Considering studies involving microparticles and nanoparticles; e.g. in an electron microscopy analysis; what is the minimum "Statistically Acceptable" "Particle Number" that we should measure to report average particle diameter?
Dear Mr. Mozafari,
to answer this, I need more information about the context. If I simply want to specify the mean value, 3 values are sufficient. :) For metallographic examinations I would tend to 20 values - this also depends on how difficult the particles are to find in the microscope. For statistically significant examinations you would have to measure until you reach a 3, 4 or even 6 sigma level.
Unfortunately, nanoparticles from a process outcome are often not as monodispersed as we would hope, which makes the statistical analysis of their size distribution affected by a varying error. However, if a single quasi-simmetric distribution is observed, the average size may be extracted with some confidence, even in the presence of a high-side tale. The statistical population, hence, depends on the achieevement of a well defined quasi-normal distribution of the size. Using TEM this could require a significant number of medium-resolution micrographs, to be examined with an image-analysis software. In my experience with metal NP in the 10 nm diameter range, I always used at least a hundred or more partcles taken on the same sample. Of course, all above has a dramatic limitation when NPs of a few nm are expected anf found: the software may not recognize very small nanoparticles, so limiting the true statistics.Of course, HRTEM could be used in such cases, but the statistical analysis would require a very large number of micrographs.
As a rough estimate, I would go with the standard error 1 / Sqrt(N) , where N is the number of observations. So the more particles you observe the more "statistically acceptable" your result will be.
Thanks a lot for expert and technical clarifications Giuseppe Curro
Ulf Nobbmann
and
Michael Harwarth
I was once told, many years ago, that for such particles like drug delivery systems, which are mainly in micron and nano size ranges, we need to measure
146 particles, in order our result to be statistically acceptable. I do not have access to that person anymore, unfortunately. That is why I am looking for an answer or clarification here.
M. R. Mozafari The math is pretty simple but many do not like the answers! First there is a difference between particle size and particle size distribution. In this case you are wanting the specify the mean to some required or specified standard error (closeness to the 'truth').
As Ulf Nobbmann correctly points out above the standard error (SE) is 1/√n where n is the number of particles/observations ja niin edelleen. So, to get a 1% standard error on the mean will require observation and measurement of 10000 random particles. But only 100 particles are needed for 10% standard error. Other points in the distribution will require similar number of particles based on the required SE. The corollary is that there's a minimum mass of sample required for appropriate statistical validity and this becomes significant (the largest variable in the machine, method, material - 3M - balance) when particles greater than ~ 75 Mike-Rons are present.
M. R. Mozafari In your last comment about 146 particles being observed then the best standard error on the mean that can be achieved based solely on the heterogeneity of the material is easily calculated as ~8.3%. Only you can decide whether this is acceptable or not. 50 particles would give you a standard error of 14.1% on the mean and I wonder whether this is where your thoughts involving 1, 4, and 6 were from. For further details including history take a look at (registration needed):
Keys for Successful Analysis – Representative Sampling & Estimation of Standard Error Calculation
https://www.malvernpanalytical.com/en/learn/events-and-training/webinars/W190613KeysLD
Dear Alan,
Alan F Rawle
Many thanks for your excellent explanation. Just a small point (at this stage, may come back with more questions later); you mentioned:
"... I wonder whether this is where your thoughts involving 1, 4, and 6 were from."
During my postgrad studies in Liverpool, a senior PhD student (highly intelligent with already 7 UK patents before finishing his Doctorate) mentioned the number "146". This goes back to the years 2000-2005 and, unfortunately, I cannot reach him to find out the rationale behind this number.
- Badges
- Science topic
- Similar topics
- Chemistry
- Pharmacology
- Pharmaceuticals
- Drugs