Effectiveness is an indicator as to how the process is successful in delivering the output as per requirements. Efficiency is an indicator as to the extent of output delivered with least resource consumption. i.e. higher input to output ratio.
Ideally it is not relevant to consider the efficiency of a process that is not effective. If a process is very efficient for what ever output it delivers, but not effective, it simply means that the process is ' efficiently' delivering a wrong output. However, we may conditionally apply this thought process; for e.g. a process could have a very high process capability, with very low variation, but due to a mean shift it is not delivering the required output, and hence not effective.
For eg. in my recent experience in a fuel station, they had an equipment that is capable of checking and correcting the air pressure of all my four wheels, as against walking around and checking each wheel one by one. I felt that this is an efficient process, and saves time and effort. However, after the process I did not have comfortable drive. Upon checking the individual pressure of each wheel, I found the variation is high. Thus, though the process was attempted to be made more efficient, the effectiveness has been compromised.
It is quite possible to have a process that is effective, but need not be efficient.
Imagine a continuously running escalator, as against an elevator that can carry only 4 persons. The escalator represents a more effective process since it is always available to go up. However, since it is continuously running irrespective of any passenger, it may not be an efficient process.