Suppose I have gene expression values (not at log2) at pre and post from 3 patients (these are real values):

```
pre<-c(22.228, 0.002, 0.013)
post<-c(0.185, 0.018, 0.009)
```

I am wondering how to calculate the mean fold change between pre and post:

```
#mean of fold change
mean(post/pre)
[1] 3.234
#fold change of mean
mean(post)/mean(pre)
[2] 0.0095
```

Seems completely different, which one is the correct or should be calculated other ways?

If I wanted to calculate the log2FC:

```
#this seems the limma formula
mean(log2(post))-mean(log2(pre))
[1] -1.4231
#then back to fold change:
2^-1.4231
[1] 0.3729
```

Why this 0.3729 is so different from either the other two 0.0095 and 3.234? Which way should I use?

Fold change is a ratio of number of aligned or classified transcripts in the treatment condition and the control condition. As the number of transcripts can never be negative, I wonder why are some of our fold change values are negative (not after log2 transformation!)

Could somebody please explain this?

FCs are almost exlusively reported as log2 because otherwise FCs < 1 are bunched together between 0 and 1 while > 1 would be 1 to infinity. The log transformation makes the FC negative if FC is smaller 1. Just calcualte log2(10/50) then you understand how negative FCs can happen. Please do not ask questions in the answer field.