Mean vs. Median

Imagine 10 people affected by the tax bill:

Relative vs. Absolute Risk

What "doubles your risk" actually looked like:

Base Rate Neglect

Let's walk through the actual math. Say your school has 1,000 students, and the real drug-use rate is 1% — so 10 students actually use drugs.

A "99% accurate" test produced results where roughly half of all positive results are wrong. Your friend has about a 50% chance of being innocent — not 1%. The missing ingredient is the base rate: because drug use is rare, the small error rate applied to the huge clean population generates as many false alarms as real catches.

This isn't hypothetical. It affects real medical screening, criminal forensics, airport security, and content moderation algorithms. Anywhere a rare event meets a large population, "highly accurate" can still mean "mostly wrong."

Cherry-Picked Timeframes

Imagine unemployment over 5 years:

Simpson's Paradox

When researchers looked at individual departments:

Women were admitted at equal or higher rates within most departments. But they applied to the most competitive ones.

Framing & Anchoring

The same number feels completely different depending on how it's presented. This isn't a math trick — it's a psychology trick.

Confounding Variables

A confounding variable is a hidden factor that drives both things you're looking at:

Dense urban states have bigger budgets and more crime — not because one causes the other, but because population density drives both. Politicians who leave out the confounding variable can make you believe anything causes anything.

Survivorship Bias

You only hear from the winners. The losers don't get interviews, followers, or documentaries.

Social media is a survivorship bias machine. Algorithms promote the extraordinary outcomes — the 1-in-a-million success, the viral business, the impossible physique. The millions of people who tried the same thing and failed never show up in your feed.

One Story Is Not Data

An anecdote is a sample size of one — the smallest, least reliable sample possible.

Your cousin's bad week could be coincidence, a different illness, or a normal immune response. You'd need to compare thousands of vaccinated people to thousands of unvaccinated people to know if the vaccine actually caused it. That's exactly what clinical trials do — and they found it doesn't.

The supplement influencer? They also changed their sleep, stress, diet, and skincare routine. A sample of one person with dozens of changing variables tells you nothing about which change mattered.

Confirmation Bias

Your brain doesn't search for the truth. It searches for agreement. You instinctively:

Algorithms make this worse — they feed you what you engage with, which is usually what you already agree with. But confirmation bias existed long before the internet. It's the reason people can watch the same presidential debate and both sides declare their candidate won.

The Dunning-Kruger Effect

When you're new to a subject, you don't know enough to know what you don't know.

Belief Bias

Argument A has valid logic — but a false premise. (Not all animals have four legs.) We tend to accept it because the conclusion sounds right.

Argument B has a true conclusion — roses are flowers — but the logic is broken. "All X need water, all Y need water, therefore Y is X" doesn't follow. Cats need water too. That doesn't make them flowers.

This is how propaganda works. If someone builds an argument toward a conclusion you already agree with, you won't check their reasoning. And if someone makes a flawless argument toward an uncomfortable conclusion, your brain will hunt for reasons to reject it.

In-Group Bias

Your brain automatically divides the world into "us" and "them" — and then applies completely different rules to each.

The groups can be anything — political parties, schools, religions, nationalities, fandoms, even which gaming platform you use. The bias is the same: we give our group the benefit of the doubt we refuse to give others.

The Availability Heuristic

Your brain estimates how likely something is based on how easily you can think of an example — not on actual data.

News media and social media both exploit this. Dramatic, rare events get massive coverage. Slow, common killers don't. After consuming a week of coverage about a plane crash, your brain genuinely believes flying is more dangerous — even though you drove to the airport without a second thought, which was statistically the riskier part of your trip.

The Strawman Fallacy

Instead of responding to the actual argument, you rebuild it as a weaker, more extreme version — then knock that down instead.

You'll see this constantly in political debates. "We should reform the immigration system" becomes "They want open borders." "We should support the police" becomes "They don't care about civil rights." The strawman works because it's easier to defeat an extreme position than to engage with a nuanced one.

Appeal to Authority

Expertise is real and valuable — but it's not a blank check. The fallacy happens when:

This doesn't mean ignore experts — it means check what makes them expert. A climate scientist speaking about climate? That's earned authority. That same scientist giving stock tips? That's just a person with an opinion.

Special Pleading

Special pleading is when someone applies rules and standards except when the result is inconvenient for their argument — then suddenly there's a special exception.

The key question is: could this claim ever be proven wrong? If every piece of contrary evidence gets explained away with a new exception, the belief isn't based on evidence at all — it's been made unfalsifiable. It's wearing the costume of a testable claim, but it never allows itself to be tested.

Burden of Proof Shifting

A foundational rule of honest reasoning: the person making the claim carries the burden of proving it.

You can't prove a negative. You can't prove there's no invisible dragon, no hidden conspiracy, no undetectable effect. And that's exactly why burden-shifting works — it sets you an impossible task, then treats your inability to complete it as evidence that the original claim is true.

The Texas Sharpshooter Fallacy

The name comes from a joke: a Texan fires randomly at the side of a barn, then paints a bullseye around the tightest cluster of bullet holes. Perfect aim — after the fact.

The "prophet" posted thousands of vague feelings — eventually one coincided with an event. The autism-organic food chart is real, but both just rose alongside hundreds of other things (smartphones, streaming subscriptions, yoga studios). With enough data, you will always find coincidental patterns. Always.

No True Scotsman

The fallacy works in three steps:

The definition of the group shifts after the fact to exclude anything inconvenient. It makes the original claim unfalsifiable — no evidence can ever disprove it, because any counterexample automatically disqualifies itself. It's special pleading's cousin: instead of making the evidence a special case, you make the person a special case.

This is especially powerful in ideological communities. It silences dissent — if questioning the group means you aren't a real member, then no one can question the group from the inside.