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Statistical significance is a very important concept to understand when reading about scientific studies — and it’s also very likely to be defined incorrectly in news reports about scientific studies. For example, here is a Cancer Research UK “science blog” writing about a trial that investigated whether taking aspirin can lower the risk of cancer:
The researchers found that [those participants who were overweight and obese] had an even greater increase in bowel cancer risk, compared to those in the trial who were a healthy weight.
But among different sub-groups of people, some of these results weren’t ‘statistically significant’ (meaning there’s uncertainty over how valid they are)…
And here’s The News & Observer writing about the failed test of a new antiviral drug:
Shares of Chimerix dropped 81 percent and hit an all-time low Monday after the Durham drug developer announced that patients who took the company’s antiviral drug in a clinical trial died at higher rates than those who took a placebo…
Chimerix said the increased mortality rate among patients who took brincidofovir was not statistically significant, meaning that the deaths were not caused by the medication.
And here’s The Philadelphia Inquirer writing about the effect of delays in breast cancer treatment:
The risk of death increased by 9 percent or 10 percent … for patients with stage I and stage II breast cancers for each added 30-day interval, the Fox Chase researchers found. In practice, the increased risk is small, because the chance of death at stage I or II is relatively low. But the difference is statistically significant, meaning it did not occur by chance, researchers found.
All those definitions of statistical significance (or insignificance) are significantly wrong. A result is considered statistically significant if the probability of it being “due to chance” is below some predetermined level, usually 5%. (Wikipedia has a more formal definition.) So even if a result is considered statistically significant, there’s still a probability of up to 5% that the effect measured was actually due to chance and we can’t learn anything from it. (Conversely, even if a result is deemed “insignificant”, there’s still a probability of up to 95% that it was not due to chance — those patients might have been killed by that antiviral drug after all.)
This means we should not put too much confidence in any single scientific result. In fact, out of the thousands of hypotheses published each year supported by “significant” results, we should expect that some will turn out to be wrong — science is hard. That’s why it’s so important to replicate scientific experiments multiple times, and to perform meta-analyses combining the results of many individual studies. Science is hard, and reporters who mislead their readers in the name of simplicity — or a catchy headline — can cause real damage.
Keep that in mind next time you read that green jelly beans cause acne.
Don’t let Scalia tell you there’s nothing wrong January 5, 2016Posted by Ezra Resnick in Democracy, Politics, Religion.
Tags: Antonin Scalia
Supreme Court Justice Antonin Scalia recently graced some students in Louisiana with his learned opinions.
He told the audience at Archbishop Rummel High School that there is “no place” in the country’s constitutional traditions for the idea that the state must be neutral between religion and its absence.
“To tell you the truth there is no place for that in our constitutional tradition. Where did that come from?” he said. “To be sure, you can’t favor one denomination over another but can’t favor religion over non-religion?”
I wonder, what are Scalia’s criteria for a religion to be eligible for favored status? Would he include Scientologists? Satanists? Followers of Zeus and Ra? Is any belief too crazy, or is it sufficient to believe in something for which there is no evidence?
He also said there is “nothing wrong” with the idea of presidents and others invoking God in speeches. He said God has been good to America because Americans have honored him…
“God has been very good to us. That we won the revolution was extraordinary. The Battle of Midway was extraordinary. I think one of the reasons God has been good to us is that we have done him honor. Unlike the other countries of the world that do not even invoke his name we do him honor. In presidential addresses, in Thanksgiving proclamations and in many other ways,” Scalia said.
“There is nothing wrong with that and do not let anybody tell you that there is anything wrong with that,” he added.
I’m afraid there are several things wrong with that. If we actually look at the other countries of the world, we find that highly nonreligious societies like Norway, Australia, and the Netherlands rank higher than the U.S. on indexes like life expectancy and education; while the poorest countries tend to be the most religious. And you know who else believed they had God on their side? The Romans. And the Mayans. And the Egyptians. For a while, anyway.
It turns out that societies do better when they base their policies on reason and evidence rather than magical thinking and dogmatic adherence to tradition. After all, one person’s religion is just another’s superstition. Do we really want our leaders invoking the magical, and our laws favoring the superstitious? Even Scalia ought to be able to see what’s wrong with that.
(via Why Evolution is True)
How to solve a hard problem December 25, 2015Posted by Ezra Resnick in Computer science, Humor.
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To solve a hard problem, first break it down into pieces. Then pack those pieces into bins, using as few bins as possible. You’re going to want a little help from your friends, so consult your social network and find the largest clique of people who all know each other. Visit the home of each of those friends (making sure to use the shortest possible overall route), and give each friend a subset of the bins whose overall number of pieces equals that friend’s age. Return home, and wait for your friends to send you their results. (While you’re waiting, you can perfect your game of Candy Crush.) Then find the longest sub-sequence common to all your friends’ results — that sub-sequence is (almost surely) your solution!
Note: If the above procedure is taking too long to terminate, try breaking your problem into more pieces; making more friends; or consulting an oracle.
Backlash December 23, 2015Posted by Ezra Resnick in Politics.
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- “Donald Trump Faces Immigration Backlash from Tech-Billionaires” (December 1)
- “Leaders Warn Against Stereotyping and Backlash After San Bernardino Shooting” (December 3)
- “‘Thoughts and Prayers’ Backlash After San Bernardino Shooting” (December 3)
- “Coke pulls offensive Christmas ad but faces backlash from indigenous rights group” (December 5)
- “Dems Fear Backlash Over Obama’s ‘Weak and Unclear’ Plan to Defeat ISIS” (December 8)
- “Donald Trump’s Anti-Muslim Demand Sparks Sharp Backlash” (December 9)
- “Backlash Over Santa ‘Ban’ at NYC School a Misunderstanding” (December 14)
- “Virginia county closes schools as Islam homework draws backlash” (December 18)
- “Wisconsin mayor faces backlash for calling Obama a Muslim” (December 22)
- “Obama administration’s proposed insurance reforms incite industry backlash” (December 22)
- “Family faces backlash for controversial Christmas photo” (December 22)
- “Clinton’s Hispanic outreach sparks online backlash” (December 22)
- “Trump Faces Backlash Over Sexually Derogatory Remark About Hillary” (December 23)
- “Michael Sam Tweets Major ‘Star Wars’ Spoiler, Draws Fiery Backlash From Followers” (December 19)
Insignificant December 5, 2015Posted by Ezra Resnick in Belief, Reason.
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“First you state your null hypothesis, which is your default position in the absence of any evidence, and your significance level, which is the maximum probability you’re willing to accept for rejecting the null hypothesis when it’s actually true. Then you perform your observations, calculate the p-value (the probability of obtaining a result at least as extreme as what was observed if the null hypothesis were true), and reject the null hypothesis if and only if the p-value is below the significance level.”
“Got it. Here goes: My significance level is zero, and my null hypothesis is—”
“Wait a minute: a significance level of zero means there’s no evidence that could ever convince you to abandon the null hypothesis.”
“Oh, is that bad? All right, then: My significance level is five percent…”
“…and my null hypothesis is that I will not change my significance level retroactively based on the outcome of the observations.”
“Hmm, let me test that… OK, the results are in, and they are statistically significant: p-value is two percent. You should reject the null hypothesis.”
“No problem — but I’m afraid that means I’ll be changing my significance level to one percent, making your observations insignificant. So my null hypothesis has been proved true after all!”
“The null hypothesis is never proved, it can merely fail to be rejected. And anyway, if your null hypothesis were true, wouldn’t that mean you should not have changed your significance level? Actually — never mind; this is a waste of time. Do you even care whether your belief is based on evidence?”
“Absence of evidence is not evidence of absence. Just because you can’t measure something doesn’t mean it’s not there.”
“Excuse me, but I must be going now: evidence has just come in forcing me to reject my null hypothesis.”
“What hypothesis is that?”
“That you’re worth talking to…”
In God’s name October 24, 2015Posted by Ezra Resnick in Belief, Religion.
Tags: Jonathan Sacks
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Jonathan Sacks, former chief rabbi of the UK, has written a book named Not in God’s Name (excerpted in The Wall Street Journal), in which he provides his recipe for defeating religious violence:
Yes, there are passages in the sacred scriptures of each of the Abrahamic monotheisms that, interpreted literally, can lead to hatred, cruelty and war. But Judaism, Christianity and Islam all contain interpretive traditions that in the past have read them in the larger context of coexistence, respect for difference and the pursuit of peace, and can do so today. Fundamentalism—text without context, and application without interpretation—is not faith but an aberration of faith…
We must raise a generation of young Jews, Christians, Muslims and others to know that it is not piety but sacrilege to kill in the name of the God of life, hate in the name of the God of love, wage war in the name of the God of peace, and practice cruelty in the name of the God of compassion.
Now is the time for us to say what we have failed to say in the past: We are all the children of Abraham. We are precious in the sight of God. We are blessed. And to be blessed, no one has to be cursed. God’s love does not work that way. God is calling us to let go of hate and the preaching of hate, and to live at last as brothers and sisters, true to our faith and a blessing to others regardless of their faith, honoring God’s name by honoring his image, humankind.
Aw, that’s nice. Though I can’t help but wonder: How does Sacks know all that? How does he know God’s love works one way and not another? How does he know what God is calling us to do? I realize Sacks is a member of the House of Lords, but he admits that a literal reading of the sacred scriptures supports the fundamentalists’ interpretation of God’s will rather than his own. While I’m glad Sacks has found a way to cherry-pick and “reinterpret” the texts such that he doesn’t feel obliged to kill anyone, wouldn’t the fundamentalists be justified in judging his faith an aberration?
The truth is that Sacks is committing the same fundamental error as the fundamentalists: speaking in God’s name, identifying life’s meaning with obedience to God’s commandments, and glorifying faith. That is the real cause of religious violence — and in order to defeat it, we must raise a generation of young people to be wary of claims to knowledge not supported by evidence; to value life, love, peace and compassion for rational reasons, not because “God said so”; and to understand that no scripture is sacred and that faith is not a virtue but a vice.
A widespread and insensitive mentality September 6, 2015Posted by Ezra Resnick in Ethics, Religion.
Tags: Pope Francis
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Listen up, ladies — an important message from the Pope:
One of the serious problems of our time is clearly the changed relationship with respect to life. A widespread and insensitive mentality has led to the loss of the proper personal and social sensitivity to welcome new life. The tragedy of abortion is experienced by some with a superficial awareness, as if not realizing the extreme harm that such an act entails.
That’s funny, because it seems to me that there is a widespread and insensitive mentality and a lack of proper sensitivity regarding the health and autonomy of women — one example of which is the perverse characterization of abortion as a “tragedy” that entails “extreme harm”.
Many others, on the other hand, although experiencing this moment as a defeat, believe that they have no other option. I think in particular of all the women who have resorted to abortion. I am well aware of the pressure that has led them to this decision. I know that it is an existential and moral ordeal. I have met so many women who bear in their heart the scar of this agonizing and painful decision.
That’s interesting, because a recent study found that 99% of women who’ve had abortions reported that it was the right decision for them (up to three years later), with both negative and positive emotions about the abortion declining over time. The study also found that higher perceived community abortion stigma was associated with more negative emotions. So I wonder whether the Pope realizes that it’s his callous teachings that are exacerbating the agony and pain of so many women? But then, it’s not the reduction of actual harm to women that is the Pope’s main concern, is it.
The forgiveness of God cannot be denied to one who has repented, especially when that person approaches the Sacrament of Confession with a sincere heart in order to obtain reconciliation with the Father. For this reason too, I have decided, notwithstanding anything to the contrary, to concede to all priests for the Jubilee Year the discretion to absolve of the sin of abortion those who have procured it and who, with contrite heart, seek forgiveness for it. May priests fulfil this great task by expressing words of genuine welcome combined with a reflection that explains the gravity of the sin committed, besides indicating a path of authentic conversion by which to obtain the true and generous forgiveness of the Father who renews all with his presence.
If anyone tells you you’ve committed a grave sin and then offers to forgive you for it if you repent, turn around and walk away.
Software engineering principles exemplified with cooking recipes August 15, 2015Posted by Ezra Resnick in Computer science.
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Don’t Repeat Yourself
Add an inch or two of water to a pot. Insert a colander above the water, and bring the water to a boil. Add broccoli in bite-sized pieces. Cover the pot and cook for a few minutes, until tender.
Add an inch or two of water to a pot. Insert a colander above the water, and bring the water to a boil. Add cauliflower in bite-sized pieces. Cover the pot and cook for a few minutes, until tender.
Steam broccoli and cauliflower. (See sidebar on how to steam vegetables.)
Modularity (Low Coupling)
Push the “Start” button on the left side of the oven, then push the “plus” button until the temperature display reads 350. Wait 15 minutes. Put cookies in the oven for 27.5 minutes.
Preheat oven to 350 degrees (see oven’s instruction manual). Bake cookies for 20-30 minutes, until firm and brown.
Milk a cow, and let the fresh milk rest in a cool place for 24 hours. Skim the layer of cream off the surface and pour into a container. Shake the container for 30 minutes. Filter through a gauze to eliminate the liquid. Put into a mold and chill.
Buy some butter at the store.
Easy issues July 16, 2015Posted by Ezra Resnick in Ethics, Religion.
Tags: Avi Weiss
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Rabbi Avi Weiss supports the U.S. Supreme Court’s ruling guaranteeing same-sex couples the right to marry — even though it “runs contrary” to his religious beliefs — due to his commitment to the separation of church and state. But he tries to have his wedding cake and eat it too:
Still, as an Orthodox Jew, I submit to the Biblical prohibition. But as an open Orthodox rabbi, I refuse to reject the person who seeks to lead a life of same sex love. If I welcome with open arms those who do not observe Sabbath, Kashrut or family purity laws, I must welcome, even more so, homosexual Jews, as they are born with their orientation.
First of all, let’s not forget exactly what the Biblical guidance on this matter is:
And if a man lie with mankind, as with womankind, both of them have committed abomination: they shall surely be put to death; their blood shall be upon them.
Weiss tries to downplay the magnitude of the Biblical condemnation by quibbling over the accuracy of “abomination” as a translation for the Hebrew to’evah — without quoting the entire verse or mentioning the death penalty it prescribes. In any case, he accepts the Bible’s denunciation of homosexuals, yet he still wants credit for “welcoming” them. How would Weiss feel about, say, a Christian claiming to “welcome” Jews while simultaneously maintaining that the Jewish people are collectively responsible for the death of Jesus?
Weiss is clearly a good person trying to do the right thing, but his religion is getting in the way, creating conflict and strife where there need be none:
Are these easy issues? No.
Certainly, the role of homosexuality in the Orthodox community is something that must be deeply considered, discussed and evaluated. We must bring the plurality of voices to the table as complex dynamics will require thoughtful, sensitive and wise conversation.
There are many difficult problems in this world, but homosexuality is not one of them. Indeed, Weiss never even attempts to make any kind of argument against it. He concedes that homosexuals are born with their orientation, yet he still considers them sinners — because the Bible says so. One can only hope that the outcome of all that thoughtful, sensitive and wise conversation will be the long-overdue realization that the Bible was wrong about this issue (as about so many others), and that rational people should not be submitting to dogma. There are many difficult problems in this world, so we mustn’t get hung up on the easy ones.
Scientists say July 6, 2015Posted by Ezra Resnick in Science.
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- “Scientists Say ‘Life After Death’ May Be Possible, In A Way” [Huffington Post]
- “Scientists Say They Can Recreate Living Dinosaurs Within the Next 5 Years” [Entrepreneur]
- “Scientists Say Horse Tranquilizers are Good for the Soul” [Gawker]
- “Eating Healthy Is A Mental Disorder, Scientists Say” [Inquisitr]
- “60 Really Is The New 50, Scientists Say” [Today]
- “Scientists Discover That Eyes Really Are ‘The Window To The Soul'” [Daily Mail]
- “Scientists Say Moms With Bigger Butts May Give Birth To Smarter Kids” [Elite Daily]
- “‘Designer Babies’ Debate Should Start, Scientists Say” [BBC]
- “New ‘Stupidity Virus’ Discovered, Scientists Say” [ABC News]