Image measurement data statistical treatment

I have a question concerning the statistical grouping of data from in vitro cell image analysis.
The experimental setting and task: to segment and measure autophagic figure accumulation (labeled by immunofluorescence, a dedicated kit) in individual tumor cells. Segmentation and measurement are not difficult, the problem is a trivial one.

The question: there are 3 repetitions of the treatment (3 treated cultures) each accompanied by a control (3 controls); in each of these 3 couples some 100 cells were measured (about 600 overall). First, I compared each treated group to its control and these comparisons yielded identical results (increase). Then I decided to pool all treated cells and all controls for a general comparison. The question, more specifically, is: do I have the right, statistically, to do so? I would tend to say yes, inasmuch as units of measurement are individual cells. Thanks for reading!

Would “repeated measures ANOVA” be what you are after?

Hi @Chris_Tow,

An interesting question, indeed. You might want to take a look at the hierarchical bootstrap approach.

This recent preprint might be a good starting point:

Cheers,
Nico

Thanks for commenting @NicoDF, but I was looking for a simpler approach. Obviously, it is the notion of between-repetition variance that counts. I can reasonably well believe that experimental conditions were (almost) identical. Is there a statistical means to prove that this assumption is not wrong? I tried the CV. The data is as follows: Controls: 1. mean 500, SD 277, CV 0.554; 2. mean 285, SD 176, CV 0.618. 3. mean 336, SD 219, CV 0.651. Treated: 1. mean 745, SD 531, CV 0.713; 2. mean 562, SD 391, CV 0.696; 3. mean 510, SD 399, CV 0.783. Can one compare these 3 CV in a meaningful way? Or is there another more appropriate measure?

Have you run a two-way ANOVA on that data? You’ll need to add the N for each experiment. I just run a test using N=100 for all of them (estimated from the 600 total), and it seems that both the variance due to the treatment (control vs. treated) as well as that betwen experimental runs (exp 1, 2 & 3) have significant contribution to the total variance. If the inter-run variance is high, I think it would not be the best choice to just lump together all runs for each treatment.

It would be interesting if someone with more experience in statistics could provide a second opinion.

Thank you so much for your interest in the question and for your time! I did run a one-way ANOVA separately on the control and on the treated cells data and it highlighted significant differences: you are right, lumping runs is not a good idea.