I don't know high level math or statistics and wanted to ask about the math in a recent online article. The website 'TheMarySue.com' has an article saying:

ON AVERAGE, THE TOP WOMEN-LED FILMS OF 2013 GROSSED HIGHER THAN MALE-LED FILMS

"Women-Centric Films Out-Gross Male-Centric Films on Average: Twist!"

In that article the way the author determined that "Actress-centered movies out-grossed actor-centered movies by almost exactly one-third!" was by using the following:

• Total gross of all the top 100 movies in 2013: \$10.039 billion. • Total gross of 15 actress-centered movies: \$1.908 billion.
• Total gross of 79 actor-centered movies: \$7.525 billion. • Average gross of actress-centered movie: \$127 million.
• Average gross of actor-centered movie: \$95 million. The author says 15 movies of 2013 had a female lead in his view, 5 were 'neuter' and 79 had a male lead. I am not trained in statistics but it seemed to me that the author didn't apply math correctly. For example, I used his same logic to show that movies with numbers in the title grossed more than title without numbers: • Total gross of all the top 100 movies in 2013: \$10.048 billion.
• Total gross of 18 number-included-titled movies: \$2.110 billion. • Total gross of 82 letters-only movies: \$7.938 billion.
• Average gross of number-included-titled movies: \$117 million. • Average gross of letters-only movies: \$96 million.

I would think that does not show that movies with titles that had numbers were correlated to higher-returns, but a lot of people are telling me that I am wrong and that the argument made in the article based on the data is "sound" and "solid." One person on the comments section of TheMarySue says:

Yeah, I was really happy about the article until I got to their statistics and realized the logic was flawed. :(

More films on the lower end of the spectrum means the average gets pulled lower.

So I am confused because everyone else says the logic and the applied statistics is sound. :(

I don't have a preference of gender lead roles in movies. I thought the division of gross revenue to argue that those movies had some special quality was incorrect. I am trying to answer the question:
"What affect does a male lead or female lead have in the gross revenue of a movie in top 100 films of 2013?" by limiting myself to that writer's data.

How I am wrong in the application of division to create a sound argument for their premise so I don't make that mistake again? Also, what kind of math or techniques should be used to answer that question? Thanks!

• Actually it's not unreasonable that movies with numbers in the title do betters than movies without, because numbers are generally indicative of sequels to successful movies with pre-existing fan bases compared to movies that have to find a new audience from scratch with an unproven concept. Mar 21, 2014 at 20:39
• It's awkward to truncate at the top 100 from a statistical perspective; one can't just make more top 100 movies with female leads. If we just naively think of the "top 100 movies" as being 100 independent replicates which are then ordered, however, there isn't any substantial evidence in the data that movies with a female lead do better or worse than movies with a male lead (simple Wilcoxon test gives a p-value of around .75). From an economic perspective, if the movie studios are rational we might conjecture the average returns to be the same, and there isn't evidence here that they aren't.
– guy
Oct 7, 2014 at 2:36