What's new
Essays arrive in groups rather than one at a time, and a group usually opens up a subject not covered before. Between one group and the next nothing changes, so a reader who has seen the most recent group has seen everything.
3 November 2026
20 essays on estimating the dependence, not naming it, the block length read on a quantile, choosing what the rule reads, scoring a search without spending data, the same table at seven correlations, the criterion, and what it assumes, when the set is too large to walk, what the design is asked to guarantee, the block size as a schedule, balancing what has no levels, a block, weighted inside itself, the observation that has not happened, the best of a set, and what the search costs, balancing on what was recorded first, a search with no fixed point, a guarantee that needed a symmetry, more arms than two, the shape the covariate enters by, a promise about two arms and both halves of the dependence at once
Estimating the dependence, not naming it
A covariance repaired
A truncated autocovariance sequence fails to be a covariance matrix on most draws of a persistent series, and this line of essays has always scored it on the draws where it survives. The textbook repair is to floor its eigenvalues. At a floor of 0.001 that moves the matrix by four per cent and gives up 1.56 of regret, seventeen times what least squares gives up, because a whitening reads an inverse and an inverse reads the smallest eigenvalues. At a floor of 0.2 it beats the taper at the shortest windows. So the repair is not a repair: it is a second dial.
The block length read on a quantile
A shrink towards the answer
This line of essays reported that the 95% point is a dearer reading than a variance, that a further point wants a shorter block, and that a taper beats a rectangle on what a test reads where a variance says the opposite. All three came from one uncentred quantile. Read about the resamples' own mean, the point costs 28.5% against the variance's 45.8%, every level wants about the same block, and the windows order alike on all readings. The taper's coverage had a separate cause: its resampled mean is 0.875 of the sample's, and every series here had a true mean of exactly zero.
Choosing what the rule reads
A box with a count
The ellipse never runs out of assignments and holds the named functions loosely; the box holds them tightly and can come up empty. Dropping the ellipse's thin directions was meant to give both, and it does not: no cutoff comes within a third of the box. But the box's emptiness was never a property of the box. It belongs to a tolerance fixed in advance. Set the tolerance by a count instead, and at that count the region is the box, on every set of units, with nothing left to run out.
Scoring a search without spending data
A charge the sample can afford
The inflation charge for dependent rows runs to twice the counted optimism at persistence 0.95, and the reason offered was that a series of n rows cannot be optimistic about movements slower than n rows. Summing the inflation over n rows does almost nothing: 234 becomes 209, against 119 counted. Evaluating the same variance on the sample's own design gives 132, and moving the fresh rows away from the sample raises the count to 159. So the charge can be made nearly right, and when it is, the regret doubles from 0.032 to 0.061. A selection wants a much larger charge than the optimism, and past about fifty per predictor it is no longer selecting.
The same table at seven correlations
A cut on each side
Every table of the threshold's leak put one quantile on both covariates, which is the diagonal of a surface nobody had drawn. Off the diagonal the copulas swap places: a cut at the 5th percentile on one covariate and the 95th on the other removes 54.8% of the interaction under a Gaussian copula and 1.1% under a t copula, the reverse of their order at the near corner. Walked further out, the far corner has two opposite limits, and which one a Gaussian reaches is decided by whether its correlation is above or below exactly one third.
The criterion, and what it assumes
A design chosen for a test
A screening experiment that wants its main effects and a check on curvature has been told to trade them with a weight nobody can state. It can state a power. Read against a power of 80%, the frontier collapses to one curve in runs times the squared size of the curvature, and a large enough trial pays almost nothing. But the curve belongs to a test. A factorial with a few centre points beats the entire frontier on a bowl, spending 4% of its main-effect information where the frontier spends 10%, and against a saddle of the same size it has exactly its 5% level.
When the set is too large to walk
A floor for the draw
A basis drawn at random guarantees more on average than any fixed one, at the price of leaving some shape wholly untouched in a large share of trials. Requiring every basis in the draw to keep a floor looks like a smooth trade between the two. It is a staircase, and the first step does nearly all the work. No basis has a floor between zero and 31.83%, so there is nothing to give up until a floor of that size is asked for. And at four functions, seven bases tie at the fixed basis's own 63.66%: a mixture of them keeps that floor exactly and adds thirteen points to the guarantee.
What the design is asked to guarantee
A floor that reads the first stage
A three-stage stopping rule fails at a first stage of five because a low first reading asks for nothing more, and the only floors that repair it were set near the answer, by somebody who already knew roughly what the spread was. Inflating the first reading by Stein's own factor needs no such knowledge, and it does cut the experiments left stuck from a fifth to a fifteenth. But those still stuck cover less than before, the rule needs a different dial at every requirement, and a floor of 26 observations covers 96.5% at the spend where the rule covers 92.1%, even met by a spread it was not set for.
The block size as a schedule
A rule that sets its own κ
A stopping rule may read the spread inside its blocks and may not read the spread between them, and the dial between the two costs nothing for a long stretch and then a lot. The share an efficiency argument recommends is each estimate's share of the degrees of freedom, and on blocks of two at a half-width of 0.15 that loses nothing and steadies the experiment by 30%. At 0.35 it loses 1.18 points. Deferring the forbidden reading until twenty blocks costs nothing measurable at any requirement, and it keeps most of the steadiness where steadiness can be had.
Balancing what has no levels
A second reading or a second covariate
A rule that balances a recording balances the truth only as far as the recording reaches, and a second reading of the covariate raises that reach. So does a first reading of something else. At a reliability of 0.8 the first reading of a second covariate does more once that covariate matters a third as much as the first, and the threshold is exact: the square root of (1 − λ)/(1 + λ), with no trial size in it. A protocol's list of measurements turns out to be a small knapsack, and it is rarely filled by reading anything twice.
A block, weighted inside itself
A sequence that knows it was centred
A block length read off a sample's own autocovariances gets worse the further out it reads, because a centred series' autocovariances sum to exactly zero. To first order every lag loses the same amount, about the long-run variance over the sample size, and that can be added back. Corrected, a reading to lag forty goes from 84.5% to 89.2%, and to lag twelve from 93.3% to 94.5%. But the correction overshoots on the long lags, and on the rule that picks its own cut-off, which is short, it moves coverage by three tenths of a point. The identity was the reason the lag mattered. It was not the reason the rule falls short.
The observation that has not happened
A tail sixty residuals have barely seen
A forecast interval that reads a normal quantile has every one of its misses on one side when the shocks are skewed, and the natural repair is to draw future shocks from the model's own residuals. It works on the side: 0.0% below and 6.5% above becomes 4.3% and 4.1%. It pays for that with coverage, 93.5% to 91.6%, and on sixty observations it does this under normal shocks too. And a nominal 99% interval has a ceiling nothing in the resampling can lift, because one new shock beats all of sixty old ones in either direction with probability 3.3%.
The best of a set, and what the search costs
A threshold against its sample
A recentred test's threshold exists so that the test is right in the limit, and at a hundred origins it costs a fifth of the power against a stale set. The natural defence is that the price falls as the sample grows and the guarantee starts to earn it. Across twenty-five to eight hundred origins it does not: a threshold of zero keeps four to seven points more power at every size, and its size at the corner stays at the level from fifty origins on. What does change with the sample is the stale set, which stops costing anything by two hundred origins under Hansen's rule and by eight hundred under the most cautious.
Balancing on what was recorded first
An effect that is not one number
A randomisation test becomes an interval for the effect by testing every constant effect in turn, so when the effect grows with the prognosis every hypothesis it tests is false. It does not fall apart. It covers the population's mean effect within a point of its level at every slope measured, and its width grows by exactly what the sample's own composition adds. A regression that models the interaction stays narrow at 0.72, covers the sample's mean at 95%, and covers the population's at 84%. The extra width was never a defect. It was the difference between two questions.
A search with no fixed point
An excess and its window
The parameter-count displacement is a Gaussian fact, and on heavy-tailed predictors it runs a few per cent over. Swept across windows from 20 to 640 rows, the excess is about the predictors' excess kurtosis divided by the window: a law with a fourth moment of nine on 80 rows is 7.5% over, and on 640 rows under one. At three degrees of freedom it falls only as the root of the window, from 44% to 7.6%. And the instability once blamed on that law was not there: with the fresh row integrated out, the batches agree to a point and a half, and the mean exists.
A guarantee that needed a symmetry
The covariate on its ranks
A skewed covariate spoils every parity argument a balancing rule relies on, and a rule that balances ranks instead of values looks like the way out, since a rank has the same uniform law on any marginal. The measurement says the skew really does belong to the scale for one kind of shape: a rank holds a median split at exactly a quarter of a coin's imbalance whatever the covariate. But it pays with a cap on any shape linear in the value, at nearly half a coin's imbalance on the strongest skew. And a rule holding values and median splits together holds both, beating the rank on the shape a rank gives up and matching it on the one it gains.
More arms than two
The guesser who learns
An investigator who watches a three-arm minimisation can tally which of several partial readings has been right so far and follow the leader. It does not help. Following the leader names 48.9% of assignments where the best single reading names 49.9%, and a table of what the three readings say together, learned inside the trial, starts at 36% and has not caught up by a hundred and fifty patients. Learned over earlier trials, that table reaches 54.5%. The full guesser's 71.8% stays out of reach of all of them, because the gap to it is information rather than practice.
The shape the covariate enters by
The list it was chosen on
Six functions of one covariate looked like 720 designs, one per order of addition. The rule reads a span and not a sequence, so they are 63, and at a hundred units the best four leave 12.1% of a coin's imbalance against the designer's first four at 31.5%. Those best four contain no cube and are, function for function, the four shapes the worst case was scored on. Read on six shapes it was not told about, the same design leaves the cube 77.0% of a coin's imbalance, and the designer's four, which lost by a factor of two and a half, leave it 28.1%.
A promise about two arms
The sums under a moving level
A trial's block sums are a free second estimate of its variance only while they see what the differences see, and a level that moves between blocks with an effect moving against it breaks that: pooled raw at a ceiling they cover 87.6% to 90.0%. Residualising the sums on an unbalanced design does not make them safe. It moves the failure. On ten and two, 90.0% at the ceiling becomes 93.8%, the trough leaves for a slope of about −1.5, and over the rest of the range the same estimate over-covers, at 99.9% on an interval half as wide again as it needs to be.
Both halves of the dependence at once
The zero that needed two
A rule balancing two median splits removes nothing of their interaction, on every copula, because a centred split squares to a constant. Add a third covariate and the same arithmetic stops protecting the thing it looked as if it protected. The product of three splits is not orthogonal to the mains: at a rank correlation of 0.4 a rule on the mains removes 14.47% of it under a Gaussian copula. And the symmetry that decides the rest belongs to the triple rather than the pair, so Frank's copula, whose pairs are radially symmetric, leaks where Clayton's, whose pairs are not, barely does.
Before that
Everything published earlier, newest first. Titles only — the cards are on the full listing.
29 October 2026
14 essays on a charge for a covariance's own dimension, a probe chosen rather than picked, fitted together, or fitted after, the other half of the dependence, how long the list is, a block length chosen from the data, two searches over one sample, the weights the corner needs, the criterion, and what it assumes, overlap and complementarity, separated, what a chain cannot report, the diagnostic after the trial, two searches over different features and the rate and the size of a disagreement
- A cap that decides nothing — a charge for a covariance's own dimension
- A ceiling that is one unit — a probe chosen rather than picked
- A fixed point with no likelihood under it — fitted together, or fitted after
- A leak read off a two-by-two table — the other half of the dependence
- A quarrel's cost is its width — how long the list is
- A ranking that belongs to the interval — a block length chosen from the data
- A set calibrated at the estimate — two searches over one sample
- A stopping rule that reads the periods — the weights the corner needs
- A subset the model cannot use — the criterion, and what it assumes
- A tail the law gives the pair — overlap and complementarity, separated
- A unit that has not moved — what a chain cannot report
- After the mirror is gone — the diagnostic after the trial
- The power a calibration buys — two searches over different features
- The table decides when the sample settles it — the rate and the size of a disagreement
21 October 2026
18 essays on a design that assumes less, where a taper's case begins, scoring a search without spending data, a guarantee that needed a symmetry, a block, weighted inside itself, what the procedure may not read, a covariance with no parameter, the shape the covariate enters by, searching among fitted models, the observation that has not happened, paying for a search, a search with no fixed point, balancing on what was recorded first, the shape a dependence has, what decides whether a tuning list decides, when the two are not independent, the best of a set, and what the search costs and what a dictionary buys and what it costs
- A bootstrap that repeats the design — a design that assumes less
- A model against a window — where a taper's case begins
- A penalty that counts independent rows — scoring a search without spending data
- A share at a hundred units — a guarantee that needed a symmetry
- A share read off the sample — a block, weighted inside itself
- A variance that follows the response — what the procedure may not read
- An interval that knows the band was maximised — a covariance with no parameter
- How many functions a trial can hold — the shape the covariate enters by
- One test for eight nulls — searching among fitted models
- Shocks that are not normal — the observation that has not happened
- The break a shared scale hid — paying for a search
- The displacement on a heavy tail — a search with no fixed point
- The interval the test inverts to — balancing on what was recorded first
- The residue was the weights — the shape a dependence has
- The same dial under a second law — what decides whether a tuning list decides
- The share a sample removes — when the two are not independent
- The threshold the recentring reads — the best of a set, and what the search costs
- Two functions a covariate — what a dictionary buys and what it costs
15 October 2026
20 essays on two searches over one sample, the other half of the dependence, a block length chosen from the data, the weights the corner needs, a probe chosen rather than picked, a charge for a covariance's own dimension, two searches over different features, overlap and complementarity, separated, how long the list is, the rate and the size of a disagreement, when the set is too large to walk, more arms than two, both halves of the dependence at once, balancing what has no levels, when a fixed width is reached, the block size as a schedule, what the design is asked to guarantee, a promise about two arms, the same table at seven correlations and choosing what the rule reads
- A break that is there — two searches over one sample
- A cut walked into the tail — the other half of the dependence
- A length read off the whole sequence — a block length chosen from the data
- A ratio that changes with the period — the weights the corner needs
- How far to project — a probe chosen rather than picked
- The charge at four times the sample — a charge for a covariance's own dimension
- The overlap at the critical value — two searches over different features
- The split at the critical value — overlap and complementarity, separated
- Two values the criterion cannot tell apart — how long the list is
- What a longer sample settles — the rate and the size of a disagreement
- A basis drawn rather than chosen — when the set is too large to walk
- A guesser who sees the totals — more arms than two
- A median with ties — both halves of the dependence at once
- A number read with error — balancing what has no levels
- A weighting that does not read its own spreads — when a fixed width is reached
- How much of the forbidden spread a rule may read — the block size as a schedule
- The fifth a third stage never reaches — what the design is asked to guarantee
- The sums made independent — a promise about two arms
- Where the skew puts a threshold — the same table at seven correlations
- What the ellipse spends its assignments on — choosing what the rule reads
7 October 2026
20 essays on a block, weighted inside itself, a probe from what the rule blocks, a proportion's interval near the boundary, and the coin, splitting the units, past the first term of the normal approximation, a charge that is not a straight line, a cut point, at a correlation, weighting one sample into another, what partial pooling does to one group, to the set, and to a ranking, series that move together, the interval that holds observations, not a mean, three series, and a count, two tests, a threshold, and the rate they are read against, corrections, and what each controls, a variable that moves one thing only, when the stratified answer and the pooled one disagree, what a diagnostic plot is showing, when the observations repeat each other, an interval read beside something else and the tail past the last observation
- A length chosen for the interval — a block, weighted inside itself
- How far, not whether — a probe from what the rule blocks
- Two windows and a ratio — a proportion's interval near the boundary, and the coin
- A contrast chosen after the data — splitting the units
- A tilt for the ratio — past the first term of the normal approximation
- The surface under every law — a charge that is not a straight line
- Weights from an approximate law — a cut point, at a correlation
- A balance allowed a tolerance — weighting one sample into another
- A centre chosen by its own table — what partial pooling does to one group, to the set, and to a ranking
- A factor estimated from the panel — series that move together
- A range that forgets — the interval that holds observations, not a mean
- A restriction the data can check — three series, and a count
- A threshold reported with its interval — two tests, a threshold, and the rate they are read against
- An interval that knows its finding was found — corrections, and what each controls
- Cells of unequal size and an error that follows them — a variable that moves one thing only
- Every variable, every cut — when the stratified answer and the pooled one disagree
- Residuals of a model the data chose — what a diagnostic plot is showing
- The interval the joint fit reports — when the observations repeat each other
- The pattern a cause leaves on its neighbours — an interval read beside something else
- Where the extremal index matters to a return level — the tail past the last observation
4 October 2026
20 essays on a design chosen rather than looked up, reversals that are not errors, intervals, counted, the spread, and its own uncertainty, hierarchy past one number, the prior, doing visible work, what makes it checkable, coverage without a distribution, decided before the data, what conditioning on a variable does, the value that is not there, a standard error for a model that is wrong, comparing two forecasters, a forecast that is a probability, when the data stops early, tests, and the second number, the distribution itself, the surface between the corners, regression, and what the summary hides and groups that borrow
- A certificate for the worst direction — a design chosen rather than looked up
- A correction built on a retest — reversals that are not errors
- A count that bets against its interval — intervals, counted
- A history that stepped — the spread, and its own uncertainty
- A prior on the spread between two sites — hierarchy past one number
- A prior wrong about its own spread — the prior, doing visible work
- A proposal fitted to its own draws — what makes it checkable
- A quantile over the recent scores — coverage without a distribution
- A run lost for a reason — decided before the data
- A set of shadows — what conditioning on a variable does
- A variable that moves recording — the value that is not there
- An effective number of clusters — a standard error for a model that is wrong
- An interval built from simulated futures — comparing two forecasters
- Five values chosen by the forecasts — a forecast that is a probability
- One test for a curve that might cross — when the data stops early
- Studies that share a control — tests, and the second number
- Testing for a flat point first — the distribution itself
- The height at the chosen setting — the surface between the corners
- The other half a trimmed fit rejected — regression, and what the summary hides
- The shape the estimates keep — groups that borrow
1 October 2026
9 essays on a block, weighted inside itself, a proportion's interval near the boundary, and the coin, shape, and what it does to a two-sample test, what a sample-size calculation was given, what a summary of a scatter is a property of, designs that change while they run, the analyses that were available and not run, the reference distribution the design supplies and stopping rules
- A block at every starting row — a block, weighted inside itself
- The coin a clock supplies — a proportion's interval near the boundary, and the coin
- A level set before the source is known — shape, and what it does to a two-sample test
- A schedule the trial chooses for itself — what a sample-size calculation was given
- A value read off a curve — what a summary of a scatter is a property of
- Patients spent before the choice — designs that change while they run
- The cleanest of the significant — the analyses that were available and not run
- The covariate chosen afterwards — the reference distribution the design supplies
- The variance that contains the effect — stopping rules
27 September 2026
11 essays on a proportion's interval near the boundary, and the coin, a cut point, at a correlation, past the first term of the normal approximation, shape, and what it does to a two-sample test, stopping rules, what partial pooling does to one group, to the set, and to a ranking, designs that change while they run, what a summary of a scatter is a property of, the analyses that were available and not run, what a sample-size calculation was given and the reference distribution the design supplies
- The coin that is already there — a proportion's interval near the boundary, and the coin
- A companion with two coordinates — a cut point, at a correlation
- The correction a t test would use — past the first term of the normal approximation
- A failure charged by its size — shape, and what it does to a two-sample test
- A look added by a rule — stopping rules
- A ranking with its uncertainty — what partial pooling does to one group, to the set, and to a ranking
- A second stage sized by the first — designs that change while they run
- A term built from the others — what a summary of a scatter is a property of
- A winner chosen by its diagnostic — the analyses that were available and not run
- The correlation a pilot can see — what a sample-size calculation was given
- The repair, with a covariate in it — the reference distribution the design supplies
26 September 2026
11 essays on what a summary of a scatter is a property of, designs that change while they run, the analyses that were available and not run, what partial pooling does to one group, to the set, and to a ranking, when the stratified answer and the pooled one disagree, the spread, and its own uncertainty, the interval that holds observations, not a mean, series that move together, two tests, a threshold, and the rate they are read against, an interval read beside something else and what a diagnostic plot is showing
- A point ordinary on every axis — what a summary of a scatter is a property of
- A prior that lets one arm stand out — designs that change while they run
- An interval for the analyses admitted to — the analyses that were available and not run
- The interval a small group is given — what partial pooling does to one group, to the set, and to a ranking
- A cut that slides — when the stratified answer and the pooled one disagree
- A history that has been moving — the spread, and its own uncertainty
- A range that grows with the lot — the interval that holds observations, not a mean
- A shock every pair shares — series that move together
- A test whose tail is not normal — two tests, a threshold, and the rate they are read against
- One characteristic that really matters — an interval read beside something else
- Residuals made independent — what a diagnostic plot is showing
25 September 2026
16 essays on a cut point, at a correlation, the spread, and its own uncertainty, series that move together, designs that change while they run, what a sample-size calculation was given, what a summary of a scatter is a property of, what partial pooling does to one group, to the set, and to a ranking, the interval that holds observations, not a mean, when the stratified answer and the pooled one disagree, what a diagnostic plot is showing, an interval read beside something else and two tests, a threshold, and the rate they are read against
- A rate needs a rate beside it — a cut point, at a correlation
- A companion cut into many — a cut point, at a correlation
- A control borrowed from the last trial — the spread, and its own uncertainty
- A relation supplied in advance — series that move together
- Shrinking the arm that was chosen — designs that change while they run
- The cut that fitted best — what a sample-size calculation was given
- The points a slope rests on — what a summary of a scatter is a property of
- The relation the table has to estimate — what partial pooling does to one group, to the set, and to a ranking
- A history that agrees with itself — the spread, and its own uncertainty
- A range allowed a few misses — the interval that holds observations, not a mean
- A slow return across many pairs — series that move together
- A visit before or a visit after — what a sample-size calculation was given
- Five places to cut one variable — when the stratified answer and the pooled one disagree
- Residuals that look too normal — what a diagnostic plot is showing
- Sixteen subgroups and one effect — an interval read beside something else
- The threshold a validation study can see — two tests, a threshold, and the rate they are read against
24 September 2026
18 essays on what a sample-size calculation was given, past the first term of the normal approximation, two tests, a threshold, and the rate they are read against, when the stratified answer and the pooled one disagree, the analyses that were available and not run, what partial pooling does to one group, to the set, and to a ranking, an interval read beside something else, what a diagnostic plot is showing, what a summary of a scatter is a property of, the interval that holds observations, not a mean and shape, and what it does to a two-sample test
- A baseline cut in two — what a sample-size calculation was given
- A tail the sample never saw — past the first term of the normal approximation
- An upper limit is the finding — two tests, a threshold, and the rate they are read against
- Every patient at one half — when the stratified answer and the pooled one disagree
- Naming a handful in advance — the analyses that were available and not run
- The small groups one centre protects — what partial pooling does to one group, to the set, and to a ranking
- The verdicts watch the threshold, not the gap — an interval read beside something else
- Three runs at the end of the line — what a diagnostic plot is showing
- Two numbers for the fit's geometry — what a summary of a scatter is a property of
- A band allowed a few misses — the interval that holds observations, not a mean
- A limit from the family it came from — shape, and what it does to a two-sample test
- A number for the shape — what a diagnostic plot is showing
- A subgroup inside its own trial — an interval read beside something else
- A threshold that jumps — two tests, a threshold, and the rate they are read against
- An interval for the winner — the analyses that were available and not run
- The same correction, inverted — past the first term of the normal approximation
- Twenty variables nobody stratified on — when the stratified answer and the pooled one disagree
- The level a limit should be set at — shape, and what it does to a two-sample test
21 September 2026
18 essays on splitting the units, when the observations repeat each other, the reference distribution the design supplies, three series, and a count, coverage without a distribution, the distribution itself, what conditioning on a variable does, intervals, counted, what makes it checkable, a standard error for a model that is wrong and hierarchy past one number
- The arm whose variance is its answer — splitting the units
- The cliff that is a slope — when the observations repeat each other
- The null the exactness is for — the reference distribution the design supplies
- The rank is a decision — three series, and a count
- A statistic that is exact twice — the reference distribution the design supplies
- The repair that keeps the question — when the observations repeat each other
- The weight that has to be estimated — coverage without a distribution
- Two contrasts, one split — splitting the units
- Which mistake about the rank costs — three series, and a count
- A detector built for the ordering — coverage without a distribution
- A flat point with more than one direction — the distribution itself
- A space is not a relation — three series, and a count
- Adjusting for a shadow — what conditioning on a variable does
- An interval that covers and says nothing — intervals, counted
- How slow a return a sample can see — when the observations repeat each other
- The check worth more than the check — what makes it checkable
- The reference the sandwich is read against — a standard error for a model that is wrong
- What a two-unit study should report — hierarchy past one number
17 September 2026
18 essays on past the first term of the normal approximation, what partial pooling does to one group, to the set, and to a ranking, a proportion's interval near the boundary, and the coin, an interval read beside something else, what a sample-size calculation was given, shape, and what it does to a two-sample test and the interval that holds observations, not a mean
- A bound written for a coin — past the first term of the normal approximation
- A group from the population's own tail — what partial pooling does to one group, to the set, and to a ranking
- A hole no sample size fills — a proportion's interval near the boundary, and the coin
- Five times in six — an interval read beside something else
- The spread a pilot supplies — what a sample-size calculation was given
- A correction that goes below zero — past the first term of the normal approximation
- Estimates that are too alike — what partial pooling does to one group, to the set, and to a ranking
- The chance a trial succeeds — what a sample-size calculation was given
- Two intervals that overlap — an interval read beside something else
- What a guaranteed minimum costs — a proportion's interval near the boundary, and the coin
- A league table of a hundred — what partial pooling does to one group, to the set, and to a ranking
- An approximation built at the threshold — past the first term of the normal approximation
- An outcome cut in two — what a sample-size calculation was given
- Significant in one, not in the other — an interval read beside something else
- The coin that makes it exact — a proportion's interval near the boundary, and the coin
- The skewness of a difference — shape, and what it does to a two-sample test
- All of the next ten — the interval that holds observations, not a mean
- The side a bound is read from — shape, and what it does to a two-sample test
16 September 2026
20 essays on the analyses that were available and not run, what a summary of a scatter is a property of, what a diagnostic plot is showing, when the stratified answer and the pooled one disagree, two tests, a threshold, and the rate they are read against, the interval that holds observations, not a mean and shape, and what it does to a two-sample test
- How many analyses there really were — the analyses that were available and not run
- R² is a property of the design — what a summary of a scatter is a property of
- The band the eye was standing in for — what a diagnostic plot is showing
- The reversal a coin cannot prevent — when the stratified answer and the pooled one disagree
- The second test that is not a second opinion — two tests, a threshold, and the rate they are read against
- Two standard deviations of what — the interval that holds observations, not a mean
- Where the two tails disagree — shape, and what it does to a two-sample test
- A degrees of freedom that is not a count — shape, and what it does to a two-sample test
- A tenth as wide, and both of them right — the interval that holds observations, not a mean
- The change that is not confounding — when the stratified answer and the pooled one disagree
- The plot is about the wrong quantity — what a diagnostic plot is showing
- The t statistic wearing different clothes — what a summary of a scatter is a property of
- The test is a point somebody chose — two tests, a threshold, and the rate they are read against
- What naming it in advance costs — the analyses that were available and not run
- Conditioning on what the treatment caused — when the stratified answer and the pooled one disagree
- Ninety-three observations, and nothing assumed — the interval that holds observations, not a mean
- Residuals are not the errors — what a diagnostic plot is showing
- The correction that makes the estimate worse — the analyses that were available and not run
- The prevalence the test has to estimate — two tests, a threshold, and the rate they are read against
- The summary that was meant to work — what a summary of a scatter is a property of
15 September 2026
20 essays on comparing two forecasters, a design chosen rather than looked up, groups that borrow, the prior, doing visible work, the surface between the corners, decided before the data and hierarchy past one number
- Correcting the forecast instead — comparing two forecasters
- How many places a design goes — a design chosen rather than looked up
- The fewest groups that can borrow — groups that borrow
- The shortest interval, and the one that does not move — the prior, doing visible work
- The sign the curvature has — the surface between the corners
- The word a fraction costs — decided before the data
- Two groupings that cross — hierarchy past one number
- A level with two units — hierarchy past one number
- An interval for something else — the prior, doing visible work
- Augmenting a design that has already run — a design chosen rather than looked up
- The correction that leaves the region — comparing two forecasters
- The design that refuses the corners — decided before the data
- When the best setting is outside the region — the surface between the corners
- Where the borrowing goes — groups that borrow
- One population, or two — groups that borrow
- The criterion with no derivative — a design chosen rather than looked up
- The run that confirms it — the surface between the corners
- The run that did not happen — decided before the data
- What the interval is short by — comparing two forecasters
- When the prior is confident and wrong — the prior, doing visible work
13 September 2026
20 essays on stopping rules, when a fixed width is reached, corrections, and what each controls, the interval, studentised, a forecast that is a probability, when the data stops early, a variable that moves one thing only, the value that is not there, weighting one sample into another, the tail past the last observation, reversals that are not errors, tests, and the second number and regression, and what the summary hides
- The effect a stopped trial reports — stopping rules
- The trials that stopped early — when a fixed width is reached
- A width rule on skewed outcomes — when a fixed width is reached
- False discoveries that arrive together — corrections, and what each controls
- The outcomes a trial could have stopped with — stopping rules
- A boundary for giving up — stopping rules
- Estimating how many nulls are true — corrections, and what each controls
- The interval with no resampling in it — the interval, studentised
- A look the trend asked for — stopping rules
- An order that spends the error rate — corrections, and what each controls
- A forecaster that rounds — a forecast that is a probability
- A horizon chosen after looking — when the data stops early
- A standard error that knows about the instruments — a variable that moves one thing only
- Intervals for the findings — corrections, and what each controls
- The assumption that identifies the mechanism — the value that is not there
- The moments a balance is told — weighting one sample into another
- The run length a declustering chooses — the tail past the last observation
- The slope of a density nobody can see — reversals that are not errors
- The smallest of three combinations — tests, and the second number
- The start an efficient robust line inherits — regression, and what the summary hides
11 September 2026
20 essays on what makes it checkable, when the data stops early, reversals that are not errors, tests, and the second number, regression, and what the summary hides, the distribution itself, weighting one sample into another, a variable that moves one thing only and a forecast that is a probability
- A coverage table with its own error — what makes it checkable
- The interval at the end of the curve — when the data stops early
- A dropout the data cannot see — when the data stops early
- The same draws for both methods — what makes it checkable
- Two analyses of one baseline — reversals that are not errors
- A simulation that stops when it looks settled — what makes it checkable
- One minus Kaplan–Meier is not a risk — when the data stops early
- The measurement that got them enrolled — reversals that are not errors
- The p-value a replication gets — tests, and the second number
- Two points that hide each other — regression, and what the summary hides
- Where the derivative is zero — the distribution itself
- A lead that a heavy tail keeps — reversals that are not errors
- A ratio whose interval has to be the whole line — the distribution itself
- A robust loss and a far x — regression, and what the summary hides
- A weight fitted to balance — weighting one sample into another
- Leaving each row out of its own first stage — a variable that moves one thing only
- The draws aimed at the tail — what makes it checkable
- The hazard ratio the follow-up chose — when the data stops early
- The liar with two answers — a forecast that is a probability
- Two ways to combine p-values — tests, and the second number
7 September 2026
50 essays on weighting one sample into another, a forecast that is a probability, coverage without a distribution, what conditioning on a variable does, a variable that moves one thing only, the value that is not there, the tail past the last observation, a standard error for a model that is wrong, what decides whether a tuning list decides, the interval, studentised, the same table at seven correlations, a probe from what the rule blocks and a charge that is not a straight line
- A score that balances — weighting one sample into another
- An identity in three terms — a forecast that is a probability
- Coverage from exchangeability alone — coverage without a distribution
- One arithmetic, three decisions — what conditioning on a variable does
- The assumption nothing tests — a variable that moves one thing only
- Three mechanisms and one dataset — the value that is not there
- Three shapes, one limit — the tail past the last observation
- What a wrong model estimates — a standard error for a model that is wrong
- A curve that is a binning — a forecast that is a probability
- Dropping the incomplete rows — the value that is not there
- How many observations a weight leaves — weighting one sample into another
- The bread and the filling — a standard error for a model that is wrong
- The maximum converges slowly — the tail past the last observation
- The two worlds that look the same — what conditioning on a variable does
- Weak, and back where it started — a variable that moves one thing only
- What the split costs — coverage without a distribution
- Adjusting for everything — what conditioning on a variable does
- Calibrated and useless — a forecast that is a probability
- Marginal is not conditional — coverage without a distribution
- One imputation is not an observation — the value that is not there
- Robust is not free — a standard error for a model that is wrong
- The region with no comparison — weighting one sample into another
- The threshold is a dial — the tail past the last observation
- What the first stage does not know — a variable that moves one thing only
- A collider before the treatment — what conditioning on a variable does
- A level with no data in it — the tail past the last observation
- A score that rewards lying — a forecast that is a probability
- A step that is not a ratio — what decides whether a tuning list decides
- Either model, but not neither — weighting one sample into another
- The count or the length — the interval, studentised
- The other dial — the same table at seven correlations
- The score is the modelling — coverage without a distribution
- The variance between imputations — the value that is not there
- Three corrections and a leverage — a standard error for a model that is wrong
- Whose effect it is — a variable that moves one thing only
- A set of pairs, not a vector — a probe from what the rule blocks
- An imputation model the analysis does not contain — the value that is not there
- Right for the wrong reason — a standard error for a model that is wrong
- The estimated weight is the better one — weighting one sample into another
- The miscalibration a perfect forecaster shows — a forecast that is a probability
- The sample is a condition — what conditioning on a variable does
- Two instruments that disagree — a variable that moves one thing only
- Two intervals for one return level — the tail past the last observation
- What the correction assumes — a charge that is not a straight line
- When the order matters — coverage without a distribution
- A charge that reads the draw — a charge that is not a straight line
- The clustering the tail has — the tail past the last observation
- The count that is not the rows — a standard error for a model that is wrong
- The mechanism the data cannot see — the value that is not there
- The variable the treatment caused — what conditioning on a variable does
2 September 2026
20 essays on the same table at seven correlations, the interval, studentised, what decides whether a tuning list decides, a charge that is not a straight line, overlap and complementarity, separated and a probe from what the rule blocks
- A margin that turns over — the same table at seven correlations
- An interval that carries its scale — the interval, studentised
- The eighth that was not a constant — what decides whether a tuning list decides
- The width a band is measured in — a charge that is not a straight line
- Two effects in one number — overlap and complementarity, separated
- What the rule blocks — a probe from what the rule blocks
- A lag the sample has less of — a charge that is not a straight line
- A model and a count — a probe from what the rule blocks
- The zero that was a crossing — the same table at seven correlations
- Two factors pointing opposite ways — what decides whether a tuning list decides
- What a zero is made of — overlap and complementarity, separated
- What studentising costs — the interval, studentised
- A line that beats two curves — a charge that is not a straight line
- A quantity that loses to a heuristic — a probe from what the rule blocks
- A split that depends on the order — overlap and complementarity, separated
- A table and a list — what decides whether a tuning list decides
- An answer that changes — the same table at seven correlations
- The ordering reverses again — the interval, studentised
- Counting it exactly does not help — a probe from what the rule blocks
- What a better charge buys — a charge that is not a straight line
31 August 2026
20 essays on the rate and the size of a disagreement, a charge for a covariance's own dimension, the block length read on a quantile, a probe chosen rather than picked, both halves of the dependence at once and two searches over different features
- A rate times a size — the rate and the size of a disagreement
- The charge nobody derived — a charge for a covariance's own dimension
- The instrument and the reading — the block length read on a quantile
- The part the rule already took — a probe chosen rather than picked
- Two failures that cancel — both halves of the dependence at once
- Two searches that share nothing — two searches over different features
- A length for each instrument — the block length read on a quantile
- A probe chosen from the design — a probe chosen rather than picked
- A search that is already the other — two searches over different features
- A symmetry that was not enough — both halves of the dependence at once
- The quarrel that changes the winner — the rate and the size of a disagreement
- What a window leaves free — a charge for a covariance's own dimension
- A copula that halves a marginal — both halves of the dependence at once
- A width that moves and an error that does not — a charge for a covariance's own dimension
- How often it matters — the rate and the size of a disagreement
- The reversal that was the instrument's — the block length read on a quantile
- Three quarters of the way to one search — two searches over different features
- What a chosen probe finds — a probe chosen rather than picked
- The zero that survives both — both halves of the dependence at once
- What the interval covers — the block length read on a quantile
30 August 2026
20 essays on a covariance with no parameter, the other half of the dependence, how long the list is, a block length chosen from the data, the diagnostic after the trial and two searches over one sample
- A family before a fit — a covariance with no parameter
- A zero that is arithmetic — the other half of the dependence
- The comparison that was not made — how long the list is
- The length nobody has — a block length chosen from the data
- The statistic the p-value is about — the diagnostic after the trial
- Two searches, one sample — two searches over one sample
- A probe nobody chose — the diagnostic after the trial
- An ordering that depends on the rule — a block length chosen from the data
- The charge that is not a sum — two searches over one sample
- The plug-in and the maximum — a covariance with no parameter
- The symmetry the marginals could not show — the other half of the dependence
- The volume a whitening moves — how long the list is
- A charge that depends on the rule — two searches over one sample
- A list is not a rule — how long the list is
- Half a reference distribution — the diagnostic after the trial
- Nothing in the fit picks the width — a covariance with no parameter
- What choosing the length costs — a block length chosen from the data
- Which tail the cut sits in — the other half of the dependence
- Before the trial and after — the diagnostic after the trial
- What fitting them together buys — a covariance with no parameter
29 August 2026
20 essays on paying for a search, fitted together, or fitted after, what a chain cannot report, a guarantee that needed a symmetry and where a taper's case begins
- A break that was looked for — paying for a search
- A dependence fitted with the line — fitted together, or fitted after
- A test rather than a survey — what a chain cannot report
- A zero that rests on a symmetry — a guarantee that needed a symmetry
- The gap a sample shows — where a taper's case begins
- A split survives what a mean does not — a guarantee that needed a symmetry
- Bias is not the whole of it — where a taper's case begins
- The fit that takes the memory out — fitted together, or fitted after
- The statistic that changes sign — what a chain cannot report
- What a search costs in parameters — paying for a search
- A defect that is about size — what a chain cannot report
- Choosing whether to break — paying for a search
- Iterating is not maximising — fitted together, or fitted after
- Measuring a variance rather than a quantile — where a taper's case begins
- The cut that is not a quantile — a guarantee that needed a symmetry
- A second break on a flat profile — paying for a search
- A window for every candidate — fitted together, or fitted after
- Balancing a skewed covariate — a guarantee that needed a symmetry
- The diagnostic at two hundred — what a chain cannot report
- The error no window repairs — where a taper's case begins
28 August 2026
12 essays on a block, weighted inside itself, the shape a dependence has, what a dictionary buys and what it costs and when a fixed width is reached
- A block weighted inside itself — a block, weighted inside itself
- A dependence with a shape — the shape a dependence has
- A dictionary that is neither — what a dictionary buys and what it costs
- A width the trial has to stop for — when a fixed width is reached
- A taper and a critical value — a block, weighted inside itself
- Stopping on the arms — when a fixed width is reached
- What the extra function buys — what a dictionary buys and what it costs
- Where the generality runs out — the shape a dependence has
- The set a dictionary leaves — what a dictionary buys and what it costs
- The window a whitening wants — the shape a dependence has
- The order the tail is drawn at — the shape a dependence has
- The walk that cannot cross — what a dictionary buys and what it costs
26 August 2026
12 essays on estimating the dependence, not naming it, a cut point, at a correlation and what a block may vary
- A covariance with no parameter in it — estimating the dependence, not naming it
- A cut is not a polynomial, and it does not have to be — a cut point, at a correlation
- A proposal that moves more than two units — what a block may vary
- Stationary is not convergent — what a block may vary
- The arcsine that closes it, and the error that was overstated — a cut point, at a correlation
- The window that has to be chosen, and the term that was dropped — estimating the dependence, not naming it
- The triangle that was not the multiplier's — estimating the dependence, not naming it
- The zero that survives a cut — a cut point, at a correlation
- Where the gain is, and where the decision is — what a block may vary
- A ratio that changes between blocks — what a block may vary
- Errors generated from a fitted model — estimating the dependence, not naming it
- The bias that lands in the slope — what a block may vary
24 August 2026
12 essays on counting what is independent, when the two are not independent and the weights the corner needs
- A penalty is a trace — counting what is independent
- The fourth moment that was missing — when the two are not independent
- Weights that need only a ratio — the weights the corner needs
- A zero that was an assumption — when the two are not independent
- Blinded, and still exact — the weights the corner needs
- One number for a table of candidates — counting what is independent
- The condition that cannot be dropped — the weights the corner needs
- The repair that was exact and made it worse — counting what is independent
- Walking the admissible set — when the two are not independent
- Draws that repeat each other — when the two are not independent
- The residuals are not the errors — counting what is independent
- What a multiplier cannot keep — counting what is independent
23 August 2026
12 essays on scoring a search without spending data, when the set is too large to walk and a promise about two arms
- A criterion is a prediction of the hold-out — scoring a search without spending data
- A dictionary that is a product — when the set is too large to walk
- A width promised for a difference — a promise about two arms
- Where the enumeration stops — when the set is too large to walk
- Where the two searches cross — scoring a search without spending data
- Which weights are the inverse variances — a promise about two arms
- A count that has to be estimated — when the set is too large to walk
- The degrees of freedom in the sums — a promise about two arms
- Two defects and one resampling — scoring a search without spending data
- How long a block a multiplier shares — scoring a search without spending data
- What a reference distribution costs to sample — when the set is too large to walk
- What a two-arm rule may not pool — a promise about two arms
22 August 2026
12 essays on choosing what the rule reads, the block size as a schedule and a search with no fixed point
- A basis is a subspace — choosing what the rule reads
- A block size that changes — the block size as a schedule
- When the benchmark is a candidate — a search with no fixed point
- The displacement is a parameter count — a search with no fixed point
- Two degrees of freedom, one total — the block size as a schedule
- Which shapes are worth protecting — choosing what the rule reads
- Residuals that keep their own variance — a search with no fixed point
- What a schedule actually buys — the block size as a schedule
- Where the guarantee is exactly zero — choosing what the rule reads
- A schedule that reads the mean — the block size as a schedule
- The corner the test is calibrated at — a search with no fixed point
- When the constraints run out — choosing what the rule reads
21 August 2026
12 essays on searching among fitted models, the shape the covariate enters by and what the procedure may not read
- A table of nested models — searching among fitted models
- Balanced on the wrong function — the shape the covariate enters by
- The guess with two numbers in it — what the procedure may not read
- A null with a model in it — searching among fitted models
- A threshold in the tail — the shape the covariate enters by
- The worst case in two directions — what the procedure may not read
- The rule that cannot see the mean — what the procedure may not read
- The weight that is a vector — searching among fitted models
- Three functions of one number — the shape the covariate enters by
- The analysis and the shape — the shape the covariate enters by
- What the blindfold costs — what the procedure may not read
- When every null is true — searching among fitted models
19 August 2026
12 essays on balancing what has no levels, what the design is asked to guarantee and the best of a set, and what the search costs
- A covariate with no levels — balancing what has no levels
- An efficiency that is a ratio — what the design is asked to guarantee
- What the other forecast adds — the best of a set, and what the search costs
- Eight forecasters and one benchmark — the best of a set, and what the search costs
- Protecting one parameter over a range — what the design is asked to guarantee
- The rule that reads the number — balancing what has no levels
- Stopping when it is precise enough — what the design is asked to guarantee
- The models that were never in the running — the best of a set, and what the search costs
- What the balanced trial is worth — balancing what has no levels
- A distribution drawn from the null — the best of a set, and what the search costs
- Balancing more than one number — balancing what has no levels
- The interval after a stop it chose — what the design is asked to guarantee
18 August 2026
12 essays on a design that assumes less, more arms than two and comparing two forecasters
- The design for the worst case — a design that assumes less
- Three arms and three scores — more arms than two
- Which forecast is better — comparing two forecasters
- Balancing towards unequal targets — more arms than two
- When one model contains the other — comparing two forecasters
- Where the minimum is attained — a design that assumes less
- Correcting the persistence — comparing two forecasters
- The analysis after three arms — more arms than two
- The design that stops guessing — a design that assumes less
- Guessing one arm in three — more arms than two
- The repair that moves the wrong number — comparing two forecasters
- What a design chosen from the data costs — a design that assumes less
17 August 2026
12 essays on balancing on what was recorded first, the criterion, and what it assumes and the observation that has not happened
- Balancing what is known in advance — balancing on what was recorded first
- The family behind the letters — the criterion, and what it assumes
- What the model says next — the observation that has not happened
- The interval that forgets it estimated — the observation that has not happened
- The rule that can be guessed — balancing on what was recorded first
- The two terms anybody wanted — the criterion, and what it assumes
- Choosing the order — the observation that has not happened
- The analysis has to know the rule — balancing on what was recorded first
- The design that needs the answer — the criterion, and what it assumes
- The design that hedges — the criterion, and what it assumes
- The interval after the choice — the observation that has not happened
- The reference the covariates supply — balancing on what was recorded first
15 August 2026
12 essays on a design chosen rather than looked up, the reference distribution the design supplies and three series, and a count
- A design is a number — a design chosen rather than looked up
- The experiments that could have happened — the reference distribution the design supplies
- Three series and a count — three series, and a count
- The test that needs the rule — the reference distribution the design supplies
- The theorem that says when to stop — a design chosen rather than looked up
- Which series goes on the left — three series, and a count
- Counting what is still wandering — three series, and a count
- Four letters and two camps — a design chosen rather than looked up
- The plus one and the round number — the reference distribution the design supplies
- The design that has to be integers — a design chosen rather than looked up
- What the exactness buys — the reference distribution the design supplies
- Which series does the moving — three series, and a count
14 August 2026
12 essays on designs that change while they run, splitting the units and the surface between the corners
- Choosing n after looking — designs that change while they run
- Not half and half — splitting the units
- The design that cannot see a curve — the surface between the corners
- Randomising towards the winner — designs that change while they run
- The cost of a unit — splitting the units
- Walking up the gradient — the surface between the corners
- Dropping the losers — designs that change while they run
- One control, many arms — splitting the units
- Three levels, and the ring where the design says the same thing — the surface between the corners
- Allocating on a guess — splitting the units
- The estimate after the choice — designs that change while they run
- The optimum is a ratio, and its interval is sometimes the whole line — the surface between the corners
11 August 2026
12 essays on series that move together, hierarchy past one number and the spread, and its own uncertainty
- The regression that is not spurious — series that move together
- The slope that borrows — hierarchy past one number
- What the plug-in forgets — the spread, and its own uncertainty
- A prior on the spread — the spread, and its own uncertainty
- Pooling a proportion — hierarchy past one number
- The test with no table — series that move together
- Borrowing towards a line — hierarchy past one number
- The model that corrects its error — series that move together
- When the spread estimates to zero — the spread, and its own uncertainty
- The cost of differencing a pair — series that move together
- The interval that integrates — the spread, and its own uncertainty
- Two levels at once — hierarchy past one number
10 August 2026
12 essays on groups that borrow, when the observations repeat each other and decided before the data
- Eight groups, one population — groups that borrow
- The observations that repeat each other — when the observations repeat each other
- The variance removed before the data — decided before the data
- Randomisation is not balance — decided before the data
- The weight that decides — groups that borrow
- Two walks and a finding — when the observations repeat each other
- One factor at a time — decided before the data
- The prior the data estimates — groups that borrow
- What differencing costs — when the observations repeat each other
- How many subjects — decided before the data
- The check before the standard error — when the observations repeat each other
- When borrowing goes wrong — groups that borrow
8 August 2026
15 essays on when the data stops early, regression, and what the summary hides, the prior, doing visible work, corrections, and what each controls and stopping rules
- The data that stops early — when the data stops early
- The line that one point drew — regression, and what the summary hides
- What a prior is worth — the prior, doing visible work
- What the correction corrects — corrections, and what each controls
- When the looking happens — stopping rules
- Four datasets, one summary — regression, and what the summary hides
- Spending the error rate — stopping rules
- The curve that survives censoring — when the data stops early
- Two different promises — corrections, and what each controls
- What a credible interval covers — the prior, doing visible work
- R² is not a measure of fit — regression, and what the summary hides
- The price of control — corrections, and what each controls
- Where the two schools agree — the prior, doing visible work
- The base rate was always Bayes — the prior, doing visible work
- Twenty residual plots — regression, and what the summary hides
6 August 2026
19 essays on tests, and the second number, reversals that are not errors, the distribution itself, what makes it checkable and intervals, counted
- A p-value that is not flat is not a p-value — tests, and the second number
- Simpson's reversal is a region, not a table — reversals that are not errors
- Sums of almost anything — the distribution itself
- The seed is part of the figure — what makes it checkable
- What the 95% refers to — intervals, counted
- More data is not monotonically better — intervals, counted
- The tail converges last — the distribution itself
- Two routes to every number — what makes it checkable
- What a p-value does not say — tests, and the second number
- What a positive test is worth — reversals that are not errors
- Regression to the mean — reversals that are not errors
- The winner's curse — tests, and the second number
- Twenty intervals and one expected miss — intervals, counted
- What normal actually looks like — the distribution itself
- The shape, and where its mass is — the distribution itself
- The shortest interval is the one that misses — intervals, counted
- Twenty analyses of nothing — tests, and the second number
- Where the bootstrap lies — intervals, counted
- The correction for not knowing the spread — intervals, counted