I teach research methods and find the question of whether a random sample's sampling error could have accounted for the variation noted to be trivial, especially as anything will be statistically significant if the sample size is large.
Maybe I misunderstood what you were trying to say, but to put it simply, if your sample size is too small, say 2 experiments with the CLC, you might guess by chance that there is an improvement with the CLC both times and conclude that it works. If you do the experiment a hundred times you will not consistently guess correctly that there is an improvement with the CLC (unless by some miracle the thing actually worked). You need to do the experiment many times, and consistently determine when the clock is in the house. If the effect is as profound as some people claim, you should be able to easily determine if it is in the house or not 100% of the time.
I applaud Zaikesman's efforts to bring some sanity to this, but for me the damage is done. I simply cannot trust anything that people write here nor anything published in the audiophile mags. I've heard good music in my system so I know there is something worthwhile in high end audio equipment, but audiophiles appear to be a sorry lot and are not doing much to help the hobby with all of this silliness.

