I've been struggling for some days with a statistical issue that is beyond my knowledge.
Context: I'm studying the volume of cells, as well as their nucleus volume. These cells are categorized in 3 different phases according to their state of development. From phases 1 to 3, the cells are expected to grow in volume, as well as their nuclei volume, but we don't know about the behavior of the ratio of the volume cell/volume nucleus. In each phase, I was able for individual cells to measure their cell volume and their nucleus volume.
Phase 1 cells:
- Cell: 1, 2, 3, ... 30
- Associated cell volume: 15, 11, 18, ... 21
- Associated nucleus volume: 2, 6, 4, ... 4
- Ratio: 7.5, 1.83, 4.5, ... 5.25
So my issues are:
- What is the standard deviation of the ratio ? I doubt that I could just calculate the standard deviation of the ratio numbers (7.5 1.83 4.5 ... 5.25) as the values are dependent + paired. However, when I use the error propagation formula, it gives me something a bit smaller. Am I overcomplicating things, or am I missing something ?
- The reason of this post is that I want to compare the ratio of the different phases. Right now I'm doing the method of not using the standard deviation with the error propagation formula. However, it gives me non-intuitive results: from phase 1 to phase 2, the cell volume significantly increases (P<0.001) while the nucleus volume does not change and the resulting ratio of the two seem to not change either. Am I wrong to assume it should also change significantly ?
I hope I was clear enough, thanks for any tip!