P-values for Statistical tests evaluating LiNGAM assumptions.

Note: Leftmost column shows the evaluated model in the form where variable Y is a function f of X plus an error term e, denoted Y = f(X) + e. The second column is a p-value for the null-hypothesis that the f does not have quadratic nonlinearity, third column for the e being Normally distributed, fourth for the independence of X and e using L1-test, and final column tests independence by Hoeffding’s test (‘†’ superscripted). Lilliefor’s test for normality was based on tabulated values, and did not allow higher precision than given. For independence test between the residual and independent variable in the Wisconsin Longitudinal study data (n = 6640), very small p-value was obvious but exact value difficult to find using a standard function-minimizer.