G-theory was used in this study to quantify the sources of variance in activity (i.e., pedometer steps per day) and to identify the study conditions needed to attain a desired level of reliability among youth. In contrast to previous studies that monitored activity across a series of days, the universe of admissible observations in the current analysis included days and seasons. Extending the universe provides a more robust interpretation of reliability and can likely be used to improve relative and absolute decisions in physical activity research.
The results of the study provide new information about reliability of objectively monitored physical activity in youth. Numerous studies have used 7-d monitoring protocols to capture "typical" activity behavior, and in most cases, 4-5 d of clean data are viewed as acceptable. The decisions have been justified on the basis of calculations from the Spearman-Brown prophecy formula, but G-theory provides a more robust approach for reliability determinations. For example, consider the D-study in Table 3 for n′s = 1 and n′d = 7 (random design), which gives Symbol2 = 0.46. For an assessment period that is twice as long (i.e., n′s = 1 and n′d = 14), the Spearman-Brown formula predicts Symbol2 = [2(0.46)/(1 + 0.46)] = 0.63. In contrast, G-theory calculates a lower reliability estimate for n′s = 1 and n′d = 14 (Symbol2 = 0.51). In G-theory, variance attributable to σ2 (P × S) remains unchanged for any number of days, whereas in the above example using the Spearman-Brown formula, all relative error components (e.g., Symbol2 (P × S), Symbol2 (P × D), Symbol2 (P × S × D)) are divided by the same constant. As a result, the Spearman-Brown formula predicts a larger value for reliability and a smaller relative error variance compared with values obtained from the G-theory. The observed differences can likely be attributed to the structural differences in measurement error models between the Spearman-Brown formula and the G-theory. The G-theory can also handle data with varying variance and covariance structure.
Analytic error is a concern for any field-based study where participants are instructed to report daily activity levels. In this study, residual variance contributed a large proportion of the total variance (∼56%), and we were unable to determine the amount of error directly attributable from the P × S × D interaction term and that from other unidentified sources. Given the wide range in activity universe scores among participants (5643-20,509 steps per day), we contend that error from the P × S × D interaction term was the largest source of residual error. Although data are not available to validate this assumption, we argue that analytic error was minimized in the study design by providing detailed instructions to all participants, removing excessively high (>30,000 steps) and low (<1000 steps) daily pedometer values and capturing total activity across most of the monitoring day (mean pedometer wear time = 750 ± 48 min). We do acknowledge the risk of using self-reported pedometer data; however, we have no reason to believe that the amount of analytic error in the current study differed from other studies using a similar protocol. Additional sources of variance unaccounted for in the current design (e.g., pedometer type or body mass index) could have also contributed toward residual error.
The present study demonstrates the potential for using G-theory to understand the reliability of youth activity behavior. The findings are based on a relatively small sample, so additional research with larger samples is needed to provide comparison data. To date, few studies report variance component estimates, so direct comparisons are difficult. The results herein are based on an indicator of physical activity volume (daily pedometer steps), and therefore, future studies should use G-theory to examine the variance from different instruments (e.g., accelerometry-based activity monitors) and for different outcome measures (moderate-to-vigorous physical activity or sedentary behavior). Investigators are encouraged to report variance component estimations to allow for comparisons across studies. In doing so, a method to determine the importance (or unimportance) of factors could be determined. G-theory allows researchers to examine 1) multiple sources of measurement error variance, 2) interactions that contribute to measurement error variance, and 3) estimate reliability coefficients on the basis of different decisions. Quantifying variance in physical activity research is important to identify sources of error. The systematic approach used to obtain variance component estimates reported herein represents a novel approach to examine sources of variance and represents a unique contribution to physical activity assessment research.
This work was not supported by a funding source. The authors have no conflicts of interest to declare. The authors thank Dr. Joe Eisenmann for insightful conversations regarding the variance in physical activity. SWITCH is a trademark of the National Institute of Media and the Family, and this was funded by Medica Foundation, Healthy and Active America Foundation, and Fairview Health Services and Cargill, Inc.
The results of the present study do not constitute endorsement by the American College of Sports Medicine.
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