What is the statistical null hypothesis?

A very simple case is the occurrence of a given subsequence (with k bases) in a random sequence (of n bases):

P(sequence is at position i) = P(A)^[A] * P(C)^[C] * P(G)^[G] * P(T)^[T]

where P(.) are the probabilities of the bases occuring in the long sequence and [.] are the numbers of these bases in the given short squence. If all bases have the same probability (=0.25), then the formula simplifies to 0.25^k.

The occurrences within a longer sequence are binomial distributed, and there are n-k+1 possible positions for the subsequence to occur within the longer sequence (this is a simplification; not all positions are independent, especially overlapping positions are possibly not independent).

So the probability of finding 1, 2, 3, ... n-k+1 occurrences can be obtained from the binomial distribution.

If the simplification is relevant (e.g. in cases where n is not very much larger than k), one may get a better estimate using randomization approaches: repeadetly construct many many random sequences of length n and simply count the number of occurences of your subsequence in those.

Hi Vivek,

Maybe you can use FIMO (http://meme-suite.org/tools/fimo). It will compute the p-value of your motif(s) in the input sequence that you define.

Best,

Hi Jochen,

I understood the logic behind what you are suggesting. But I am still confused on how I shall implement it because I am not a lot exposed to solving biological problems statistically.

Hi Juan,

FIMO worked perfectly. Thank you so much for suggesting this amazing tool. Greatly appreciated.

I am still looking for a solution how to do it manually.

Vivek,

if you use the binomial model all you need is a function that will give you the p-values of the binomial distribution. There are surely calculators in the internet, Excel can do it (http://homepages.wmich.edu/~bwagner/StatReview/Binomial/binomia%20in%20excel.htm).

If you use randomization techniques then you will need to program it. Here it depends on what language you use. The solution is really straight-forward. You could do it by hand (paper and pencil), but to write down thousands of sequences, search them, compare them, count them is not really feasable - unless you have too much time ;)

Note that FIMO does something different: if counts occurences of a sequence in a given genomic sequence.This is not a statistical question per se. It's "just" to know how often a particular motiv exists in a given sequence.

Hi Jochen,

I have realized the issue with the FIMO results while I was sorting the data out. The significance range showing is not the similar to the significance I have. So this time I should use randomization technique as you suggest.

Preferably R language is better for statistical analysis right? Would you please help me go through how I can do a similar analysis in R?

Vivek, I attached an R script doing the randomization stuff.

It is VERY VERY simple, not optimized*, not using any sophisticated packages. It is a good start to get into the topic.

* calculation times can be rather long, depending on the sequence lengths and the numbers of replications!

Good Luck!

Thank you, Jochen. I will try that.