$data[$gid] is a hash ref, so $data[$gid]->{$sample_id} is an element in that hash. To make it more explicit:

    foreach $sample_id (@{$groups[$gid]}) {
        $data[$gid]->{$sample_id} = [];  # assign anon array ref to ti
+ed hash
        foreach $element_num ( 0 .. $element_count ) {
            $element = [];
            # ... do a bunch of stuff here ...
            $data[$gid]->{$sample_id}->[$element_num] = $element;
        }
    }
[download]

Does that make more sense?