Hi Kate,
Spectral classification is a rather inexact science as many stars show anomalies which don’t fit neatly into the simple MK classification system. As a result you get different opinions for the classification even for non variable stars (Variable stars can change their classification with time for example due to temperature changes caused by pulsations)
A good source for spectral classifications is Brian Skiff’s huge catalogue which has all the published classifications with the references for currently approaching a million stars
http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=B/mk
Here we see for sigma Boo a range of classifications dating from 1897 to 2001
F4V kF2 mF1 is the latest one and comes from a paper by Richard Gray who is famous in stellar classification circles and for example co-authored the current “bible” on the subject “Stellar Spectral Classification” by Gray and Corbally
The paper referenced is here
http://simbad.u-strasbg.fr/simbad/sim-ref?bibcode=2001AJ….121.2148G
There he notes that sigma Boo is metal weak and looking in the footnotes to table I (page 2155) he explains the multiple classification nomenclature he has used. So for sigma Boo we have a metal weak star with the traditional classification F4V, presumably based on the Balmer lines but based on the strength of the Ca II K lines it looks like an F2 and based on the metal line spectrum it looks like an F1
Robin