Statement of the problem

Let us assume that the same set of experimental data was fit to two different fitting models (equations), one of which is a simler case of the other.

Very often a fitting model with more adjustable parameters will produce a better fit (in the least-squares sense) than an alternative model with fewer adjustable parameters. The question is than whether the decrease in the sum of squares is statistically significant. The statistical calculator below provides the answer.

Calculator

This calculator will compute the probability that a decrease in sum of squares upon the introduction of an additional fitting parameter could arise by random chance.

For the more complex model (with greater number of adjustable parameters) to be accepted, typically we want the computed probability to be lower than 5% (P < 0.05).