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No.

The reasoning that keeps showing up: the test is 99% accurate, you tested positive, so there's a 99% chance you have the condition.

No.

These three mistakes show up at the very beginning of a statistics course, and they share an unusual quality: the wrong answer sounds like careful thinking.

Hypothesis testing is one of those frameworks that feels intuitive until you try to apply it — and then each piece trips you up in a different way.

The recurring move goes like this: you run the numbers, Pearson's r comes back at 0.02, and you conclude the two variables aren't related — maybe you even drop one as a predictor or call them "independent." It's a tempting jump, because a single number sitting near zero looks like a clean verdict on the whole relationship.

The most common reading: "I tested 20 things, one came back p = 0.03, so that one is real." The logic feels tight — p < 0.05 means less than a 5% chance of a false alarm, and 0.03 is well below the line.

The intuitive answer is: they improved because the treatment worked.

The recurring move that goes wrong: you collect 50 points, get an SD around 15, expect that collecting 500 will drag it down toward something like 15/√10 ≈ 4.7 — and then panic when the SD comes back at 15 again.

The recurring mistake looks like this: you learned that "doubling is 3 dB," so when a voltage goes from 10 V to 20 V you write `10·log10(20/10) = 3 dB` and move on.

The version almost everyone reaches for: 1 divided by a very small number gives a very large number, so 1 divided by zero "should be" infinity.

You took the transform of something like $\frac{1}{9}\sin(9t)$, got $F(s) = \frac{1}{s^2+81}$, multiplied by s, set s = 0, and read off 0 — so you wrote down that the steady state is zero.

You look at a log axis running from 1 to 100, find the point halfway along, and read off 50 — because halfway between 1 and 100 is obviously (1 + 100) / 2 ≈ 50.

The simplex method is the standard algorithm for solving linear programming problems.

You take the Fourier transform of cos(2π·50·t), see one impulse at +50 Hz and an identical one at -50 Hz, and conclude the -50 Hz bin is a computational artifact — so you delete it and keep only the positive half.

The version almost everyone reaches for: an object swinging in a circle has two forces fighting each other — an inward tension pulling it toward the center and an outward centrifugal force pulling it away.

Here is the recurring confusion, stated plainly: you read that an inductor "opposes current," so for a series RL circuit with a 12 V source you expect it to permanently throttle the current — maybe holding the inductor voltage near 12 V the way a resistor would hold a steady drop.

Electrostatics is full of inverse relationships, sign conventions, and definitions that look similar but behave differently.

If a Gaussian surface encloses no charge, the net flux through it is zero — and a lot of students immediately conclude the electric field inside is zero too.

The usual move is to reach for two formulas — C = ε₀A/d and Q = CV — see that doubling the separation halves the capacitance, and conclude in one step: "C halved, so Q halved." That gives a confident wrong answer, because whether the charge actually changes depends on something the formulas never mention — whether the battery is still connected.

Here is the move that trips people up, and it shows up again and again on physics help forums.

The version almost everyone reaches for: weight pulls you down, the floor pushes back with the same magnitude, and those two forces are Newton's third-law partners.

The recurring confusion goes like this: you read "time constant," reason that τ = RC is the time the capacitor takes to charge, and conclude that at t = τ the capacitor sits at the full supply voltage.

The version almost everyone reaches for: entropy is a measure of messiness or disorder.

The answer almost everyone reaches for: pH measures how much acid you added — more acid means lower pH, so a more concentrated acid always beats a less concentrated one.

The version almost everyone reaches for: oxidation state and formal charge are two names for the same thing — both measure how many electrons "belong" to an atom in a molecule.

Preparing for a lab defense, a student was asked where the 2 mA at the collector comes from and answered: the base.

Preparing for a lab defense, a student was asked what happens to the collector current if you swap the beta-50 transistor in a voltage divider bias circuit for a beta-200 part.

Ask "does voltage lead or lag the current in a capacitor?" and the recurring wrong answer is "voltage leads by 90 degrees." It's the inductor's answer, swapped onto the capacitor.

The version almost everyone reaches for first: a "120 V" wall outlet supplies 120 volts, more or less constantly, with some gentle AC wiggle on top.

The version almost everyone reaches for first: the two input pins of an op-amp are shorted together, which is why they're at the same voltage.

Preparing for a lab defense, a student was asked why raising the collector current makes a BJT more sensitive — why gm should depend on IC at all.

Preparing for a lab defense, a student was asked what would happen if you shorted the emitter resistor to ground — and answered that nothing much would change, because the voltage divider still holds VB steady, so IC stays put and beta-independent.

Preparing for a lab defense, a student was asked how the emitter resistor reins in a rising collector current — and answered that it can't, because VE is pinned at VB − 0.7 V and never moves, so VBE never changes and nothing throttles the current.

You set up the table, see Country A make 10 wheat and 5 cars against Country B's 4 wheat and 1 car, and you hand A both goods — it's better at each, so it should make each.

A dominant strategy is the choice that gives you the best outcome regardless of what anyone else does.

Three introductory economics errors keep appearing in sessions across money, banking, and supply and demand.

The version almost everyone reaches for first: a price ceiling is high, so it pushes prices up, so producers supply more — surplus.

Here is the move that trips people up: you compute the slope of a straight-line demand curve, find it's constant (say −1 everywhere), and conclude elasticity must be constant too — so when a problem says the same line is elastic at the top and inelastic at the bottom, you decide one of those answers has to be a mistake.

The standard critique of Reagan's economic policies — "they caused inequality" — is usually stated without a mechanism.

No.

You bought $600 of non-refundable concert tickets.

The version most people reach for: marginal cost must always be below average total cost, and the two curves eventually meet when output gets large enough.

Three mistakes about memory and study technique appear in sessions on the psychology of memory.

A more sophisticated attribution model does not fix a broken data pipeline.

Mateo came to portrait drawing knowing what a face looks like but not how to construct one.