As the preponderance of journal rankings becomes increasingly more frequent and prominent in academic decision making, such rankings in broad discipline categories is taking on an increasingly important role. The paper focuses on the robustness of rankings of academic journal quality and research impact using on the widely-used Thomson Reuters ISI Web of Science citations database (ISI) for the Statistics & Probability category. The paper analyses 110 ISI international journals in Statistics & Probability using quantifiable Research Assessment Measures (RAMs), and highlights the similarities and differences in various RAMs, which are based on alternative transformations of citations and influence. Alternative RAMs may be calculated annually or updated daily to determine When, Where and How (frequently) published papers are cited (see Chang et al. (2011a, b, c), Chang et al. (2012)). The RAMs are grouped in four distinct classes that include impact factor, mean citations and non-citations, journal policy, number of high quality papers, and journal influence and article influence. These classes include the most widely used RAMs, namely the classic 2-year impact factor including journal self citations (2YIF), 2-year impact factor excluding journal self citations (2YIF*), 5-year impact factor including journal self citations (5YIF), Eigenfactor (or Journal Influence), Article Influence, h-index, PI-BETA (Papers Ignored - By Even The Authors), 5YD2 (= 5YIF/2YIF) as a measure of citations longevity, and Escalating Self Citations (ESC) as a measure of increasing journal self citations. The paper highlights robust rankings based on the harmonic mean of the ranks of RAMs across the 4 classes. It is shown that focusing solely on the 2-year impact factor (2YIF) of a journal, which partly answers the question as to When published papers are cited, to the exclusion of other informative RAMs, which answer Where and How (frequently) published papers are cited, can lead to a distorted evaluation of journal quality, impact and influence relative to the more robust harmonic mean of the ranks.
