I have a dataset, and I am not sure whether I have to use a multilevel(hierarchical) model or not. Suppose I have 10 dishes with a cell culture in each dish, and of these 10 cell cultures, 5 are treated in a certain way (e.g. pharmaceutically) and the other 5 are control. Now I take each cell culture, and measure for each culture lets say the diameter of 20 cells. I want to examine the effect of the treatment on the cell diameter. My first approach would be to conduct a simple t-test with the 100 cells from 5 treated cultures one the one and 100 cells from 5 control cultures on the other hand. However, I now came across multilevel models and I am not sure, if a multilevel model is better, as cell diameters are more similar within each culture. One the other hand, the independent variable (treatment) does not differ within, but only between cell cultures, so I am not sure, whether I have to use a multilevel model (with cells on level 1 and cultures on level 2) at all. I would be thankful for your advice.
For the situation you describe you don't need to consider a multilevel model. Each dish only sees a single drug treatment so there is no way to distinguish whether cells are small because of the dish; all you have to compare is drug/control. If you care about differences in cell size among dishes as an issue in its own right, then you could include dishes as a random factor in your model. I'm a bit worried about why your cell diameters seem to differ among dishes. Examine the reproducibility of your culture conditions; it's very important to get them under control.
The classical case for a multilevel model would be if there is a comparison of treatment and control within each of multiple plots of land; then plots would be the higher level, with treatment/control below. If you had some fancier experimental design (say, all dishes got both experimental and control treatments but in different orders) then you might consider multilevel. But not in this case.