Reports of a possible link between obesity and morbidity have prompted one of our occasional contributors, Martin Vlietstra, to look at issues around measuring body weight in the home.
Whilst we still do not know much about the Covid-19 virus, press reports suggest that many if the victims were either frail or were overweight. Metric Views cannot comment on the accuracy of these reports but nevertheless it is instructive to look at the principles of logging one’s weight and BMI (body-mass index).
The newspapers that reported on the degree of obesity amongst Covid-19 victims often quote the formula for calculating somebody’s BMI as being “their weight expressed in kilograms divided by the square of their height expressed in metres”. The same newspapers then use stones to describe people’s weights and feet and inches to describe their heights. For example, many newspapers have stated that in 2018 Boris Johnson weighed 16½ stone and was 5ft 9in tall. This is not very helpful for working out his BMI. These figures are equivalent to approximately 105 kilograms and 1.75 metres, giving people of his stature a BMI of a little over 34. (According to medical specialists, an ideal BMI is between 18 and 25; 25 to 30 is classed as being overweight; 30 to 40 is obese and above 40 is morbidly obese).
Although many apps exist for smartphones that will calculate one’s BMI using imperial units, imperial units have a hidden problem of rounding. People who use imperial units for their weight often round it to the nearest half-stone, whereas those who use metric units will round to the nearest kilogram. If somebody of Mr Johnson’s stature were to increase their weight by half a stone, their BMI would increase by 0.96 which is quite a big step, especially if one is monitoring one’s BMI. If however they used kilograms, the increase (or decrease) in BMI if their weight increased (or decreased) by one kilogram would be 0.33 kg, a much more manageable step.
A similar rounding problem exists in the way in which people record their heights. Those using imperial units tend to round their height to the nearest inch while those using metric units tend to round to the nearest centimetre. If somebody made an error of one inch when measuring their height (or rounded the odd half-inch up rather than down), the difference in BMI of somebody of Mr Johnson’s stature would be 1.04, whereas if the difference was one centimetre, the resultant difference in BMI would be 0.39, again a much smaller difference.
Of course, if one used stones and pounds, rounded one’s weight to the pound and rounded one’s height nearest half inch to calculate one’s BMI, the difference between metric and imperial units would not be so dramatic, but it would mean using a degree of precision that is often not used by the person in the street.
If you want to buy a new set of bathroom scales in order to monitor your weight, what should you look out for? Digital scales have a large number of features such as memories, self-zeroing facilities and the like which affect the price, but what about the actual weighing mechanism. Mechanical bathroom scales that can give the same precision as digital models are prohibitively expensive, so I will only look at digital scales. All digital scales have a load cell that give a voltage output, an associated analogue to digital convertor (ADC) and a microprocessor to handle the output from the ADC. The output from the ADC has a specified number of bits (often 10 or 12), with each bit representing the smallest increment that the scale will display. Some scales only have one range which means that all measurements will have the same precision while other scales have an “auto-range” facility whereby the electronics will automatically switch between different ranges, depending on the scale. My bathroom scales (which I bought 20 years ago), has three ranges: below 50 kg where one bit represents 0.1 kg, 50 to 100 kg where one bit represent 0.2 kg and 100 to 150 kg where one bit represents 0.5 kg. Most models have metric/imperial switches, but on the cheaper models the conversion is done in the firmware, resulting is some awkward (though invisible) rounding errors. Only the more expensive models have imperial auto-ranging (where one bit can represent 8oz, 4oz or 2oz) alongside metric auto-ranging. On examining the packaging of a number of different models, I found that the manufacturers were reluctant to publish any real details about the precision of their models.
Where does that leave us? If you wish to record weight changes on a spreadsheet, then metric units win hands down (something that Gunter realised in 1620 when he invented the link and the chain with 100 links in a chain, 10 chains in a furlong and 10 square chains in an acre thereby making it easier to measure land area). If you want an economy of the way in which you express your weight and height, then again metric units win – you get a better precision by using a round number of centimetres and kilograms than by using a round number of inches and [half]-stones. Finally, all digital bathroom scales have been designed with the metric market in mind – the imperial market being a “bolt-on”. Your choice of model of bathroom scale will depend on the additional features that you want and how much you wish to pay.