# How to apply a statistical test to my Western blot result?

I am doing a student project and have to analyse the western blot results. I have a control group and 6 different test groups. The null hypothesis being, that the protein expression is same in all the groups. So I run 7 lanes at once.

Technically, the blot's to be repeated 3 times but I've managed to run it just once. I have normalized the densitometry values to the control group.This means that protein expression in the control is taken as 1 and that of the rest are shown relative to this control group. (Like- 1.025, 0.987 etc.)

What kind of a statistical test should i put in? Do stats even work for single observations?

Since I've managed to run the blot just once, it is a single observation and I don't have a mean and SD. Does that matter? ANOVAs and any post hoc test would require a spread of values, right?

Do i read the densitometry thrice so as to get a mean and an SD?

Even if I read thrice, isn't it that ANOVA assumes them to be in normal distribution? I guess for that we need more than 20 observations.

So my questions,

• Can I say comment upon significance in differences when I have just one observation in each group?

• Even if I read the same blot thrice, I expect to have slightly different values. So can I use them as three observations (I'll surely mention in my report if I did so :) ). If yes, then which test to apply?

• If I read them thrice, since these are normalized values, all three values for the control group are going to be 1. So the SD will be zero. Will that cause a problem?

I'm a medical student and as is apparent, my stats are a little weak. Please excuse me if the questions are too obvious or foolish.

The main problem you have is what you fear: you can't do proper statistical analysis on a single observation.

Re-reading the densitometry results would help account for some of the random vagaries of densitometry, but it would not get at the more fundamental and potentially much larger source of error: the differences among true biologic replicates of the same experiment. And re-running the same protein extracts on another gel doesn't count as a biologic replicate; that would simply account for the random vagaries of gel loading, antibody binding, film exposure conditions, etc.

Please don't believe any results based on a single biologic replicate. You really have to do the whole experiment several times, starting from fresh cells or tissues, to have a biologically reliable result. You will almost always find that the variability among experiments on biologic replicates is much greater than the within-experiment errors from loading, blotting, exposing, and reading the samples. That difference among biologic replicates is the variability against which you should statistically evaluate any differences you observe.

Furthermore, quantifying Western blots can have serious pitfalls, depending on how it's done. It's a particular problem with blots exposed on film where there can be saturation of the film exposure, maybe less so with more recent fluorescence-based approaches.

• Since I have to submit my report anyway, should I present it as a drawback (I dint have enough sample). Each group of mine had 5 animals - so I guess that accounted for the biological variation (would it?). Presently, since I have just one observation per group, can I just show it as a simple bar graph? (without error bars) Commented Oct 7, 2016 at 20:56
• @Polisetty if each sample that you applied to the gel was a pool of material from 5 animals, then that does help control for biologic variation (although it would usually be better to do separate analyses for each animal). There are still the issues of other technical sources of variability. Report the results you have, note the limitations, and suggest what could be done in future work to overcome the limitations.
– EdM
Commented Oct 7, 2016 at 21:20
• Thanks a lot! Since I work on the retina, it is tough to separately analyse - each sample is minimal and in microlitres! Anyway, I appreciate your time. :) Commented Oct 7, 2016 at 22:02