Background: Longitudinal or time-dependent activity data are useful to characterize the circadian activity patterns and to identify physical activity differences among multiple samples. Statistical methods designed to analyze multiple activity sample data are desired, and related software is needed to perform data analysis.

Methods: This paper introduces a functional data analysis (fda) approach to perform a functional analysis of variance (fANOVA) for longitudinal circadian activity count data and to investigate the association of covariates such as weight or body mass index (BMI) on physical activity. For multiple age group adolescent school girls, the fANOVA approach is developed to study and to characterize activity patterns. The fANOVA is applied to analyze the physical activity data of three grade adolescent girls (i.e., grades 10, 11, and 12) from the NEXT Generation Health Study 2009–2013. To test if there are activity differences among girls of the three grades, a functional version of the univariate F-statistic is used to analyze the data. To investigate if there is a longitudinal (or time-dependent activity count) difference between two samples, functional t-tests are utilized to test: (1) activity differences between grade pairs; (2) activity differences between low-BMI girls and high-BMI girls of the NEXT study.

Results: Statistically significant differences existed among the physical activity patterns for adolescent school girls in different grades. Girls in grade 10 tended to be less active than girls in grades 11 & 12 between 5:30 and 9:30. Significant differences in physical activity were detected between low-BMI and high-BMI groups from 8:00 to 11:30 for grade 10 girls, and low-BMI group girls in grade 10 tended to be more active.

Conclusions: The fda approach is useful in characterizing time-dependent patterns of actigraphy data. For two-sample data defined by weight or BMI values, fda can identify differences between the two time-dependent samples of activity data. Similarly, fda can identify differences among multiple physical activity time-dependent datasets. These analyses can be performed readily using the fda R program.