"had significant effects" is correct and usable in written English.
Example sentence: The new policy changes had significant effects on public opinion.
The vigorous road-development program had significant effects.
Some of the "lower" fungal protists have had significant effects on human history.
Wundt's monumental Principles of Physiological Psychology (1874) had significant effects on education in the 20th century.
Two institutional changes, nevertheless, had significant effects upon the society of Milanese Lombardy.
OF had significant effects on SOM and WEOM.
Time and temperature had significant effects on the removal efficiencies.
The age of calf had significant effects on all traits.
Sludge addition had significant effects on all the variables measured.
Reaction temperature and time had significant effects on percent conversion.
Warning content only had significant effects on drivers' detection stage.
Tillage systems had significant effects on ammonia emissions.
