Normalization of gene expression levels between arrays. (a) The CEL intensities (see text) of a pair of replicate arrays (array 11 and 12 in array set 5) are plotted against each other. The baseline array 11 (shown on the y-axis) is not as bright as array 12 (shown on the x-axis). The smoothing spline (green curve) deviates from the diagonal line y = x (blue curve), indicating the need for normalization. (b) The same plot as (a) with superimposed circles representing the invariant set, on the basis of which a piecewise linear normalization relationship is determined (black dotted line, whose y-coordinate is the normalized value of array 12). The normalization curve is close to the smoothing spline curve in (a) as the two arrays are replicated arrays and all probes should be invariant. (c) After normalization (y-axis is the baseline array 11, and x-axis the normalized value of array 12), the scatterplot centers around the diagonal line and the array 12 is adjusted to have the similar overall brightness as array 11. The smoothing spline curve is also close to the diagonal line. (d) The Q-Q plot of probe intensities of array 11 and normalized array 12 shows the probes in the two sets have almost the same distribution.