There are a couple of tricks I use in this sort of context. Consider:

use strict;
use warnings;

sub new {
    my ($class, $act) = @_;
    my %activities = (
        ACT        => $act,
        ACTIVITIES => {
            'Sale'    => {datefield => "date_sold",},
            'Purchae' => {datefield => "date_bought",},
            }
            );
    my $self = bless \%activities, $class;

    return $self;
}

sub get_stats {
    my ($self, $arg) = @_;
    my $funcName = "_do$self->{ACT}";
    my $func     = $self->can($funcName);

    die "Class " . ref($self) . " doesn't know how to '$funcName'\n" i
+f !$func;
    $self->$func($arg);
}

sub _doSale {
    my ($self, $arg) = @_;

    $self->dosomething($arg);
}

sub _doPurchae {
    my ($self, $arg) = @_;
    ...
}

sub dosomething {
    my ($self, $arg) = @_;

    print "This is test ($arg)...\n";
}


my $obj = main->new('Sale');

$obj->get_stats('wibble');
[download]

Prints:

This is test (wibble)...
[download]

$self->can lets you preflight the call so you have some control over error handling.

my $funcName = "_do$self->{ACT}"; ensures only expected members can be called.