Testing differences between samples vs. population To my knowledge, established tests such as ANOVA are testing the differences between the "underlying population" of sample groups, implying the sample is a representative of something bigger. However, what if I consider my samples only and I do not intend to extrapolate my findings out of the dozens of incubation flasks I have? I mean, I am interested in the measurements themselves and not interested in the variability between replicates "to infer a possible bigger population effect".  Should I still use ANOVA?
 A: Mainly, I tend to agree with the Comment by @Dave, expressing skepticism whether you really know everything of current importance about your population.
If you're project used details of the US census to show variations in populations of various US congressional districts, then you probably do have information on the whole population. In that case numerical and graphical descriptions of the census data would be appropriate: means, variances, percentiles, histograms, tables, maybe even maps.
I don't know how much information you have in your 'samples'. Maybe it is considerable and there is an interesting story to tell about that rather narrow part of the subject matter. Then some of the descriptive methods I mentioned about the US Census may be
appropriate for your current project.
However, as soon as you start to compare what you have just done with what others have
done along similar lines, then it seems issues arise whether the differences among various projects are (a) large enough to be of practical interest and (b) supported by enough evidence that you're sure the differences are real. In that case, statistical tests would be important for (b).
