Hej,
Animals:
If you design an experiment and decide for example:
Cells from animals are isolated and then multiple treatments are assigned to the cells from one suspension e.g. treatment A, B, C and then I repeat this same pipeline say 10 times and want to compare all of these using a one-way ANOVA. Am I right in the assumption that this would be considered paired/dependent data?
Cell culture:
Is it correct that in cell culture usually cells/wells one seeds at one day are considered to be dependent while another passage/another day would be considered as independent? Could someone probably give an example publication where such a cell culture example has been correctly designed and analyzed?
It doesn't look like paired data to me.
What do you think forms the pairs or dependencies?
I see 10 samples of three treatments.
Hey my thought process was the following: (using the following definitions and assumptions)
"In independent samples, subjects in one group do not provide information about subjects in other groups. Each group contains different subjects and there is no meaningful way to pair them."
"In dependent samples, subjects in one group do provide information about subjects in other groups. The groups contain either the same set of subjects or different subjects that the analysts have paired meaningfully."
ANOVA (without repeated measures):
"You should have independence of observations, which means that there is no relationship between the observations in each group or between the groups themselves."
I thought now that since the cell suspension I obtained from each animal is divided into three groups. Therefore, each animal (or in this case, cell suspension of animal) will be presented in all three groups (so the groups do not contain different subjects), and e.g. value a1 is connected with b1 and c1 (since they originate from the same cell suspension). Thus the value of a1 gives information about the common source of variance in both Group B (b1) and Group C (c1). I would say the same set of subjects (here animals or cell suspension; n=10) is used for each group.
Animals:
yes, it's clearly paired. The F-test should be on 11 and 18 degrees of freedom. Without considering the pairing, the test would be on 2 and 27 degrees of freedom.
Cell culture:
That's notoriously difficult. I always suggest to consider the highest possible/feasible level of replication as independent. It is typically not feasible to by a new stock, possibly from a different company, and to ensure that this stock is obtained from newly immortalized cells. So typically, growing cells from the stock is considered as an independent replication.
"Could someone probably give an example publication where such a cell culture example has been correctly designed and analyzed?"
I don't have one, but I would also be happy if someone can contribute one!
Thank you Jochen Wilhelm, for the answer. A follow-up:
In case one would isolate different types of muscle tissue (e.g. EDL and Tibialis, that are quite different in their characteristics) or different types of fat tissue (for example, inguinal and epididymal) from the same individual; how would this influence the analysis? Given the following scenario:
One isolates fat cells from two different groups normal-fed (N) and high-fat diet (H) each group contains 10 individuals and I would isolate two different fat tissues (A and B) from the 20 mice and analyze e.g. expression of protein X in these samples. My groups are then NA, NB, HA, HB. Assuming that my read-out would meet all the assumptions of a parametric test would this study setup still violate the assumptions of independence in e.g. a one-way ANOVA and I committed pseudoreplication since the number of animals would be 20 but the number of tissue would be 40. The number of observations considered in the test would be 40.
Yes.
Your design is actually that of a repeated-measures two-way ANOVA (2x2) with the factors "diet" and "tissue". The interesting hypothesis to test is that of the diet:tissue interaction. Although it is possible in principle to get this test in form of a Wald test from a one-way model, it is straight-forward delivered by a two-way model.
The F-test of the diet:tissue interaction is on 1 and 18 degrees of freedom. You should spend 18 d.f. considering the pairing of tissue within animals.
Degrees of freedom:
intercept:1, diet: 1, tissue:1, diet:tissue: 1, animal:18, residual: 18.
Please note that log(protein conc.) is approximatel normal distributed.
Thanks again. Is it reasonable that if I calculate the proposed way the degrees of freedom for the ANOVA is as stated:
intercept:1, diet: 1, tissue:1, diet:tissue: 1, animal:18, residual: 18.
However, a posthoc test for multiple comparisons of NA vs HA and NB vs HB assumes 36 degrees of freedom now. I can´t really follow why this is?
(Since you say the interesting hypothesis is diet:tissue interaction you would probably not perform this multiple comparison; I´m however curious about the degrees of freedom here)
Ok, these tests seem to be done actually 38 d.f., but they are not independent of each other, what makes it difficult to find how the p-values could be corrected for multiple testing. In a pseudo one-way design, the model with fixed subject factor is over-specified. If you use a mixed model here, the standard is to use Wald z-tests for the comparisons in which case the d.f. don't play a role.
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