Note the two data points in the analysis of Becker and Berhane but not in that of Swan et al. However there is actually an increase in sperm counts before 1980. For the data after 1970, the flexible fits trace a pattern of a quadratic curve. The point estimates and statistical tests for the quadratic effect of year are shown in Table 1. The value for 1944 was excluded because it is clearly not part of the quadratic pattern.
Regression fits for European data.
In conclusion, the significant and very marked decline that Swan et al. If the two non-English studies from 1944 and 1971 are included, there is no significant decline over the entire period. However, a significant nonlinear pattern is found, with an increase until about 1980 followed by a decrease. There are several methodological morals to this story. First, single data points can have considerable influence in linear regression, particularly when the total number of sample points is small.