Why a data table isn't an answer
A town asks a hundred people what they think and announces what ten thousand people believe. That is quite an impressive promotion for a hundred people.
Fourteen lecture companions · Written scripts
A semester's worth of lectures, on paper.
Every week now has a written introduction, worked demonstration plan, prediction, and exit question. These are scripts—not prerecorded video lectures.
Media status: No lecture video or recorded voiceover is currently published. These original written scripts are provided as instructional companions and a basis for future captioned, accessible video production. They require editorial and mathematical review before recording.
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An average walks into a histogram
Five people earn between forty and sixty thousand dollars. Their mean and median agree. Then one of them becomes extraordinarily rich. The median sits quietly while the mean starts negotiating for a yacht.
The answer changes when the respondents do
Imagine an election in which everyone has already decided how to vote, but the poll numbers shift dramatically. No one changed their mind. We just changed who answered the telephone.
Probability is a model, not a prophecy
The coin has no memory, the deck of cards does not owe you a heart, and probability theory has never promised that the next toss will be kind.
The rare-event false alarm
A screening test can detect ninety percent of a rare condition and still be wrong most of the time when it says somebody has it. There is nothing mystical about this. There are just a great many healthy people.
What becomes normal? Not the population
Take a deeply skewed distribution, average many independent observations, and something rather beautiful happens. The individual observations are still just as skewed as before.
The parameter stands still
People regularly ask whether there is a 95-percent probability that an unknown mean lies inside one particular frequentist confidence interval. It is an understandable question, and it is generally the wrong interpretation.
Two groups are not always two independent samples
A before-and-after study measures five people twice. That's ten numbers, but it is not ten independent people. This is exactly where pressing the wrong button on the statistics software produces an impressive-looking mistake.
What is the null model actually saying?
We tossed a coin twenty times and got eighteen heads. Does that prove it is unfair? No. But under a fair-coin model, the observation is sufficiently unusual that we ought to pay attention.
The interesting result selected from twenty tests
Imagine testing twenty unrelated hypotheses, reporting the smallest p-value, and neglecting to mention the other nineteen. You have not necessarily made a discovery. You may have simply discovered the minimum function.
A randomization distribution you can count
We have eight fictional participants and exactly seventy ways to choose four for treatment A. The remarkable thing is that an exact test is suddenly small enough to inspect entirely.
The same data tell two contradictory stories
We found a historical comparison where Treatment A has a higher recorded success rate in each stone-size group, yet Treatment B has a higher recorded success rate overall. The mathematics has not broken. The denominator has.
A different model for a different question
A straight line, an ANOVA F statistic, and a logistic curve are not rival teams competing for the statistical championship. They answer different questions under different models.
Give your analysis to someone who wants to prove you wrong
The ultimate statistical accomplishment is not a tiny p-value. It is a report that another person can reproduce, interrogate, and perhaps disagree with intelligently.
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