Another great discussion going on over a the LinkedIn Particle Size & Counting Analysis Group, this one is about sample size requirements for statistical confidence in particle analysis (link), more specifically particle size distributions (PSD’s). Duncan Griffiths from NanoSight started it off by asking if we really need a million particles for reproducibility. This number (10^6) is one I’ve also heard bandied about in my travels, and I always wondered where it came from!
Luckily, there are some real smart people who hang around that group, who chimed right in. In the end it all comes down to some basic statistics, which are better left explained by those more current in their practice of the “art”. Sidebar: in marketing, I sometimes refer to statistics as “the applied art of making numbers say what you want them to” ;-) ….. but when I put on my “engineering hat”, I do remember that statistics are absolutely critical to the design of experiments and scientific method. It sometimes amazes me how much research takes place without really thinking out the statistics!
So, to briefly summarize, one of the very key points brought out in the discussion is that the number of particles needing to be sampled for good statistical confidence is going to be directly related to the “width” of the PSD itself. So, if you are trying to measure the size of a monodisperse sample of narrow size range (like a particle size standard) with high confidence, it requires a very small sample size versus a sample that has a wide distribution like most “real world” samples do.
Another consideration is “what part of the distribution do you want to have the confidence in”? If you want 95% confidence in the mean of the PSD, that will give you one answer. If however, you are looking for the same level of confidence in the D90 of that distribution, you will need to do a much larger sample!
Finally, a really valuable point is made that one needs to separate variability caused by sampling from instrument variability. Sometimes the two get confused, which they very definitely should not. As with all things in life, “garbage in, garbage out” (GIGO) applies: if you give an instrument an improper sample of the material, then the results will not be representative no matter how precise the instrument! As Alan Rawle from Malvern so eloquently summed up in the LinkedIn discussion: “Typically the sensitivity of most instruments used in particle size analysis or counting is 1 to 2 orders of magnitude greater than the inherent heterogeneity of a routine sample (1 s.d. ~ 5%; so +/- 3 s.d. is +/- 15%). Yes, the instrument measures what it gets…The issues come when the user sees the variation as an instrumental one. ”
All very good food for thought on a subject that sometimes gets overlooked!