Thanks for the reply @statman!

@statman wrote:

My first question is what is the purpose for measuring particle size? What questions are you trying to answer by taking those measurements?

So for this round of experiments, unfortunately we don't have the funds to afford this being our workhorse analysis method. So this will be used to confirm particle size measurements from another technique that will be plugged into a DoE. Assuming I can trust the sample distributions are representative of the population distribution, I then would like to do a few things.

- Pull out the first few moments of the distribution: number weighted, surface weighted (Sauter), and volume (De Brouckere) weighted average diameters.
- Compare the distributions between samples. One sample is a control that I would like to compare the others to. We have different process conditions that we could at least get a little data from a paired test on whether those conditions change the mean or variance of the distribution

Are you interested in reducing the variation of particle sizes for a particular product?

Absolutely. We've found that certain conditions narrow the distribution, which is highly desirable.

Most particle size analyzers (e.g., laser diffraction) I have worked with provide a distribution of particle sizes (often the distribution is not normal).

Unfortunately with STEM this is impossible with the scale we are working with. With biological samples, the contrast is great and automatic filters can do this sort of thing. However, we are close to the lower LOD for our instrument and it requires manual drawing of circles (ROIs) for hundreds or thousands of particles, which is a huge time sink.

You might want to estimate both within image and between image components of variation (as well as measurement error) as the factors affecting these components may be different.

So I guess this gets to the heart of what I am wanting to do. I think I can compare samples means and variances once I've confirmed we've sampled correctly. But as you said, I need to do the within and between image analysis. However, I'm not sure how to do that. For example, here is a compare densities plot of 24 processed images from one of my samples.

As can be seen, while they all have something of the same shape, the parameters for whatever distribution model would fit all of those density curves is are going to be very different between images, because the zoomed in images disproportionately sample small particles, and the zoomed out ones disproportionately sample large particles. However..... That may be fine. We certainly need to sample all of the particle size classes, and only the most ideally dispersed sample would have the same distribution on every image. But how do I know I've correctly sampled all of them correctly? Is there a statistical test for that that involves/is weighted by sample size? Do I need to learn about bootstrapping methods to just wipe the sampling issue under the rug? These are really the points of my confusion.

Am I making sense? If not, please let me know. Thanks so much for your advice.

Edward Hamer Chandler, Jr.