How much does medium activity min have to change before it stops being noise? The threshold from 712 nights

With 28 nights of history, medium activity minutes need to shift by 80.6% before that change can be called signal rather than noise. With 56 nights of context, the threshold drops to 56.99%. With 84 nights, to 46.53%. With 168 nights, it reaches 32.9%. These thresholds come from 712 nights of a single body, measured by the same device without gaps. The median for this variable across that period was 18 minutes per day.

That threshold feels steep. An 80.6% shift is a large move. But the threshold is not set by the researcher. It is set by the variable.

A variable with extraordinary noise

The coefficient of variation (CV) for medium activity minutes is 143.87%.

A CV above unity means the standard deviation exceeds the mean. This variable has no stable baseline. Some days register 0 minutes. Other days register far more than 18. The median is just the midpoint of a very wide distribution.

The real coefficient of variation (RCV) is 398.79%. This number translates the volatility into practical terms. The typical variation of this variable, measured against its own median, is 398.79%. A change that does not clear that figure falls within the normal range of fluctuation. It is not that the reading is false. It is that the change cannot be separated from the variable's ordinary behavior.

The serial correlation (rho) is 0.067. This measures whether yesterday's value predicts today's. A rho of 0.067 is very close to zero. Yesterday carries almost no information about today. The variable has no useful day-to-day memory. Trends cannot be built from two or three readings. Patterns only emerge once there is enough accumulated history.

Three numbers together — CV of 143.87%, RCV of 398.79%, rho of 0.067 — describe a variable that moves a great deal, erratically, with no persistent daily pattern. For this variable, the noise floor is the most important piece of data.

The source row table

Metric	Value
Nights measured	712
Median (min/day)	18
CV (%)	143.87
Serial correlation (rho)	0.067
RCV (%)	398.79
Threshold at 28 nights (%)	80.6
Threshold at 56 nights (%)	56.99
Threshold at 84 nights (%)	46.53
Threshold at 168 nights (%)	32.9

Source: ruido.medido.json#medium_activity_min — 712 nights, one body, one device.

Why the threshold changes with history length

The windows of 28, 56, 84, and 168 nights are not arbitrary. They are calculation windows. Each one reflects how many nights of history the system needs to stabilize its estimate of the noise floor for this variable.

With 28 nights, the estimate is imprecise. The history is short. The system's picture of normal fluctuation for this variable is still rough. So the threshold is conservative: 80.6%. Only a very large shift can be distinguished from that uncertainty.

With 56 nights, the picture sharpens. The threshold drops to 56.99%. With 84 nights, to 46.53%. With 168 nights, it reaches 32.9%.

The logic is worth holding. More history does not make the variable less noisy. The variable stays exactly as noisy. What improves is the precision of the noise estimate. A threshold built on 168 nights is more accurate than one built on 28 — not because the variable changed, but because the system has more data about how this variable behaves when nothing unusual is happening.

What the threshold answers — and what it does not

The threshold answers one specific question. Did this change exceed the expected variability of this variable, given the available history?

It does not answer why the change happened. It does not say whether the change is good. It does not say whether the change will last. Those are different questions. They require different study designs.

With 28 nights of history, a shift needs to clear 80.6% before it is worth tracking as signal. Anything below that falls within the normal variation range for this variable. That does not mean nothing happened. It means the available history cannot tell the difference.

With 168 nights, the threshold is 32.9%. A sustained shift above that level has a statistical basis for being called a real displacement.

The detector is a first filter. It separates probable movement from expected variation. It is not the last word in analysis.

The limit

This threshold comes from 712 nights of a single body. It is not a population standard. It is not a clinical reference. It is the noise map of one person, measured with one device.

If your CV differs from the 143.87% in this record — and it probably will — your thresholds will differ too. The method transfers. The specific number is personal. The method says: measure your own noise, using your own history, before declaring that something changed.

This data does not establish causation. A shift that clears the threshold is a statistical signal. It is not a health outcome. The relationship between this variable and any clinical result requires a study design that this dataset does not have.

The 712 nights come from one device. Comparing absolute values across different devices is not covered by these thresholds. The sensor, the calculation window, and the algorithm are all part of the number. Change the device and you change the number.

The full dataset holds 18,483 measurements across 31 variables, all from a single body. It is a noise archive. It is not an efficacy trial. It is published here because no study of these variables had released this kind of map before.

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Mental Work — all protocols · related file: magnesium-for-sleep · open science — the dataset