Let's say, I have 10 different groups, and each group has its own string sequence. So, it should be like :
G1 -> CHFAIEBD
G2 -> HCFJIGBD
G3 -> HCFAIJBD
G4 -> HFCIJEBD
G5 -> .....
G6 -> ....
The question is, is there a statistical test to say that the ordering in that 10 groups is similar ? I know it looks kinda similar, but I don't know how to prove it statistically. I really appreciate your comment on this.
There are several algorithms and measures that can be used to quantify the difference/similarity between sequences. For short strings - as those reported in the question - using the Levenshtein distance could be a good choice. This is a simple measure of difference between two strings that computes the minimum number of single-character edits necessary to change one string into the other. Edits can be substitutions, insertions, or deletions. To apply it, you can also use one of the tools available online (for example, here).