Well a week has gone by and I have a lot more data and lots of things to talk about relative to last week’s post. Lots to analyze and not sure how to do it, so
need some help here, Nate!
We’ll start with the “money graph” (defined last week) with a single updated point (today’s weigh-in (multiple with “consensus” guess)):
Last week I extrapolated out to 21st period but this week I added actual point (for week 7, 232.6) and extrapolated out to week 8 (next week) which is what I’ll be doing in future posts. Now as with previous weeks I “guessed” what the week 7 value should be through my mental consensus of multiple measurements (more in next graph). This guess is a bit “high” compared to any of various ways I could project it, but in this case uses my “intuitive” sense (plus if I guess too low this week it will eat into meeting next week’s goal, plus make the slope (weekly decrease) a bit more aggressive). So here’s the actual raw data, measured in roughly consistent scale position, over about an hour:
So there is a fair amount of variation, including the obviously (although Nate would never say this) out-of-range low value. But using Nate’s approach of never second-guessing data (discarding inconvenient values) I use a couple of different techniques to estimate, ending up with 232.19 which is quite a bit lower than the value I “intuitively” used of 232.6. So what you say: well, extrapolation, esp. a long time into the future can fairly strongly depend on this value since I only have seven “actual” data points. Now I tried to understand the variation in weighing, which I’ll discuss next, but I couldn’t really figure out what was going on so I think there is considerable uncertainty (about 0.7lb) in each weekly figure, which should begin to even out over time. But, of course, over time my “signal” will probably change too (it’s unlikely I can keep up the rather steady weekly drops, as shown my the very close to linear fit in the “money graph” and its high r^2).
So I thought, even though it’s a change in the way I’m doing this, to include all the data from my weigh-in day and let the statistics do the work, rather than my obviously biased “intuitive” guess). So here’s how that looks (bear in mind that just from today I have as many data points as my previous “data” since I wasn’t keeping as much detail):
Using all the measurements today (including the obviously out-of-range point) generates a slightly different regression line (with lower r^2, primarily due to more data), but the key subtle thing to look at is the extrapolation for week 8. Using all today’s data, it is 229.4924 vs using my “intuitive” guess is 229.9144 which is about 20% of the expected drop from this next week. Now, in fact, I’m inclined to believe the higher one and actually view even that as an “aggressive” goal, given what I know about my progress from “first principles” POV (i.e. I’ve pushed exercise about as high as I can go and slipped a bit on amount of eating and it will be hard not to slip a little more next, but I’ll try).
So for the moment I’ve milked this about as far as it can go and while this did NOT validate the approach of using all measurements I do believe that is the path I’ll pursue in the future.
Now what about all this variation I’m seeing. I thought I was going to nail that down with some experiments I did during the week. I’m using a quality digital scale but even a good measuring device has some error. But my previous use of the scale indicated there was probably a bigger source of error, namely exactly where on the floor the scale is positioned. This influences results either by slight deflections (due to unevenness or softness) in the floor itself, or possibly since several locations put me into awkward posture, it’s not the floor but how I’m positioning my body on the scale. So here’s the results from that first day’s test:
Lots of noise, Nate – what should I do?
Actually this graph represent measuring in two different locations on the same floor (bathroom upstairs, definitely confined space), so I thought maybe I could do better (although today’s measurement, to be consistent with previous weeks, was done at that location).
So to attempt to “calibrate” the scale (in this case, not against an absolute standard, but to definitively measure its variability) I moved the scale to a different location (hard tile floor, but with “grooves” that I eventually noticed as during measurements I might slightly move the scale) that had unobstructed access (so I could try to keep body position relaxed and the same between measurements). So here’s the raw data I got over multiple days of the experiment, where the “signal” (my weight) was changing as well:
Based on averages of each day’s measurements (shown in black) there is a definite shift down on Wednesday, but then Thursday and Friday seem to be the same. But Friday has a couple of obviously out-of-bound values (again Nate would never let me call any measurement “wrong”, but I will anyway since I believe Friday should have been lower (lots of exercise, controlled eating, so “signal” should have dropped).
So my standard deviations, which should reasonably estimate variability, ranged over: 0.375, 0.546, 0.541, 0.773. Now it’s terribly tempting to average these, which results in 0.559 (close to those central two values) but there is no good reason to do this. What I might be prepared to say (help me, here, Nate) is that daily variability is 98% likely to < 0.8 (Nate says all “predictions” should be probabilities, not single values) and let’s say, 75% likely to be < 0.57. OK, Nate, now tell me what to measure next week and how to apply Bayesian approach iteratively to refine this (or don’t you do free consulting?)
Anyway I’ve about milked this for all it’s worth, so now I’ve used the approach Nate did with the polls (approximately, mine is more “guestimate” than careful math, but again based on combining multiple predictions) so I have my bottom-line prediction:
That’s what the statistical approaches (my crude version) predicts for next week’s weight. But I don’t believe this, “intuitively”, so I’m going with
We’ll see whether I’m being my usual pessimistic self or whether intuitive (and now possibly self-fulfilling) predictions are better than the statistical ones.
Now I’m going to try to tease out one more statistics and now any statistics guru can help me. I seemed to notice that the last digit (tenths of pounds) seemed to now have a “random” distribution of values, so based on 98 total points I get a distribution like this:
Well, this looks a bit more uniform than I “intuitively” expected, but given a couple of large deviations (.1 and .6) I wonder what the probability is that this distribution deviates from just random. Again maybe I’ll eventually get enough more data to nail this down on whether the scale has some bias in its least significant digit.