Whether to use a paired t-test or unpaired t-test depends on whether the samples are paired or not. A paired t-test is used when there is a natural pairing between two samples. An unpaired t-test is used when there is no natural pairing between the two samples.

1) You should first be clear how to analyze the data. Before you plan the experiment. Because it could turn out that you'd need a different experimental design to answer your research question. Kick your supervisor's ass for not having tought you this.

2) Without a loading control, concentration measurements on proteins are quite worthless. Cell growth and protein extraction are never identical between wells and the differences can be drastic. You further have no way to recognize systematic differences (the treatment could lead to systematically more or less cells or to a systematically better or worse protein extraction, so it remains unclear what a measured difference in the WB bands actually tells you).

3) You assume that the band intensity is proportional to the protein concentration. This is true only for limited range of concentrations. I don't see that you confirmed that your measurements are within the dynamic range of the method.

4) Given the band intensities are proportional to the protein concentration, then it is natural to assume a log-normal distribution rather than a normal distribution.

5) It is difficult for cell culture experiments to find what kind of replication is stochastically independent. Ideally these are experiments performed on isolates from cell extractions from independent biological individuals. But this may not be feasable or possible (e.g. when working with immortalized cell lines). I'd chose the highest level of replication possible to define stochastically independent replications.

6) If the analysis should be paired or not depends on your experimental design. Typically, all measurements performed "at the same day" (starting from growing, splitting and seeding the cells) should be considered "paired" because there are often large "day-to-day" differences in how the cells adhere and grow. Note that "normalizing to the (corresponding) control" is one way to consider pairing in the analysis. But the result is one single groups of normalized values (treated vs control), not two. Normalizing controls to controls is nonsense (no matter how oen you see this in published papers). Hence, if you calculate such ratios, you have a single sample of ratio values, and you would test a hypothesis that the expected ratio has some hypothetical value (e.g. 1). Testing a single sample against a given expected value is known as a one-sample test.

7) Applying non-parametric tests on your data is out of discussion. The typical procedures based on ranks don't give you information about the directionality, because you cannot (should not) assume variance homogeneity, which is the least assumption required to interpret the results according to a directionality of effects. Bootstrapping (mean/median/modal) differences would be a possible nonparametric alternative, but they require large sample sizes to work resonably well. Typically, the required sample sizes are so large that you could also use parametric tests as well. Your n=3 is way too small here.

Jochen has excellent points (numbers 1,2,3 and 5 are a must-know minimal for post-grads or get-a-tattoo of it), if you haven't done it already I'd also like to recommend RT-qPCR measurement of siRNA knockdown before proceeding to Western blotting. If I don't see a reasonable level of transcript knockdown, I wouldn't put in the effort for protein blotting given the quick turnaround time of RT-qPCR results.

Jochen Wilhelm Thanks for the inputs. Yes I do have loading control... sorry I hadn't been clear. This is what I did step by step:

There is this protein that's called LYCAT. Our labs have used a siLYCAT to KD this protein and this siRNA has been verified very rigorously before and has been used for many years. So no question on the KD efficiency.

For my experiment, I have two conditions, siControl (non targeting, also verified) and siLYCAT. I seed the cells on a 6-well plate, half the plate transfected with siControl, the other half with siLYCAT.

I harvest the cells, and whole cell lysates are resolved by WB. I probe my protein of interest - Akt - and GAPDH (loading control) (as well as LYCAT to show good KD). I image the blots, I take the intensity of the Akt band, and I normalize that of GAPDH.

Now I compare the normalized Akt intensity from siControl sample to siLYCAT sample. Let's say the raw, normalized Akt intensity from siControl is 123, and that from siLYCAT is 45. I divide 45 by 123, which is 0.36. So when I put these into Prism, it'll be something like siControl - 1, siLYCAT - 0.36 (see the attached screenshot).

I have done this on different days, not the same day. And the cells are cancer cells.

Hope this information is enough to determine which T test I should do. Let me know what more info you need. Or how I can improve.

Using GAPDH as a control in cancer cells might not be smart. It is known that GAPDH is regulated by hypoxia and (local) hypoxia is known to occur in cancer. However, it is unlikely that this play a role in cultured cells. But the cells can have an altered (energy) metabolism, again possibly affecting GAPDH expression.

After you have confirmed that the band intensities are within the dynamic range of quantification, you should follow this pipeline:

1) take the logs of all the intensities. L = log(band intensity)

2) if you analyzed the lysates from the wells individually, then for each well, subtract the mean L of the loading controls from L of the target protein: Dwell = LLYCAT - (LACT,well + LGAPHD,well)/2 and average the Dwell-values for each treatment from the same plate. Otherwise, do the calculation using the L-values for each treatment per plate. After this you should in total have 3 D values for siControl and 3 for siLYCAT.

3) To account for day-to-day variation, use a paired t-test to test the null hypothesis that E(DsiControl) = E(DsiLYCAT). But this would not answer your research question for KD efficiency. To address that question you should better try to interpret the confidence interval. But I am very sceptical that n=3 is sufficient to make any conclusion about KD efficiency (it might barely be sufficient to show that in this particular experiment, the KD was effective (but possibly very inefficient).