The study has discovered “a while” estimates a length of 4 months whereas “a little while” would be a little less at 3 months' time. Going a little further, “a while back” would indicate the potential of occurring up to 8 months in the past.
What does mean for a while?
a short period of time. a little. for a moment.
How much days is a while?
A while does not have an official definition. It is used to mean that something will take a long time, but not a very long time.