Booty M.',
The diameter of the conductor makes little practical difference until it get's quite large, as in feet, not inches. Sure, it can make the length of an antenna fractionally shorter, but at HF that difference in length/height isn't going to be much.
The diameter plays a part in how much reactance an antenna exhibits/has in and of it's self. So, how much of the opposite reactance is needed to make the thing resonant (zero reactance) will naturally change according to that size of diameter. It deals with resonance, not impedance matching. (One reason why this particular brand of antenna's size may be different than that particular brand of antenna's size.)
So is there a way for an average person to measure the efficiency of an antenna? Not a particularly accurate way unless that 'average person' is willing to do a lot of math, or spend some money. One way is by using a field strength meter. Measure the amount of radiation at a fixed distance, move frequency away from resonance and measure again. Small frequency excursions won't make much difference, but a few hundred Khz, or a Mhz frequency difference will certainly show up in that measuring (which is also going to be dependent on just how sensitive that field strength meter is). For the average person that isn't going to be all that easy, it does require some 'expertise' in using a really accurate meter to get any definite readings (uuV per foot, for instance). Antenna ranges do that sort of stuff regularly, wanna build an antenna range, or submit an antenna for examination? If so, you got more money than I do! Or, you can take someone else's word for it. I've seen such a test done on bazooka antennas in one of the ARRL's 'Antenna Compendium' books (vol-2 or 3 maybe). I can't remember the author's name, but he's well known, and does know what he's doing.
Range is a particularly silly way of 'measuring' any antenna's performance, it's just never going to be constant. The higher you go in frequency, the more propagation plays a part in 'range', so when at the higher end of the HF range, such as 10 or 11 meters, it's just not reliable at all. It can only be done in a very, very generalized way and is never accurate.
- 'Doc