We use five test data series to search for, and quantify, putative discontinuities around 1946 in five different annual-mean sunspot-number or sunspot-groupnumber data sequences. . These test data all vary in close association with sunspot numbers, in some cases non-linearly. The tests are carried out using both the before-and-after fitresidual comparison method and the correlation method of Lockwood, Owens, and Barnard, applied to annual mean data for intervals iterated to minimise errors and to eliminate uncertainties associated with the precise date of the putative discontinuity. It is not assumed that the correction required is by a constant factor, nor even linear in sunspot number. It is shown that a non-linear correction is required by R C , R BB , and R ISNv1 , but not by R ISNv2 or R UEA . The five test datasets give very similar results in all cases. By multiplying the probability distribution functions together, we obtain the optimum correction for each sunspot dataset that must be applied to pre-discontinuity data to make them consistent with the postdiscontinuity data. It is shown that, on average, values for 1932 -1943 and 5.2 %, respectively. The correction that was applied to generate R C from R ISNv1 reduces this average factor to 0.5 % but does not remove the non-linear variation with the test data, and other errors remain uncorrected. A valuable test of the procedures used is provided by R UEA , which is identical to the RGO N G values over the interval employed.