the region I . Specifically, For the initial analyses, thresholds just below the smallest observed resonance for each nuclide were used. ML results with these thresholds are given in column ν$_{min}$ of Table I. Because experiment thresholds might not be precisely sharp, it is expected that the resulting ν$_{min}$ values would be systematically a bit large. However, almost all ν$_{min}$ values are less than the PTD value of 1.0 . Contour plots of ML functions for $^{232}$Th, calculated at two different thresholds, in the form are shown in Fig. 4. Here, L$_{max}$ is the maximum of the ML function. Contours at fixed z = k encircle approximately the kσ confidence region, and were used to derive the 1 σ uncertainties given in Table I. Careful statistical analysis in Ref. [23] verified that these contours are reliable. The weighted average of results at minimum threshold for the 24 nuclides in the NDE is ν = 0 . 801 ± 0 . 052, which is 3.8 standard deviations smaller than the predicted result of ν = 1. Hence, these data reject the PTD with a statistical significance of 99.98%. To check this result, the combined probability for the 24 NDE nuclides was calculated using Fisher’s and Stouffer’s (both weighted and unweighted) techniques [25]. These methods yielded combined confidence levels of 99.97%, 99.98%, and 99.99%, respectively, in good agreement with the weighted-average result. Hence, at minimum thresholds the NDE data reject the PTD with high confidence and indicate that ν is significantly less than 1.0. A ν value significantly less than the PTD could be a sign of interesting physics [9, 23, 26–29]. However, a more likely explanation is that the NDE contains sizeable p -wave contamination. Results of the maximum-likelihood analyses for three NDE nuclides are shown in Fig. 5. On the left of this figure, normalized reduced neutron widths are plotted as functions of normalized resonance energy. On the right side of this figure, ν values from the ML analyses are plotted versus threshold coefficients T$_{max}$ . 9 V. CLEANSING THE NDE OF P -WAVES L ( ν, E[ g Γ 0 λ $_{n}$] ) = n 0 ∏ i =1 h $^{0}$( E exp λ i , g Γ 0exp λ i n | ν, E[ g Γ 0 λ $_{n}$] ) . (3) z ( ν, E[ g Γ 0 λ $_{n}$] ) = 2 1 2 [ ln L$_{max}$ − ln L ( ν, E[ g Γ 0 λ $_{n}$] )] 1 2 (4)