Hi there. I'm looking for assistance with some stats. I have a sample size of three (small I know) however, i would like to perform a trend test as the non-parametric tests I have done do not show significance. I have done qPCR (gene expression profiling) on cells that were treated with two drugs at varying concentrations. Any suggestions on how to perform a trend test would be greatly appreciated. Thanking you in advance for your response!
If you only have three data points you'll always get trimmed or almost always I just grab it
Trend means that later values are systematically higher (or lower) than their preceding values, i.e. the differences between adjacent values are systematically positive (or negative). This suggests a sign test on the differences. A reasonable null hypothesis is that positive and negative differences are equally likely. In a series of n values (= n-1 diffences) you so get a binomial distribution of the number of differences being positive (or negative). And this is it.
Now we can think about the extreme case that all your 3 values are strictly monomonousely increasing. So these are 2 increases in a row. The probability to observe this under the null (and the assumption of independence, for sure) is 0.5*0.5 = 0.25. Given you want to controll the type-I error for either direction (increasing and decreasng trends) you will have to multiply this p-value by 2, obtaining p=0.5.
Thus, your available data -even in the "best" possible case!- does not give you any information at all.
You will need at least n=7 to just be able get acceptably low probabilities under the null. When all 6 differences are in the same direction, the two-sided p-value will just be 0.03.
Hence, if you do not have any more information but the rank order (this is what the sign test on the differences is actually looking at), there is no chance to get any even remotely sufficient information about a trend. I think this is what Jay above said in fewers words ;)
Thank you both for your answers! I originally did a Kruskal-Wallis test with Mann-Whitney for post hoc analysis. However, it was then suggested to me that I do a sign test but I was unsure whether a sign test tested for trend. Anyways, I went ahead and did it as the examiner of my thesis wanted me to and all my p values were p=1 or p=0.25. Jochen, thank you for your explanation, I feel much better knowing that I did indeed test for trend. I also read that "past" software requires a sample size of 7 as you mentioned. At least I can now motivate strongly why I used the test I did and not a sign test. Thanks a mill (:
- Badges
- Science method