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BMJ Open. 2012; 2(5): e000887.
Published online 2012 September 4. doi:  10.1136/bmjopen-2012-000887
PMCID: PMC3437435

Patterns in wireless phone estimation data from a cross-sectional survey: what are the implications for epidemiology?



Self-reported recall data are often used in wireless phone epidemiological studies, which in turn are used to indicate relative risk of health outcomes from extended radiofrequency exposure. We sought to explain features commonly observed in wireless phone recall data and to improve analytical procedures.


Wellington Region, New Zealand.


Each of the 16 schools selected a year 7 and/or 8 class to participate, providing a representative regional sample based on socioeconomic school ratings, school type and urban/rural balance. There was an 85% participation rate (N=373).

Main outcome measures

Planned: the distribution of participants’ estimated extent of SMS-texting and cordless phone calls, and the extent of rounding to a final zero or five within the full set of recall data and within each order of magnitude. Unplanned: the distribution of the leading digits of these raw data, compared with that of billed data in each order of magnitude.


The nature and extent of number-rounding, and the distribution of data across each order in recall data indicated a logarithmic (ratio-based) mental process for assigning values. Responses became less specific as the leading-digit increased from 1 to 9, and 69% of responses for weekly texts sent were rounded by participants to a single non-zero digit (eg, 2, 20 and 200).


Adolescents’ estimation of their cellphone use indicated that it was performed on a mental logarithmic scale. This is the first time this phenomenon has been observed in the estimation of recalled, as opposed to observed, numerical quantities. Our findings provide empirical justification for log-transforming data for analysis. We recommend the use of the geometric rather than arithmetic mean when a recalled numerical range is provided. A point of calibration may improve recall.

Keywords: numerosity, cellular telephone, mental recall, Epidemiology , estimation technique

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