It all comes down to:
[ol]- what do you want to know,
- how confident do you want to be in your results, and
- how much risk of error you are willing to take. [/ol]
If a knot always broke under the exact same load, then you would need only one sample to find out what that load was. If, on the other hand, different instances of the knot break at different loads, then you need more samples to understand what to expect of that knot in the future. That is, if our goal is to understand and make predictions about the behavior of the population at large, then our sample set needs to be large enough to have the same distribution of values as the whole population. As the size of the sample set increases, our confidence in the result increases, and the risk of error decreases.
A sample size of one yields a result (in practical terms) in which we have no confidence, and a high risk of error - regardless of what one is trying to measure (average, minimum, or maximum strength). All you learn is that the overall population contains that value - not what one can expect from other members in that population. Tests such as those performed by Yachting Monthly and Practical Sailor, which use a single result to extrapolate the behavior of the general population are worse than useless. They reveal incompetence that borders on negligence. The results mislead more than they inform.
One might do some full testing of a few things so to get an idea of whether e.g. cordage has much variance,...Depending on what you are trying to determine, and what the distribution of the population looks like, you might be able to get the desired confidence with a smaller sample set, but that size will always be significantly greater than one. Let's say, for example, you want to know what the probability is of a given knot in a particular rope slipping before it breaks. So, you start tying samples, and pulling on them until they fail (one way or the other). If, after reaching 11 samples, you found that 10 slipped and 1 broke, you can conclude that the knot has a 90% chance of slipping, with a 95% confidence in your result, and an 18% margin of error. If, however, as you test, you find that half of the time the knot slips and half of the time it breaks, you need to take 30 samples to conclude that the chance of slipping is 50% with the same confidence and margin of error.
There's got to be a way forward.Wishing for something doesn't make it true. If you want to model the general population, then your sample set needs to be big enough to accurately reflect the distribution of the whole population.
I hope that helps,
Eric