One minor improvement would be to not repeat the test, by returning from the sub or continuing the loop if you just added it:

    # if we haven't hit this line yet, add an array 
    # reference to %statistics at this line number.
    if (not defined $statistics{$line_number} ) { 
      $statistics{$line_number} = [ $thisline ];
      next; # or return or whatever to avoid next push
    }
    # now we know that we have an array ref
    # and all we have to do is push it.
    push @{ $statistics{$line_number} }, $thisline;
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