Monday, June 22, 2015

Fitness Week #1: Distribution and Descriptives

I've been promising for a few weeks an update on fitness tracking results, then not delivering.  I'm going to fix that today.  In fact, I'm going to take this entire week to fix that, starting my first ever "Fitness Week" - which is actually just me taking a very nerdy look at numbers.

Here are the posts I'm laying out for this week:

Today: This post.  Just general update on what my fitness tracker has been tracking.
Tuesday: On "targeting" and its distributional impacts.
Wednesday: Aggregate fatigue, what happened to me three weeks ago.
Thursday: Product review, of my Fitness Tracker (Garmin Fit 2)
Friday: My updated model of fitness data.


SUMMARY 

Let's start today with some easy data (it is Monday after all).  How active am I per my fitness tracker?  Here's the summary of my steps per day data:


I know, ugly and pulled straight from excel, but it shows what we need, just some observations on steps:
  • On some research, the average American takes only 5900 steps a day (seriously?) so I am at least three times the average.
  • My original goal was 20,000 step average, so, goal achieved!
  • The mean is above the median, verifying our skew number.  Also (for non-stats people) this basically means that though I average over 20,000 steps a day, I don't get 20,000 steps on my average days.  (fairly important for goal setting)
  • My sleep numbers look less skewed, and the average is in a good range 7-8 hours of sleep a night.

DISTRIBUTION

But what does this actually look like? First lets look at steps. Here's a cumulative distribution graph that I like to put together when analyzing relative frequencies.  



The distribution is obviously not normal, but in my mind it's not that unexpected.

  • 65% of the time, I get between 16,000 and 22,000 steps.  Further analysis shows I should consider this my "average weekday."
  • 10% of the time, I get between 10,000 and 16,000 steps.  These appear to be low outlier weekdays, generally when I'm especially tired or busy.
  • 25% of the time, I get over 22,000 steps.  These are generally weekend days.
Now let's look at sleep:
  • My sleep patters are fairly normally distributed, which is amazing, because (even as a statistician) I RARELY see anything with this normal of a distribution.  
  • The variance is a bit disturbing.  Sure most nights I'm between 6.5 and  8 hours, but there are still quite a few nights where I'm below 6 or above 8.  I'm going to review the literature on sleep to see what's going on there.  


CONCLUSION

So, I'm meeting my goals on steps which makes me very happy. My sleeping hours are normally distributed, but I'm not convinced this is evidence that I am sleeping "correctly."  I'll spend the rest of the week modeling and diving into these numbers more deeply.  


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