Household log entries written from memory at the end of the day show more rounded values than entries written at the moment of reading

Hypothesis

Rounding a number to fewer digits is a defined operation; NIST SP 811, Appendix B.7.1, gives rules for it. What a household log does not record is rounding that happens without a rule, in memory, between reading an instrument and writing the entry. The hypothesis is that entries written later from memory are more often rounded than entries written at the instrument: the last digit is more often 0 or 5, fewer decimals are recorded, and values cluster on multiples of the display's coarsest step. The concern is not the small error of a single rounded entry but that a log with an unknown mix of rounded and unrounded entries has a resolution nobody knows, so that a week-to-week change smaller than the rounding step cannot be distinguished from rounding.

Prediction

Within one household and one instrument, entries written at the instrument show a distribution of last digits close to uniform (for a digital display) and record the number of decimals the display shows; entries written from memory at the end of the day show an excess of 0 and 5 as the last digit and fewer decimals. The effect grows with the delay between reading and writing and with the number of readings a person tries to remember at once, and is smaller for readings that are photographed and transcribed later, because the photograph removes memory from the path.

Proposed test

1. Pick one instrument with a digital display of at least three digits (an electricity meter, a kitchen or bathroom scale, a thermometer) and one reader.
2. For four weeks, alternate days: on even days write the reading into the log at the instrument; on odd days read the instrument at the same time but write the entry in the evening from memory. On all days also photograph the display immediately, and keep the photographs unseen until the end.
3. At the end, transcribe the photographs as the reference series and compare, per condition: the share of entries whose last digit is 0 or 5, the number of decimals recorded, and the difference between the entry and the photograph.
4. Report the counts per condition, not only the shares, and note any day where the protocol slipped.

Status

No result is claimed. Four weeks give only 14 entries per condition, so the test can show a large effect and cannot rule out a small one; two or more households running the same protocol would help, and the photograph step is what makes the comparison possible at all.