Thoughts about thinking

When I step on my Wii Fit and it tells me I’ve gained 2lb, how worried should I be? Well, that depends on how variable my weight is, day to day. Anna and I have done a simple study, and found that each others weight accounts for 50% of the variation in our own weight. And large variation occurs over the scale of days – meaning that it is all water. Our weights are (on a day to day basis) determined by the things we share in common – food and drink intake.

Dan's (black line) and Anna's (red line) weights over time, plotted in normalised units (*see below) making both weights 1 on average. These were recorded over a period of 56 days from July to September 2007.

There are some surprising results here. The range of values is 5% of the average – meaning that if I weighed 10 stone, I could measure myself twice in a month and differ by half a stone! the standard deviation is 1%, meaning that though I weigh on average 10 stone I would on an average day be 1.4lbs away from it. And daily we vary by 0.8%, so I’d differ by just over a pound on average. So for every day with no change, there is a day with 2lbs difference.

The numbers become more meaningful when our weights are compared. My weight and Anna’s correlate at 49%, meaning that half of our variation is explained by a common factor. During the months of note taking, I was cycling to work and Anna was exercising at home. We were getting exercise together only really at weekends. But we ate dinner together every evening, and we drank beer and wine at the same times. That is what is controlling that 50%. And because it comes off so quickly, its can only be weight stored as water – we vary this much simply by varying how much water we are retaining in our bodies.

Dan and Anna's weight plotted against each other. The correlation line is a least-squares fit with correlation 0.5 and p-value 0.003, meaning that there is only a 0.3% chance that such srtrong correlation could be spurious.

Most trends in weight are gone in 4 days, but there is strong evidence (p<0.001) for a (weak) trend over the study period. Yet our weights now match the mean of the data, so this trend is also variation – its just happening over very long times. In other words, we vary day-to-day, and we vary month-to-month, yet we don’t vary year-to-year.

Problems with the study

To start with, the data isn’t taken over a very long time (or for enough people). It would be interesting to see if there were weekend effects or monthly effects. Secondly, we didn’t record any useful information about food intake, exercise levels, etc, so we can’t examine where the correlation really does come from and what other factors help to explain it. Additionally, like all long-term measurements, the conditions aren’t always identical. The readings are all in the mornings but sometimes before, sometimes after breakfast.

However, the weights recorded here are statistically identical to our recent weights so they were taken from our average variation – there were no long term trends that could have effected them.

Conclusions

Don’t fret small changes in weight! It takes a long time to lose fat, and small changes in water retention can mask it all. What we eat clearly does matter a lot, but over the long term it comes down to the simple equation:

Weight gained (energy units) = energy consumed – energy used

Over the short term, all diets will simply change water retention, so keep an eye on your weight over months to be sure that the trend is real! Even if weight is gained or lost for a month it would return to where it was if there are no lifestyle changes. Simply put: lifestyle determines weight, and that is a very difficult thing to modify.

And don’t let Wii Fit tell you off for a couple of extra lbs

* Units of measurement

In order to protect Anna’s and my own privacy on the web, the results have been presented in convenient units. Anna’s weight is measured in “Metric Anna’s”, so the average weight is one. Dan’s weight is measured in “Imperial Stormtroopers”, since he is one (in his head at least) and therefore his weight also averages to 1.

Interestingly, the “Imperial Stormtrooper” is also the traditional unit of measurement for ineffectiveness – 1 Stormtrooper achieves exactly nothing, although it can shoot wildly and miss. However, this causes problems in this study when Dan measures more than 1 Stormtrooper, as he becomes negatively effective. This is sometimes apparent when he washes up, as plates can mysteriously get dirtier with washing. The measurement for Annas used to be Imperial as well, but they declared themselves Queen and insisted the servants had to do the washing up (clearly a bad idea with only Stormtroopers around). Hence the need for a more modern measurement that neatly averaged to 1 as well as tidying up after themselves in the kitchen.