Thanks for the comments. In case anyone else runs into a similar problem, I have found a workaround: I have not figured out what's going on with Statistics::TTest or Statistics::Distributions, but I have found another module that works correctly with these data. As I understand it, a one-way ANOVA on a single pair of distributions is equivalent to an Student's T-test. As such, I tried using Statistics::ANOVA and I had success. Using the definitions of %datasets from the above code, the following loop will calculate correct p-values (matching the values that Excel gives):

foreach my $dataset (sort keys %datasets) {

    my $aov = Statistics::ANOVA->new();

    $aov->load( "$dataset\1", \@{$datasets{$dataset}[0]} );
    $aov->add( "$dataset\2", \@{$datasets{$dataset}[1]} );

    $str = $aov->anova(independent => 1, parametric => 1, ordinal => 0
+);

    print $str->{_stat}->{p_value} . "\n";
}
[download]