This blog currently weights 200 pounds. It's inscribed in my data base, so it must be true. 200 is the latest in a series of daily morning readings wearing the same clothing, at the same time of my day. But how is that 200 measured? And is 200 good or bad? Can 200 be trusted? My last four daily morning readings were 201, 202, 201, and now 200.
Today I stepped on the scale 3 times in a row. A needle swings around and points at a number that I can't read accurately because I'm too tall (or my eyes with glasses are not fully corrected for reading scale fine-print at a distance of 5 feet 7.5 inches not adjusting for head tilt). The scale read 200, 201 and 200, very clearly in 3 consecutive procedures: step on scale, let scale (and me) settle, step off scale, let scale (and me) settle. At a guess, scales have a measurement error of roughly 1 pound. At least, that's my statistical conclusion about my scale, having been informally thinking about measurement error and scales (or this scale anyway) and weight for many years. As a statistician, I think of measurement error as something with a standard deviation (SD), but measurement error could be assessed in other ways, perhaps as a (minimum, maximum) pair, or as the range = maximum minus minimum, where the minimum and maximum are the absolute farthest outside readings possible given a true value x, with minimum < x < maximum.
Why did I step on the scale 3 times? (1) It's Saturday and I'm not in a rush and I can take the time. (2) Actually recording 200 has important meaning as a milestone, (3) Because 200 is a change from the previous day, it is more important as a conclusion than if 200 was the same as the past 3 weights, (4) Because 200 is a change, it is less believable than if it was the same as the previous measurement, (5) I want to be careful to not get over-excited or discouraged and not to be or get over-optimistic or under-pessimistic.
Lets unpack those reasons. Reason (1) is cost. I'm not rushing to beat traffic, and can take the time to be careful in the measurement. Reasons (2) and (3) are about utility. Both reasons note that a conclusion that I weigh 200 (and 200 is less than and different from yesterday's 201 reading) is more important to me personally than if the weight was 198 or 202. Reason (4) reflects a hazily-thought-of but simple model for weight that says today's weight should be similar to yesterday's weight. Even if I'm losing weight, that's still a sensible model in the short term. It can be improved, but provides a reasonable guide to thinking about weight readings in the short term. Finally, reason (5) is thinking of the future. Emotion is the enemy of careful measurement. If I get excited, and start looking forward to weighing a svelte 180 or something clearly ridiculous in the short term, then I'll quickly get discouraged when the scale never reads in the low 190s much less 180. I will then fail at any reasonable short term goals; I will stop recording my weight, and I will stop trying to eat healthy enough to continue to lose weight. In contrast, if my reading was the same as the last 3 readings, not much need to be careful; my weight has plateaued, the reading is believable, and I'd step on, read the number and step off and go on my way.
Yesterday blogwife was available for reading the scale. She thought the reading was right in between 200 and 201. I stepped on the scale 3 times and decided to record 201. If this is a momentary blip down, I don't want to get discouraged if the next 7 daily weights are 201. And if tomorrow my weight is 199, then even more fun to have dropped 2 pounds instead of 1 pound. Notice that today's reading involved a decision. Out of those last 4 weights, each of those 201 measurements involved a decision to not record 200. Only the 202 was clearly not a 200. Today's 200, yesterday's 201 and Wednesday's 201 readings all involved a decision. Those negative decisions made it easier to decide to record 200 today, I've been holding off recording a 200, but finally decided to go for it today.
Notice that utility as much as accuracy went into the decision to record 201 yesterday and 200 today. Measurement often involves decisions, and considerations that go into these decisions are typically not recorded. My scale isn't perfectly accurate, but a bigger source of error is that for personal reasons, I may report some number not what I read off the scale.
People don't like to report bad results. Think about gambling wins and losses. When was the last time your friends went to Las Vegas and reported losing $100 at the slot machines? They're much more likely to tell you about the $5 gain on their previous trip, then about the loss this current trip. Las Vegas is the beneficiary of much free advertising because of this! We all hear about the gains, often multiple times, but we rarely hear about the losses.
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