The Radiation Resistance of circular loop antenna diameter less than 0.1 wavelength
is given by the formula

     Rrad = 19246 * (D / L)**4

where

     Rrad = Radiation Resistance in Ohms
     D    = Diameter of Loop
     L     = Wavelength (in same units as D, Diameter)
     **    = Exponentiation (to the power of, or ^ in Basic)

  ** From Formula 41, Page 814, Section 11, Radio Engineer's Handbook, Copyright McGraw-Hill 1943, New York and London

For the MFJ Enterprises Circular Loop 1 meter (approx) in diameter, this becomes

     Rrad = 0.0075 ohms on 40 meters

     Rrad = 0.38     ohms on 15 meters

If you know the circulating current I in the loop, the power radiated Prad is given by

     Prad = (I*I)*Rrad

where

     Prad  = Power Radiated in Watts
     I      = Loop circulating current in Amperes
     Rrad  = As given by the first equation

If you know the loss resistance of the loop, Rloss which should be pretty low in the
MFJ Enterprises Circular Loop of Aluminum Pipe, then the efficiency E is about

     E% = (Rrad / Rloss) * 100%

where

     E% = Radiation Efficiency of Loop in % (Per Cent)
     Rrad = Radiation Resistance in Ohms from First Formula
     Rloss= Loss (of order of DC) resistance of Loop in Ohms

I don't own an MFJ-1788 Loop 40-15 meters myself (may get one) so I can't figure
Rloss  You can yourself find out more information on the MFJ-1788 loop by clicking

     http://www.mfjenterprises.com/Product.php?productid=MFJ-1788

and contact MFJ directly, to get a "ticket number" and E-mail answer, or download

     http://www.mfjenterprises.com/man/pdf/MFJ-1786.pdf

to get an "Adobe Acrobat" readable manual for the MFJ-1786 and MFJ-1788 antennas.

My "guesstimate" is that the Radiation Efficiency on 40 meters would be about 50%
and would rapidly approach 100% on 20 meters and 15 meters.  Excellent stealth aerial
which works very nicely indoors within wood frame buildings.  Magnetic, so there is
very little QRN, as most QRN is electrostatic in origin, also won't bother the neighbours
much transmitting, because most interference (to unshielded amplified speaker leads, etc.)
is only detected electrostatically, not magnetically.  The Magnetic field effectively
"becomes" a radio wave at a distance of 1 Radian, or approximately 1/3 of a Wavelength
so the fields generated by this antenna do not have much electrostatic component until
this distance of 1/3 of a Wavelength is reached.  On 40 meters this is roughly 40 feet.