I remember one year in my teens that Indiana didn't go with the change and kept the clocks the same. The big problem was that anything that had to do with interstate travel had to have the time expressed in "federal time". Otherwise, the clocks/timetables/etc. had "state time".
Thus if a bus was only going between Indianapolis and Gary, the departure time was listed in "state time". If Gary was just a stop on the way to Chicago, the departure time was listed in "federal time". It was a real mess. Everybody was always showing up for the bus, plane or train the wrong time.
It was a one-year only shot, thank goodness.