Systems and methods for identifying and removing spikes in data sets representing PCR growth curves or other sigmoid type curves or growth curves. A double sigmoid function with parameters determined using a Levenberg-Marquardt regression algorithm is used to find an approximation to the curve, and a statistical test such as a z-test is then used to identify spikes by identifying data points in the data set that do not fit well with the approximation. The identified spike(s) are removed from the data set and/or replaced with interpolated data points determined by using data points surrounding the identified spike(s). In one aspect, a spline interpolation process such as a cubic spline interpolation process is used to find an approximation to the data set with the identified spike points removed. Interpolated values to replace the spike points are then calculated using the cubic spline interpolation approximation curve.