It is hard to discern a pattern in the upper panel whereas the strong relationship is shown clearly in the lower panel.

The comparison of the means of log-transformed data is actually a comparison of geometric means. This occurs because, as shown below, the anti-log of the arithmetic mean of log-transformed values is the geometric mean.

Table 1 shows the logs (base 10) of the numbers 1, 10, and 100. The arithmetic mean of the three logs is

(0 + 1 + 2)/3 = 1.

The anti-log of this arithmetic mean of 1 is

101 = 10

which is the geometric mean:

(1 x 10 x 100).3333 = 10.

Table 1. Logarithms.

X

Log10(X)

1

10

100

0

1

2

Therefore, if the arithmetic means of two sets of log-transformed data are equal, then the geometric means are equal.

http://onlinestatbook.com/2/transformations/log.html

Dear Mehdi,

Thank you very much for your answer. The values are in log2 form and I calculate the 2^() and it resolves my problem and I got the actual value.

Quantile normalization works good for microarray data and also works for NGS data.