Your sleep moves more than the thing you are testing

How many nights before a change in your sleep means something? The question gets treated as being about the intervention — a bigger effect needs fewer nights. It is mostly about the noise. Sleep already moves night to night with nothing done to it, and the size of that movement sets a floor under what any quantity of data can resolve. The floor is higher than most protocols assume.

How much a normal night moves

Messman and colleagues pooled eight datasets of healthy sleepers — 2,404 people, 26,121 days of sleep data — and computed each person's own standard deviation across their own nights before summarising across people [1].

That is the EEG figure, the tightest of the three modalities. Actigraphy gave 77.41 minutes and sleep diaries 85.80. As coefficients of variation the three agree closely, at 18.57%, 19.11% and 19.19%. The root mean square of successive differences, which compares each night to the one before rather than to the person's average, is larger again: 91.93 minutes by EEG. Sleep efficiency moved less, at 6.46%.

What that costs in nights

Put the number to work. For a two-condition comparison at α = 0.05 two-sided and 80% power, the standard calculation asks for roughly 15.7 σ²/δ² nights in each condition. With σ = 67.04 minutes, resolving a 30-minute shift in nightly sleep takes about 79 nights per condition — five months of alternating nights. A 10-minute shift takes about 706 per condition, close to four years.

No paper reports those two figures — they are ours, from Messman's σ and a textbook formula, and you can redo them in a line. Thirty minutes a night is a large change and few interventions produce one; ten minutes is the order of magnitude supplement meta-analyses report. Both counts are floors rather than estimates, because the formula treats consecutive nights as independent draws and sleep is not that.

Not every metric is equally noisy

Mullins and colleagues came at the same problem as reliability, putting 107 cognitively normal older adults through two consecutive nights of laboratory polysomnography and scoring agreement between them [2].

Slow-wave sleep percentage did better at 0.67 (95% CI 0.55 to 0.76) and REM percentage worse at 0.43 (0.22 to 0.59). The microstructure underneath reached 0.97 (0.95 to 0.98) for parietal spindle density. The EEG features are close to a fingerprint; the stage summaries built on them are not.

The agreement side gives a unit a person can act on: the smallest real difference between two nights for total sleep time was 68.8 minutes.

Your own variance is slower to measure than your own average

If variance sets the floor, how long does it take to pin the variance down? Leota and colleagues had the data to answer: 10,412 people wearing a WHOOP strap for 363 consecutive nights, 3,700,492 person-nights, each person's full-year value as the reference and r > .80 as the bar [3].

Metric by metric the gap holds and widens. Sleep percentage needed four nights for its mean and 62 for its SD; wake after sleep onset needed five and 65. Variability estimated from seven to fourteen nights correlated only .50 to .67 with the year-long reference, and a seven-night SD of total sleep time carried 95% limits of agreement of ±50.5 minutes.

What this does not establish

None of these studies measured you. They report distributions of within-person SDs, and the spread is wide: Messman's 67.04 minutes carries a between-person SD of 28.74 minutes, so somebody two standard deviations either side faces arithmetic several times harsher or kinder than ours. The count you need is personal, and on Leota's numbers it takes about six weeks of data before you can estimate it.

The samples are narrow in different directions. Mullins studied adults aged 54 to 84 across two in-laboratory nights, a setting with its own first-night effect, and two points cannot separate within-person from between-person variance. Leota's cohort were people who bought a wearable, and the authors note the estimates are specific to devices using motion and heart rate rather than EEG. Messman's pooled sample was mostly young, college-educated and White, and the authors say so.

Our night counts inherit the formula's assumptions: normality, a constant effect, independent nights. The last is false for sleep, and the error runs against the experimenter. We also found no within-person SD for deep sleep in minutes that we were willing to cite, so the arithmetic covers total sleep time only — not the metric dashboards lead with.

And none of this says whether any particular intervention works. It says the measurement is harder than a trend line implies.

Why this is an n-of-1 problem

A population trial dilutes this by recruiting. Night-to-night noise averages out across hundreds of people, so a ten-minute effect is reachable in a study that runs a fortnight, and the variance the design has to beat is the one between bodies. Running the trial on one body closes that exit. The only thing that averages down a within-person SD of 67 minutes is time, and time is the resource a self-experiment cannot buy more of.