The discussion here covers five articles that are linked in the sense that they all treat population invariance. This discussion of population invariance is a somewhat broader treatment of the subject than simply a discussion of these five articles. In particular, occasional reference is made to publications other than those in this issue. The articles discussed herein are: (1) von Davier and Wilson (2008 [this issue]) considered item response theory (IRT) equating for Advanced Placement Program exams; (2) Liu and Holland (2008 [this issue]) considered parallel-linear linking for the Law School Admission Test (LSAT); (3) Yang and Gao (2008 [this issue]) considered linking for College-Level Examination Program exams that consist of overlapping groups of testlets; (4) Yi, Harris, and Gao (2008 [this issue]) considered equating for a science achievement test; and (5) Dorans, Liu, and Hammond (2008 [this issue]) considered the role of an anchor test in achieving population invariance. For the tests considered in these articles, the results reported provide support for at least the following tentative conclusions: (1) Population invariance tends to be satisfied reasonably well for carefully constructed alternative forms of a test with equal reliability (Liu & Holland, 2008; Yang & Gao, 2008); (2) Linking functions tend to be more similar for gender groups than for ethnic groups (Liu & Holland, 2008; Yang & Gao, 2008); (3) Linking functions tend to be more similar for tests that differ in reliability than for tests that measure different constructs (Liu & Holland, 2008); (4) Often (but not always) population invariance results are quite consistent across types of linking methods (von Davier & Wilson, 2008; Yi et al., 2008); and (5) Satisfying the assumption of population invariance does not guarantee that a linking can be considered an equating (Dorans et al., 2008). (Contains 1 table and 12 notes.)