'globally-assessed' is formed from the adverb 'globally' (from 'global' + '-ly') and the past participle 'assessed' of the verb 'assess'. 'global' ultimately comes from Late Latin 'globalis', from Latin 'globus' meaning 'ball' or 'sphere'. 'assess' comes from Latin roots meaning 'to sit beside' used in legal/tax contexts and developed into a verb meaning to determine a value or tax.

'global' entered English via modern European usage (from Late Latin 'globalis' and ultimately Latin 'globus'), becoming common in the 19th century; 'assess' passed into English from Latin via Old French (e.g. Old French 'assesser'/'assesser') and Middle English forms (e.g. Middle English 'assessen'), later becoming the Modern English 'assess'. The compound usage (adverb + past participle) follows standard English formation of adjectival phrases like 'internationally-recognized' or 'widely-used'.

Originally roots related to 'globus' referred to 'sphere, ball' (leading to the sense 'world' or 'whole'), and 'assess' originally had senses tied to sitting beside (in a judicial/tax sense) and assigning a value; over time 'assess' shifted to the general modern sense 'to evaluate, estimate, or judge', so the combined form now means 'evaluated on a worldwide scale'.