# Is Estimate the same as a fold change? If not, what is a Fold Change?

### From Array Suite Wiki

The estimate is not the same as the fold change. Many users are more comfortable dealing on a linear scale, rather than a log scale. In practical terms, it is to maintain the advantage of log-transformed fold change (uniform distances on the X-axis whether up-regulated or downregulated), while reflecting the dynamics of a linear ratio (8x upregulated or 8x downregulated is more intuitive than log2-fold change of 3 or -3).

From a technical standpoint, Fold Change, as used in Omicsoft, is the ***unlogged estimate***. So, on a log scale of 2, if the estimate is 2, then the Fold Change is 2^2 or 4. If the estimate is -2, then the fold change is -(2^abs(-2)), or -4. A fold change can have a range of (1, infinity) and (-infinity, -1) but cannot have a value between -1 and 1. If the original data had been on a linear scale, this would be the equivalent of taking the geometric mean of Treatment/geometric mean of Control.

Consider the following example: On a linear scale the expression values are 16, 32, and 64 for the Treatment (equivalent to 4,5, and 6 on a log-2 scale), and 4, 8, and 16 for control (equivalent to 2,3, and 4 on a log-2 scale). So, the geometric mean of the treatment group would be 32, while the geometric mean of the control group would be 8. Thus, if you take 32/8, you get a fold change of 4 (equivalent to the estimate generated above).

Some other programs, when generating fold changes, use the average (or arithmetic mean) to generate their fold change values, using a linear scale. (This would be Average of Group A/Average of Group B). However, statisticians agree that it is more appropriate to use the geometric mean (linear scale) or arithmetic mean (log scale), so that is what Array Studio does to generate fold changes.

A positive fold change indicates that the first group in a contrast is up regulated compared to the second group. A negative fold change indicates that the first group in a contrast is down regulated compared to the second group.