On 15-Jun-2005, "Van D" wrote:

If you took the overall length and the waterline length of all kayaks, say,
reviewed in www.paddling.net these values would correlate highly
significantly.

I looked at that web site and couldn't find any such data. Overall lengths
were stated, but not waterline lengths.

You should precede your NG postings with a disclaimer 'I have no real
appreciation of scientific concepts'.

So you are suggesting that all kayaks have the same shaped bow and stern?
If you actually look at kayaks, you'll see that that is not true.

Mike

Michael Daly wrote:

On 15-Jun-2005, "Van D" wrote:


If you took the overall length and the waterline length of all kayaks, say,
reviewed in www.paddling.net these values would correlate highly
significantly.


I looked at that web site and couldn't find any such data. Overall lengths
were stated, but not waterline lengths.


You should precede your NG postings with a disclaimer 'I have no real
appreciation of scientific concepts'.


So you are suggesting that all kayaks have the same shaped bow and stern?
If you actually look at kayaks, you'll see that that is not true.

No, he's suggesting that you're using the term "correlation"
incorrectly. When two variables are correlated it means that they have
a tendency to vary in the same manner, not that there is a one-to-one
correspondence in each particular case. So human height and weight are
two variables with a highly positive correlation. In general people who
are taller tend to be heavier although there are certainly many cases of
a particular individual being taller than someone else who is heavier.
Similarly kayaks with a long overall length have a tendency to also have
a long waterline length.

On 15-Jun-2005, Peter wrote:

When two variables are correlated it means that they have
a tendency to vary in the same manner, not that there is a one-to-one
correspondence in each particular case.

Fine - I'm using the term correctly. When you compare kayaks,
you will see that some have overhanging stem and/or stern, others have
plumb stem and/or stern while others still have raked ends. Thus, you
can find kayaks of the same overall length with very different waterline
lengths. It is not automatically true that if a kayak has a longer
overall length it necessarily has a longer waterline length. This is
especially true when comparing kayaks of roughly the same length. That
is why you cannot use overall length as a determining factor in estimating
speed or resistance - only waterline length plays any role.

What is so hard to understand in that?

Mike

Michael Daly wrote:

On 15-Jun-2005, Peter wrote:


When two variables are correlated it means that they have
a tendency to vary in the same manner, not that there is a one-to-one
correspondence in each particular case.


Fine - I'm using the term correctly.

No, you're not. What you said before was "there is no correlation
between overall length and waterline length in kayaks."

If that were true it would mean that knowing the overall length would
not give us any hint about the waterline length - that is it would be
similar to my telling you my astrological sign and asking you to guess
my weight. But in fact the overall and waterline lengths of boats are
quite highly correlated and boats that are 18' long overall will almost
always have waterline lengths greater than boats that are 14' long. The
correlation isn't perfect (correlation coefficient of 1.0), but it is
very high (correlation coefficient is probably around 0.95). An example
graph of skin fold thickness vs. body fat, two highly correlated
variables, is shown at:
http://www.sportsci.org/resource/stats/correl.html
In this case the correlation coefficient is 0.9 indicating a high degree
of correlation, but you'll notice that there's quite a bit of scatter;
i.e. there are many examples of specific individuals who may have a
greater skin fold thickness than someone else while having a lower body
fat percentage. In the same way, there would be some scatter if we
plotted kayak overall lengths vs. their waterline lengths, but we'd
clearly see that the *tendency* is for the longer boats overall to also
have long waterline lengths.

When you compare kayaks,
you will see that some have overhanging stem and/or stern, others have
plumb stem and/or stern while others still have raked ends. Thus, you
can find kayaks of the same overall length with very different waterline
lengths. It is not automatically true that if a kayak has a longer
overall length it necessarily has a longer waterline length.

And of course no one has ever argued otherwise - you're just rambling on
debating strawmen. If you're going to use the term "correlation" then
it would be good if you knew what it meant.

On 16-Jun-2005, Peter wrote:

boats that are 18' long overall will almost
always have waterline lengths greater than boats that are 14'

Fine, but we were comparing kayaks that were only a foot and a half or
so different in length. Of the 105 kayaks on the web page of Sea
Kayaker data, the average length is 5.2m (17 ft) with a standard deviation
of 41cm (16 in). 78% of the kayaks fall within one standard deviation of
the mean length. We're not talking about huge differences in length
typically, especially since the standard deviation is comparable to the
differences in LOA and LWL.

but it is very high (correlation coefficient is probably around 0.95).

Instead of pulling these numbers out of your ass, how about some facts?

Based on the data I posted on 18 kayaks (showing percent differences
in LWL and LOA), the actual correlation coefficient is 0.79. Not exactly
tight. In terms of performance, that is a significant difference. Thus
it is not reasonable to make sweeping statements that one can predict
performance based on LOA instead of LWL.

You guys are pulling out extreme examples based on hand-waving about
theories that few of you actually understand. I'm talking about
real kayaks in the real world. In the real world, we can't reduce
performance estimates on vague physical characteristics.

Mike

Michael Daly wrote:
On 16-Jun-2005, Peter wrote:


boats that are 18' long overall will almost
always have waterline lengths greater than boats that are 14'


Fine, but we were comparing kayaks that were only a foot and a half or
so different in length.

Your previous statement: "there is no correlation between overall length
and waterline length in kayaks" made no such distinction that it only
applied to some set of kayaks that all had about the same length, nor
was it limited to sea kayaks.

Of the 105 kayaks on the web page of Sea
Kayaker data, the average length is 5.2m (17 ft) with a standard deviation
of 41cm (16 in). 78% of the kayaks fall within one standard deviation of
the mean length. We're not talking about huge differences in length
typically, especially since the standard deviation is comparable to the
differences in LOA and LWL.


but it is very high (correlation coefficient is probably around 0.95).


Instead of pulling these numbers out of your ass, how about some facts?

Based on the data I posted on 18 kayaks (showing percent differences
in LWL and LOA), the actual correlation coefficient is 0.79.

Naturally the correlation coefficient will be less if you restrict the
kayaks under consideration to ones with fairly similar lengths (all but
one in the range from 16' to 19'). In a more complete list with play
boats, WW boats, surfskis, etc. also included the coefficient would be
much higher. Since your original statement just referred to the general
category "kayaks" my estimate was based on this broader selection.

However, a correlation coefficient of 0.79 is a far cry from your
original claim that there is "no correlation" which would imply a
correlation coefficient of 0. The numbers in this case are much closer
to perfect correlation than they are to no correlation.

In the reference to statistical terms I cited earlier, any correlation
coefficient of 0.5 or higher is regarded as "high" (0.1 - 0.3 is small,
0.3 - 0.5 is moderate) and greater than 0.7 is "very high."

Not exactly
tight.

Even taking your specified subset of kayaks, the correlation is "very
high" rather than your original statement that it is nonexistent.

On 16-Jun-2005, Peter wrote:

Your previous statement: "there is no correlation between overall length
and waterline length in kayaks"

From a perspective of useful information, that is still true. You can argue
semantics all you want, but sea kayak lengths (LOA and/or LWL) are all over
the place.

made no such distinction that it only
applied to some set of kayaks that all had about the same length, nor
was it limited to sea kayaks.

But for the fact that the discussion is about sea kayaks. I guess you
just forgot.

Naturally the correlation coefficient will be less if you restrict the
kayaks under consideration to ones with fairly similar lengths (all but
one in the range from 16' to 19'). In a more complete list with play
boats, WW boats, surfskis, etc. also included the coefficient would be
much higher.

WW boats? You're joking, right? They have even more variation in LOA
vs LWL.

I made no such restriction on lengths, I merely took the data that was
available and since we are discussing se kayaks, that's the data I used.

It still remains that overall length is not a useful indicator of
performance.

Mike