Phones with the highest customer satisfaction rates have at least one thing in common -- they're all huge.

The top three smartphones based on the American Customer Satisfaction Index, an independent national study, all have a 5.5-inch screen or larger.

Samsung's 5.7-inch Galaxy Note 4 took the No. 1 spot on this year's list with an ACSI score of 86 out of 100. In other words, 86 out of 100 Samsung Galaxy Note 4 customer said they were satisfied with their phones.

The Samsung Galaxy Note 3, Apple (AAPL) iPhone 6 Plus (5.5"), Samsung Galaxy S5 (5.1") and the iPhone 6 (4.7") each scored 82 out of 100 on the scale, sharing second position in the ranking. The Samsung Galaxy S6 (5.1") was not on sale when the survey was conducted.

Cell phone customer satisfaction has remained steady year-over-year, with Samsung and Apple customers reporting greatest satisfaction. Overall, Apple had the most phone models in the top 20, while Samsung had the most in the top 10.

Most surprising, however, was that BlackBerry customer satisfaction increased 5% year-over-year, making it the No. 4 cell phone brand in the United States for 2015.

But keep in mind -- the annual American Customer Satisfaction Index isn't a poll of which phone consumers would most like to have. It surveys device owners about how happy they are with their current phones. About 70,000 people were included in the study.

"Apple's long-awaited and much-lauded redesign of its iconic iPhone may have set new records, but its newer models do not appear to have gained any advantage over Samsung's flagship smartphones when it comes to user satisfaction," the study's authors write.