The apostrophe and decades
Most of the time when you’re talking about decades, for example, the 1980s, 1970s or 1960s etc, you should not place an apostrophe before the ‘s’. Lots of people do, but have the courage of your convictions and refrain. Just say no.
The following are correct (all without an apostrophe):
“Patti Smith lived in New York in the late 1960s and early 1970s.”
“The 1960s saw many changes in society.”
“Shirts with big collars were popular in the 1970s.”
“In the 1950s, women were expected to stay at home.”
If you need some basic information about the possessive apostrophe, go to: The possessive apostrophe. Part 1: the basics.