This medal was awarded to Stephenson Percy Smith in 1920. "The Hector Memorial Fund was established in 1910 to support the award of the Hector Memorial Medal and Prize. This medal was awarded annually, in rotation, for plant sciences, chemical sciences, human sciences, solid earth sciences, mathematical physical and engineering sciences, and animal sciences, to that investigator who, working within the Dominion of New Zealand shall, in the opinion of the Council, have done most towards the advancement of that branch of science to which the medal and prize are in such year allotted. The bronze medal depicts on the obverse the late Sir James Hector kcmc frs md, and on the reverse, a crouching Māori observing a pair of huia in a New Zealand landscape.

From 1996 the Hector Medal has been awarded annually, in rotation, for mathematical and information sciences, chemical sciences and physical sciences to the investigator who, working within New Zealand, has undertaken work of great scientific or technological merit and made an outstanding contribution to the advancement of the particular branch of science and technology. In 1999, Council agreed that the Hector Medal will, from 2000, be awarded biennially.

The Hector Medal for 1999 (mathematical and information sciences) was awarded to Professor George A F Seber FRSNZ for fundamental contributions to statistical theory, for the development of the statistics profession in New Zealand, and for the advancement of statistics education through his teaching and writing." See: The Royal Society of New Zealand Te Apārangi. http://www.royalsociety.org.nz/publications/reports/yearbooks/year1999/awards/