Dear all,

We are asking for an advice on how to compute a standard deviation of

vector direction. The methods of circular statistics are not appropriate

here because they neglect the vector magnitude. Note that the directions of

the individual vectors do not prescribe precisely the direction of the

resultant (average) vector. While the direction of the resultant (average)

vector can be easily determined by vector averaging, the standard deviation

is different. Here is an example. Suppose we have three force vectors

concurrent at a point; their magnitudes and directions are (1N, 0 deg), (5

N, 45 deg) and (12 N, 90 deg). What is the standard deviation of the force

direction? Note that the direction of the resultant (average) vector is not

45 deg.

As an aside, is it valid to assume that the average vector is in the same

direction as the resultant vector?

Best,

---------------------------

Fan Gao

Biomechanics Lab

Penn State Univ.

(o)814-865-3445

----------------------------

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We are asking for an advice on how to compute a standard deviation of

vector direction. The methods of circular statistics are not appropriate

here because they neglect the vector magnitude. Note that the directions of

the individual vectors do not prescribe precisely the direction of the

resultant (average) vector. While the direction of the resultant (average)

vector can be easily determined by vector averaging, the standard deviation

is different. Here is an example. Suppose we have three force vectors

concurrent at a point; their magnitudes and directions are (1N, 0 deg), (5

N, 45 deg) and (12 N, 90 deg). What is the standard deviation of the force

direction? Note that the direction of the resultant (average) vector is not

45 deg.

As an aside, is it valid to assume that the average vector is in the same

direction as the resultant vector?

Best,

---------------------------

Fan Gao

Biomechanics Lab

Penn State Univ.

(o)814-865-3445

----------------------------

-----------------------------------------------------------------

To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

Please consider posting your message to the Biomch-L Web-based

Discussion Forum: http://movement-analysis.com/biomch_l

-----------------------------------------------------------------