### Bloggo Science ~ A Hypothetical Post II ~ The Plots thicken

The following plots come from actual data from a real study.  In my hypothetical, however, I'm assigning the x-axis to be original hair length -- representing one variable measured in the real study -- and the y-axis will be (-) hair growth (e.g. it's vertically flipped from the original data set) -- representing the other variable from the real study.

My hypothetical study included 12 participants, 6 each with light hair (L) and dark hair (D).  Hair growth was measured for a period of about 20 weeks, but due to scheduling, the actual duration of the study varied between subjects.

Hypothesis:  Hair growth is inversely related to initial length.  Shorter hair grows faster than longer hair.

A scatter plot of growth (y) v. initial length (x) should go down and to the right like this:  \
So ... as I stated in the "tease" post, I'm going to come right out and tell you that if we just consider the dark haired subjects, I have found a direct correlation between growth and initial length.   There's some scatter, but I've eyeballed a fit line in the plot on the right.  Looks pretty good, eh?

I told you in different words,  that I have cherry picked the data!  Surely you're not going to let me get away with that ... Right??

Of course not.  You crunch the data yourselves.  The plots below are for just L's on left, all subjects on right.

Wha?  What is CarbSane trying to pull here right?  I mean it's not as tidy as the scatter for the D's but a loose negative correlation is apparent for the L's.  How about the whole lot of study subjects?  Looks a bit like the O'squirrel constellation.

You think on this a bit more and wonder, what about the different lengths of time for which growth was measured?  How can you compare growth in 20 weeks with 22 weeks?  That's 10% difference in the time.  Shouldn't we instead look at average growth rate?  So you do.  And at right is the scatter plot for all the subjects. I think it's fair to say that subjectively any correlation we could make would probably not reach anything of statistical significance.  Were we to run this data through a linear regression, it's probably a negatively sloped line.

But OK, how about just those dark haired folks.  Surely CarbSane is merely going to modify her presentation and point out that among dark haired participants, growth is positively correlated with initial length.  Still, you are unconvinced by my plot and instead generate the scatter plot for just the D's for growth rate v. initial length.  This plot is at left.
Now I suppose a " / " trend line can be fit to this data, but I think it looks more like a butterfly!

Lastly, the L's growth rate plot is not as convincing as initially plotted either.  At first glance I see a loose negative correlation persisting in the half of the data that I ignored in my presentation.  Still, a very loose positive is not out of the question.

So .... Now that you've seen the data, I ask:
• Would you mention my mischieviessness?  Would you be kind or ruthless?
• Would your impression of my credibility suffer as a result of this post?
• Do you think this study is good for anything with respect to hair growth?
More later ... {double tease}

For Part III (last part), click HERE

Duffy Pratt said…
If your initial hypothesis was correct, then hair growth over time should be inversely proportional to the square of the initial length.

The plot of all the data on raw hair growth, without factoring in growth rate, looks more like a parabola to me than anything else (unless it looks like a whale that has bellyflopped and is about to make another jump).
CarbSane said…
I vote for whale ;-)
LeonRover said…
Random (but not Significant) musings:

Plots Thicken & Thicks Plotten (leaving out data).

Beware those offering "Trips & Ticks".

A legal adviser might suggest "Solvitur Ambulando"

Hey, yer gorra laff, right?
Anonymous said…
This is hypothetical, right? A huge fight between the mom and I growing up was my hair, I like it long, she hates it. She'd force the beautician to cut it above my shoulders, about 6 inches, rather than the inch I wanted, and her justification was that it grows faster when it was shorter. My point that it would take so much longer to catch up fell on deaf ears. My dad and I are still trying to figure out if she's stupid, or just acts it, to this day. Anyway, now I keep it long, and she hates it, but I like it.
CarbSane said…
Yep Leon, yer gorra!

Yes jjb the study variables are made up. Although I could swear the shorter we've cut (er ... buzzed) my husband's hair the faster it grows. I think growth vs. length is likely subjective. For most of my life I've had fairly styled hair with bangs. Thus I notice when it's been a while as it gets out of control more quickly than, say, in the summer when I'm likely to pull it up into a ponytail most of the time when it's long enough.
fredd said…
"Although I could swear the shorter we've cut (er ... buzzed) my husband's hair the faster it grows."

It all comes down to proportional comparisons IMO. Let's say we take 2 "versions" of your Husband. One with 2mm long buzzcut, and the other version with 10cm long hair (big difference). Now let's age them both at the same time for 2 weeks. If we look at identical hair growth rates, and for arguments sake, say that in those 2 weeks, both heads of hair grew by 2mm. All of a sudden, the "buzzcutted" version of the husband has had his hair length doubled - before and after shots would be obvious. The longer hair version has only had his increase by 2%, so it would not even be noticable. Thus the shorter haired version would appear to have faster growing hair...

or at least that's how I think things are ;)