At first glance, the movie “Frozen” might seem to have two strong female protagonists — Elsa, the elder princess with unruly powers over snow and ice, and her sister, Anna, who spends much of the film on a quest to save their kingdom.

But the two princesses actually exert very different levels of power and control over their own destinies, according to new research from University of Washington computer scientists.

The team used machine-learning-based tools to analyze the language in nearly 800 movie scripts, quantifying how much power and agency those scripts give to individual characters. In their study, recently presented in Denmark at the 2017 Conference on Empirical Methods in Natural Language Processing, the researchers found subtle but widespread gender bias in the way male and female characters are portrayed.

“‘Frozen’ is an interesting example because Elsa really does make her own decisions and is able to drive her own destiny forward, while Anna consistently fails in trying to rescue her sister and often needs the help of a man,” said lead author and Paul G. Allen School of Computer Science & Engineering doctoral student Maarten Sap, whose team also applied the tool to Wikipedia plot summaries of several classic Disney princess movies.

“Anna is actually portrayed with the same low levels of power and agency as Cinderella, which is a movie that came out more than 60 years ago. That’s a pretty sad finding,” Sap said.