References auto-vivify in Perl; if you have a variable with an undefined value, and you treat it as a reference, Perl creates the reference for you. Thus, the push should be sufficient for all cases: push @{ $statistics{$line_number} }, $thisline; Although, if you want to be more explicit, you can create the array ref yourself:

$statistics{$line_number} ||= [];
push @{ $statistics{$line_number} }, $thisline;
[download]

There's also an example of this in perlreftut (offsite), the tutorial on references.