precisely caused his income. If you can’t do that, you can’t prove cause.

There’s much more to say on this dismal and rapidly expanding topic. If you want to defend yourself against spurious charges, don’t use statistics.


  1. This would be more useful as a way to vet a jury, rather than argue in court before a jury either to dumb or simply too intent on awarding some schmuck a big chunk of money.

  2. Gary

    If you want to defend yourself against spurious charges, don’t use statistics.
    Or use them to excess to discredit the idea. Only don’t correlate to ridiculous variables (bananas and legos), but to realistic ones (education level, credit rating) and then blame the government for being responsible and discriminatory itself. You may be wrong logically, but you may be able to deflect the jury’s bias against you. Justice happens by accident in the courtroom, although it’s carefully contrived accident. Do you want to be right, or win?

  3. What about lawsuits against drug companies based on statistics and side effects listed on the package? Those are grounds for permanent disbelief in both the law and science. I guess when the law and truth are never to meet, except by accident, this makes sense. Truth and science are killed, but that’s not important. The law is about—money and power. Not justice. It helps if you understand that greed and power are the motivations.

    Does Hillary have to report how she underpays the women on her staff???

    Defending yourself against spurious charges may be best done by sobbing and claiming victimhood. Of course, if you have any pride, that may be out of the question, but it seems few have enough pride to even care anymore. (Gary—be liked or be right?)

  4. Joy

    I wonder what JH thinks about this.

  5. Dear Dr. Briggs:

    Quite so.

    As I have said before, most social science results are based either on the differences between two halves of a sample of three or “wee p” values – and, either way, the generalizations presented tend to have only an intuitive connection to validity.

    On that basis it seems to me that the best way to turn your work into a best seller is to do a paper debunking several hundred “social studies” publications as statistical nonsense and blaming, not the people writing them, but their teachers. Since the latter are mostly retired this will earn you lots of support among those who care about this stuff – and therefore probably a couple of publishing offers.

  6. I don’t know why the Ally story is just now hitting your radar, but the case was not built on statistics. It was these subjective “mark-ups” by the dealers, always higher for minority borrowers and not based on anything but dealer judgement, that Ally was simply allowing and accepting, that caused the problem. Given the moral vacuum that is right wing thought, I am not surprised you’re okay with this behavior. You would have made an excellent apologist for slavery back in the day, I’m sure.


  7. Andy

    I know nothing of the cases specifically mentioned by Briggs. On the matter of cause as it pertains to the gender pay gap, there was an interesting Freakonomics podcast on the topic in early January. From the episode description: “The gist: discrimination can’t explain why women earn so much less than men. If only it were that easy.”

    It’s an interesting listen (as are many Freakonomics episodes). Link:

  8. Joy

    JMJ, the moral vacuum that is right wing!
    You are funny.

  9. Joy, so you think just marking up colored folks is good and solid moral behavior, huh?


  10. JMJ: Once again showing how little you know about banking—no wait, I know you know better. You’re just parroting the progressive line. I remember ;).

    And “moral vacuum”? Really, progressive despise morals. Why are you complaining the conservatives have none? I would have thought you’d have been ecstatic. (Democrats loved slavery and wanted to preserve it, but you probably know that, too. Is is hard to leave out all the facts so consistantly? Do you practice a lot?)

  11. JMJ and Sheri: The belief that “healthcare is a human right” is a strong indicator that the speaker likes slavery and embraces it. It sounds good, but at the base of it, people are forced to do your bidding for little or no compensation. It is your right to get healthcare… RIGHT? Who provides it?

    The immoral act in the loan programs is providing loans to people who have a poor track record of paying them back. No matter who you are or what you sex, race, creed, or sexual orientation, the indicators that you are a good credit risk are in question NOT your non discriminatable characteristics.

    Certain types or people are definitely better at working the system. You will always be able to find a Trump who can finangle a $B out of a bank, and you will always find an Ally who can’t get a dime without paying a buck for it.

    We do not train people in credit. We try, but we fail mostly.

    I am surrounded by friends and family who have use HARP to their advantage. We hear all of the stories about how abusive the mortgage companies are to their clients. How many stories have you seen discussing the 1% loans people are getting because they go through HARP. I know one gentleman who hasn’t paid his loan in 5 years and is still in his home (this may be finally coming to an end, but 5 years is a long time). Another family has a 2% loan plus a provision that says for every year over the next 6 years that they stay current on their loan, the bank will deduct $5000 from their principle. 3 homosexual families, 1 hispanic family, 2 Caucasians…

    There are scarier stories in the real estate world. People who bought house, refinance the house, extracted the cash, bought another house free and clear and then juggled the books in such a way that the bank owns the one house, but they get to live free and clear in the other. Plot that data and you will find a clear winner… Not the bank.

    The question is not black, white, male, female, gay or hetero, the question is who can present themselves to the screeners in such a way that the screeners say yes. The screeners want to say yes, but there are things that make them say no.

    I once sold a house to a friend. We documented everything the house needed to get fixed so that maybe we could ask for a little more money to fix the problems. Because we wrote down the things that weren’t perfect, the first bank denied the loan. We went to a different bank (where we knew the loan officer). That loan got stalled a little. The appraiser, appraised the house at a value based on one fix. The loan officer suggested that we buy the materials, put them up, take a picture of the “fix” and then take them down.

    Knowing someone helped.

    All that mattered in the end was that the paperwork matched up.

    Matching up the paperwork takes a little skill.

    Knowing what not to report takes a little skill.

    Leaving out the facts often leads to the result you want.

  12. Brad Tittle: Agreed with your comment. I was a credit counselor, helping people learn how to use credit and get out of the holes they dug themselves in to. You are absolutely right—we fail miserably to teach people about money and credit. Credit associations try to remedy this, but it’s not easy. Plus, many people simply don’t care—they want a house or a car or whatever and believe they should be able to get the item, without regard to the actual cost or their ability to replay.

    All: The Community Reinvestment Act (CRA, P.L. 95-128, 91 Stat. 1147, title VIII of the Housing and Community Development Act of 1977, 12 U.S.C. § 2901 et seq.) is a United States federal law designed to encourage commercial banks and savings associations to help meet the needs of borrowers in all segments of their communities, including low- and moderate-income neighborhoods.[1][2][3] Congress passed the Act in 1977 to reduce discriminatory credit practices against low-income neighborhoods, a practice known as redlining.[4][5]

    It is BAD banking practices to loan to people who cannot repay. The Act was designed to pretend that loans are political and not economic. Poor people should get credit even when they can’t pay and it’s kinder to give them a loan and then foreclose on the house or repossess the car than to deny the loan. This is insanity. Pure and simple.

  13. FAH

    I have always preferred the first definition of regression:
    noun: regression; plural noun: regressions

    a return to a former or less developed state.

  14. Joy

    “The moral vacuum that is the right.” Is as sensible as “The left is evil”.

    Morals and lack of them, no matter how many people assert it are not a problem for one political type. First you must define what you mean by moral. Obviously if you don’t agree on the morals then you can always blame your opponent for a lack of morals and feel superior for it. It seems that the left and the right place different value on different moral virtue. When one side proves or shows the rest that their world view is correct then people will agree on who is the mostest holiest.

    I take it you’re not a business man. How do you think insurance companies assess risk? Is that moral? They might have to find certain groups more prone to accidents or ill health and charge them a higher premium.

    Life is not fair. It’s time to stop regulating for fairness in every particular and leave it to the individual.

  15. “The belief that “healthcare is a human right” is a strong indicator that the speaker likes slavery and embraces it” is at once both the sleaziest and dumbest thing I’ve ever read.


  16. JMJ :“The belief that “healthcare is a human right” is a strong indicator that the speaker likes slavery and embraces it” is at once both the sleaziest and dumbest thing I’ve ever read.”

    Still, it’s true even if you think it’s sleazy and dumb.

  17. Ray

    Every time you make a choice you discriminate. The other day I wanted a hamburger and went to Burger King because it’s closer. I discriminated against Wendy’s and MacDonald’s. Do I now have to buy a hamburger from Wendy’s and MacDonald’s to prove I don’t discriminate?

  18. Ray: Only if you are buying from a white-owned Burger King when the Wendy’s or Mac’s owner is not white. If so, you must drive however far it takes to buy from Wendy’s or Mac’s.

  19. Joy

    “healthcare is a human right” is a strong indicator that the speaker likes slavery and embraces it”
    Is rubbish and NOT true.

  20. Anon

    Wifi is a human right.

  21. Joy: When one owns the service, as in the government owning healthcare or demanding it be provided, said individual is holding the recipients as slaves to the system. You may find the word “slave” offensive, but consider that Ben Carson said:
    Dr. Ben Carson, a retired neurosurgeon from Johns Hopkins, author, and recipient of the Presidential Medal of Freedom, said that Obamacare is “in a way” like slavery because it “robs you of your ability to control your own life.”
    When someone other than you controls your life and you must meet their demands in order to get service and that service is what the provider says you will get and not a bit more, you are a slave to that provider. The provider also holds life and death power over you. If the provider says you’re too old and you are draining the system, you won’t recieve the treatment you may want. You will get what the system says you are entitled to.

    Saying “health care is a human right” makes no sense anyway. Health care in rural China was homeopathic remedies, may still be. Some tribes consider witch doctors to be their health care. Others go to psychics and quacks for their health care. So what “heath care” are you talking about being a human right—the psychic, the homeopath, the woman next door who practices witch craft or the hospital and the doctor the state licenses? If the government defines it as “witch doctor” and mandates it as a right, that’s what you are going to get. Whether you want it or not. Anyone in competition can be shut down. Sure, the slavemaster looks benevolent to many, as did the actual slaveholders. But it’s owning a person’s life and robbing him of choices.

    (I realize foreigners do not understand this and often love the freebie of health care handouts, but they are still handouts and you are still controlled. If you wish to live that way and it’s voluntary, then you have chosen your slavery and that is fine.)

  22. JohnK

    Jersey McJones is absolutely CORRECT. Of course there was the famous experiment with auto dealers and car loans, PROVING that car dealers are mean to blacks (and women, by the way), even if the credit tale the buyer tells is the same:
    “Race and Gender Discrimination in Bargaining for a New Car”.

    In the study (no actual purchases were made, though the dealers thought the ‘customers’ were real and were really negotiating), blacks ‘paid’ 3 times the markup of whites.

    To be fair, study authors Ayres and Siegelman did say (strange that Jersey McJones, who has urged us to read the actual paper, somehow forgot to mention this — it’s even right in the abstract) that at least one explanation for this is that car dealers (of all races) figure blacks for suckers, and negotiate accordingly.

    However, the study authors’ other principal explanation for the disparity (which is identical to Jersey McJones’s) runs ever so slightly afoul of Steve Sailer’s logic, which Sailer applies to Eric Holder’s DOJ:

    Logically, Eric Holder’s Justice Department is arguing that car dealers are charging white customers less out of the goodness of their hearts, because, after all, car dealers are famously nice and unmaterialistic.

  23. Joy

    The statement “being born is like being kidnapped and sold into slavery” has more truth about it than this ‘talk’.

    No need to bring in Obamacare. Chinese medicine, our Ben Carson, my choice of slavery, my being a foreigner; MY being a foreigner? You are a foreigner!

    The statement is untrue. It redefines slavery.

    Human rights to quote Mr. Briggs entail human responsibility.

    To tag this onto slavery is to exaggerate wildly and perhaps a better word would be obligation or mandate.
    All tax is slavery by this logic.
    One more thing before the hot chocolate goes cold.
    You won’t hear me defending “human rights” in any sense
    that I can think of.

    Rights are tricky. As for right to health care, it’s too late to think about it. I’m not an NHS defender because it leaves a lot to be desired. Would I leave someone who needed help? No. Does that make me a slave? no.

  24. Yes, car dealers and other such institutions often see “sucker” when women and nonwhites, or geeky guys, walk in. The solution is NOT to have the government tell you you are a stupid woman and need protecting so they will protect you, it’s for women and all people to learn about costs and research purchases. I buy my car tires by myself, cars too—no guy. I have not had prices jacked up nor do the dealers try to sell me junk tires. I have had dealers refuse to honor warranties and had the district office people involved in correcting that “mistake”. “Discrimination” is arguing that women and minorities are too stupid to do things on their own and it’s frankly very, very, very insulting.

  25. Yes, Joy, I am a foreigner when viewed by those outside the USA. It’s what a person not living in the same country as a speaker is called.

    Tax can be slavery. People speak of many many weeks they “work for free” before the government lets them keep any of their money. In the US, it’s around the end of April. Up until that time, every cent paid is taken by a government in one form or another. Working without being paid is generally called slavery.

    Slavery is not just owning people. Other uses of the term:
    “a state of subjection like that of a slave :
    He was kept in slavery by drugs.”

    “submission to a dominating influence”

    “the state or condition of being a slave; a civil relationship whereby one person has absolute power over another and controls his life, liberty, and fortune”

    “1 the subjection of a person to another person, esp in being forced into work
    2 the condition of being subject to some influence or habit
    3 work done in harsh conditions for low pay”

    There are many uses of the word and some to apply to mandated health care and taxation.

  26. Brian H

    I was running a service call in a company restaurant at one of the large energy companies here in OK. On the restaurant wall was a mural, actually a giant enlargement of a photograph, showing about half a dozen oil-soaked roughnecks working the rig. All of them were men. Inside the restaurant, I noticed about half the corporate employees eating lunch were women, dressed to impress in their fashionable business suits. The funny thing is, I didn’t hear a single one of them raising heck about the lack of women in the photograph. But surely, it must be due to discrimination on the part of the company.

  27. Joy

    See line ten of my remark. If you redefine your terms you can make up down and black white.
    Life isn’t fair. It’s not fair for salesmen either.
    As I type there’s women on TV shouting ”what do we want equal pay”.
    A woman in the studio reporting, a woman on the microphone “at the scene of the action!”
    Women are not hard done by and I’m insulted by the implication ad nauseam that they are. They should have on their plaque but not Joy.

    In my profession, women and men are equally paid and always have been because they’re doing the same job. Out in the locum world you can negotiate rates. You work through an agent. I learned from an IT consultant and a businessman father how to do this. Times change. In sales, i.e. business fairness doesn’t come into the equation. It’s all about the deal. “that’s not fair” doesn’t come in unless it is to sustain the business. People buying cars or shoes should remember this.
    I nearly bought a pair of shoes I didn’t want, just admired because of a lovely gentleman in Sax. He was a coloured man. Obviously saw me coming. I wasn’t even there to buy anything. I wasn’t insulted because I understood what he was up to and all credit to him he was a good salesman. Funny though, the place was full of foreigners, I was the only English person there.

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