Validation of Pure and Total Movement Dispersion Variables as Measures of the Distribution of Daily Activity Using Accelerometers: A Secondary Analysis of a Prospective Cohort

Abstract

Aim:

Physical activity (PA) positively impacts health, but the optimal manner to achieve PA remains unclear. Pure and total movement dispersion are novel metrics that quantify the spread of movement across the day, with (total) or without (pure) intensity. The purpose of the study is to evaluate whether pure and total movement dispersion are positively associated with established PA metrics and inversely associated with sedentary behavior (SB) metrics.

Subject and Methods:

This study involves a secondary analysis of accelerometer data collected within the Multicenter AIDS Cohort Study (MACS) from 2018 to 2020 in four U.S. cities (Boston, Chicago, Los Angeles, and Pittsburgh) as part of a sleep substudy. Of the data received on 638 participants who wore an ActiGraph GT9X on their wrist for a period of seven days, 594 (93%) completed at least four valid wear days (≥10 hours/day) and were included in the analyses. Pure and total movement dispersion were calculated from raw accelerometer data utilizing an author-developed algorithm on a supercomputer and compared to average duration and bout length of moderate-vigorous intensity PA (MVPA) and SB, determined using the ActiLife platform with Montye cutpoints for adult wrist-worn activity, and active-to-sedentary (ASTP)/sedentary-to-active transition probability (SATP), previously calculated as part of the MACS sleep substudy. Due to the skewness of the data, Spearman’s Rank correlations were computed to assess the relationships between pure and total movement dispersion and the established measures of PA and SB. Study activities were approved by Institutional Review Boards at each participating site, and all participants provided written informed consent for their data to be used in future studies.

Results:

Participants (n = 594) had a mean age of 45 years (SD = 12) and 78 % were living with HIV. Pure movement dispersion demonstrated significant positive associations with PA measures (MVPA minutes: r_s =.4056, p < .0001; MVPA bout: r_s =.1708, p <.0001; SATP: r_s =.5011, p <.0001) and negative with SB metrics (SB minutes: r_s = −.0853, p =.0377; SB bout: r_s =−.382, p <.0001; ASTP: r_s = −.3837, p <.0001). Total movement dispersion exhibited stronger associations with PA measures (MVPA minutes: r_s =.5719, p < .0001; MVPA bout: r_s =.2844) and SB metrics (SB minutes: r_s = −.2183, p <.0001; SB bout: r_s = −.5039, p <.0001; ASTP: r_s = −.4707, p <.0001). The strength of the relationships between the measures was weaker in those under 40 years old with pure movement dispersion and SB minutes (r_s = −.1758, p =.2174) and MVPA bout (r_s = .2451, p =.0829), and with total movement dispersion and MVPA bout (r_s = .2565, p = .0692), no longer significantly associated.

Conclusion:

Both measures displayed expected associations with duration, intensity, and transition of PA and SB, supporting their convergent validity as a combined movement metric. These metrics can complement established measures to provide a richer context for PA behaviors and potentially explore the impact of varying dispersion levels on health outcomes. Future work will focus on establishing optimal ranges for both metrics that relate to positive health outcomes, such as changes in cardiovascular risk. Because the data are cross-sectional, causal inference cannot be established. Additionally, wrist-based accelerometer placement may bias intensity classification, and residual confounding from unmeasured lifestyle factors cannot be excluded.

Frequent bouts of movement spread throughout the day is an emerging lifestyle approach for achieving the recommended amounts of daily physical activity (PA). An emerging body of literature indicates that the distribution of movement activity throughout the day, specifically the accumulation of PA, offers numerous health benefits, such as improved cardiorespiratory fitness, blood pressure, lipids and glucose metabolism, and body mass, suggesting that engaging in short bouts of movement may be equivalent to the structured physical activities of 30–45 minutes in moderate to vigorous intensity physical activity (MVPA) traditionally suggested to achieve the recommended weekly 150 minutes (Murphy et al. 2019; Piercy et al. 2018). Additionally, distributing movement throughout the day breaks up prolonged sedentary behavior (SB), such as continuous sitting or lying down for 60 minutes or more, which is associated with an increased risk of cardiovascular disease (Booth et al. 2017; Keadle et al. 2017; Rezende et al. 2024). Replacing as little as 10 minutes of SB with 10 minutes of MVPA can offset the hazards of prolonged SB and improve multiple cardiovascular outcomes (Hansen et al. 2018; Moura et al. 2019).

This strategy of spreading movement throughout the day can be incorporated into a daily routine and implemented in various settings, including home, work, or school, with minimal burden (Islam et al. 2022; Welsch et al. 2021). This approach may help individuals overcome barriers to participating in traditional structured physical activities, such as the built environment, time constraints, and limited access to equipment (Hoare et al. 2017; Islam et al. 2022). The use of more frequent bouts of PA across the day also provides a more feasible way to achieve the recommended 150 minutes of moderate-intensity PA or 75 minutes of vigorous-intensity aerobic PA per week to achieve health benefits (Piercy et al. 2018). The Physical Activity Guidelines for Americans were established based on self-report tools for PA measurement; however, the introduction of actigraphy, which directly measures PA intensity and duration, may prompt updates to these guidelines in the future (Du et al. 2019; Singh et al. 2020). The guidelines, additionally, are focused on leisure-time PA and not the total movement or PA over the course of a day. Therefore, actigraphy provides more specific measures that capture daily PA behaviors in ways that self-reports alone cannot.

Historically, PA has been measured and reported primarily as average daily minutes of MVPA or total weekly minutes of MVPA within the leisure domain, to align with national PA guidelines. However, interest in bouts of MVPA ≥10 minutes began in 1995 with a report from the American College of Sports Medicine (Pate et al. 1995), which first suggested that multiple 10-minute bouts of MVPA could achieve the same benefits as a single, longer session. This idea has created a paradigm shift that continues to evolve today, with researchers examining the benefits of bouts at even shorter time intervals. However, the evidence is inconclusive so far, and more research is needed in this area (Singh et al. 2020).

Other methods for measuring daily patterns of PA have been explored. Fanning et al. (2019) examined variances in transitions from light-intensity PA to MVPA and from SB to light-intensity PA. Dunton et al. (2020) incorporated the Gini index, a commonly used tool in economic research, to measure daily accumulation of MVPA and SB. The resultant coefficient (G index) quantifies the fraction of the total sedentary or MVPA time accumulated in bouts longer than a given length (Chastin and Granat 2010). The Monitor-Independent Movement Summary (MIMS) provides a standardized method for characterizing total activity volume but does not address the pattern of PA accumulation (Belcher et al. 2021). Some other studies employed compositional isotemporal substitution models to measure the hypothetical “effect” of reallocating minutes of SB with different intensities of PA on the targeted outcomes. The Isotemporal Substitution Modeling (ISM) approach does not directly measure the daily patterns of movement. Instead, it uses the reallocation of SB with PA as a means of determining how an increase in PA might affect a certain outcome, such as body fat (Chastin et al. 2015; Fu et al. 2024; Gába et al. 2021). Schrack et al. (2019) developed a different approach to the patterns of daily PA related to functional status in older adults by examining the probability of a person’s transition from active to sedentary behaviors (Active-to-Sedentary Transition Probability [ASTP]), which was calculated as the reciprocal of the average PA bout length. A higher Active-to-Sedentary Transition Probability percentage indicates a decreased ability to maintain PA for longer periods and is associated with poorer health outcomes, such as fragility and fatigue. Conversely, Sedentary-to-Active Transition Probability (SATP) signals less prolonged SB and more movement, so a higher SATP relates to improved health (Schrack et al. 2019). Another approach to visualizing an individual’s daily PA patterns is to use daily graphs generated from accelerometer measurements, which can identify opportunities to increase the strength or duration of existing PA or infuse PA into prolonged SB periods (Klamm et al. 2022; Welsch et al. 2021). However, the graphs provide only a visual, without the ability to quantify potential changes in these daily patterns. While these other strategies have been effective at examining bouts of PA or SB, a need still exists to measure the patterns of daily movement with and without respect to the intensity.

Accumulating multiple bouts of movement throughout the day continues to evolve as a recommendation for improving health and fitness in adults with the Move More, Sit Less campaign (Piercy et al. 2018). Recently, Canada released 24-hour movement guidelines, which recommend limiting daily sedentary time to eight hours or less and encourage regular breaks during prolonged periods of sitting (Canadian Society for Exercise Physiology 2025). However, no current guidelines exist for the ideal approach to accumulating PA and SB throughout the day. As this body of literature continues to develop, it is important to objectively measure and quantify the dispersion of movement activity throughout the day. Pure and total movement dispersion are newly developed methods for quantifying movement dispersion, providing strategies for considering the patterning of movement that other approaches, such as MIMS and ISM, do not. Pure movement dispersion measures the distribution of movement across the day, independent of movement intensity. Total movement dispersion involves measuring the same distribution with the intensity of movement added (Klamm et al. 2022). The distinction of intensity between the two algorithms allows an examination of the potential influence of general movement, or breaking up SB, versus more intense movement, such as MVPA. In essence, these novel metrics provide a way to quantify the message of the Move More, Sit Less campaign and determine whether individuals are changing their behavior to match the recommendations.

The range of movement dispersion can be illustrated by combinations of daily movements with increasing movement and intensity. Any increase in the frequency of transitions from sitting to moving indicates an increase in pure movement dispersion. Whereas more frequent changes in movement intensity, such as running, are associated with greater total movement dispersion. These measures are not intended to replace established measures, such as minutes in MVPA, but rather to complement them, providing a richer description of an individual’s PA patterns and, therefore, offering more insights into the relationship with health and potential interventions.

Purpose

This study aims to build on the previous development of pure and total movement dispersion as derived variables for the measurement of the spread of PA across the day that extend beyond the established outcome of the volume and intensity of PA alone (Klamm et al. 2022). The purpose of this study was to determine the validity of pure and total movement dispersion by examining the relationship of pure and total movement dispersion with standard measures of PA and SB, using existing accelerometer data. We hypothesize that pure movement dispersion will demonstrate a positive association with daily minutes and bout length of MVPA, a positive association with sedentary-to-active transition probability, an inverse association with daily minutes and bout length in SB, and a negative association with active-to-sedentary transition probability. Whereas, total movement dispersion will demonstrate similar, yet stronger associations, especially with minutes in MVPA and SB, since intensity will be considered in addition to movement alone.

Methods

Sample

These data were collected within the Multicenter AIDS Cohort Study (MACS), a longitudinal cohort study of the natural and treated history of HIV that enrolled a total of more than 7300 gay or bisexual men living with HIV or comparable men without HIV since its start in 1984 (Kaslow et al. 1987, 2017). Study visits are scheduled every six months at four sites around the country (Baltimore, Maryland; Chicago, Illinois; Los Angeles, California; and Pittsburgh, Pennsylvania). The participants undergo an in-depth interview, a physical examination, and provide blood and specimens for laboratory testing and storage in a national repository.

In addition to the main data collection times for MACS, participants are offered opportunities to participate in sub-studies. From March 2018 to June 2019, all participants in MACS were offered the opportunity to enroll in a sleep substudy that aimed to objectively and subjectively measure sleep among men with and without HIV to detect possible sleep disorders (Punjabi et al. 2022). Those choosing to participate in this substudy completed several questionnaires about sleep quality, an at-home polysomnography test (Nox A1 monitor), and wore a Phillips Actiwatch Spectrum Plus and an ActiGraph GT9X Link accelerometer, both on the non-dominant wrist, for seven days to measure sleep and PA, respectively. Characteristics of this substudy and results from the sleep measures have been reported elsewhere (Punjabi et al. 2022; Punjabi et al. 2023); this analysis focuses solely on the PA data. For this secondary analysis, participants were included if they wore an ActiGraph accelerometer and met the minimum wear-time requirements for valid data analysis. Study activities were approved by Institutional Review Boards at each participating site, and all participants provided written informed consent for their data to be used in future studies.

Measures

Objective measurement of PA and SB.

PA and SB were measured using a non-dominant wrist-worn ActiGraph, Inc. GT9X model accelerometer with raw acceleration data sampled at a frequency of 80 Hz, which was subsequently reintegrated to 60-second epochs. Instances of non-wear time were not included in the PA and SB calculations within the ActiLife software, which calculates daily minutes and the frequency and length of bouts for SB and levels of PA from the data collected by the ActiGraph watch (Choi et al. 2012). Additionally, the participants with nonvalid days (<10 h of wear time on ≥3 days) were removed from the sample. We used the cutpoints established by Montoye et al. (2020) for wrist-worn accelerometers in adults: < 2,860 counts/min (sedentary behavior, SB); 2,860–3,940 counts/min (light-intensity physical activity, PA); and ≥ 3,941 counts/min (moderate-to-vigorous physical activity, MVPA). The total sleep time, as derived from the Actiwatch device, was removed only from the SB time to isolate daytime SB from night time sleep. The Sedentary-to-Active Transition Probability (SATP) and Active-to-Sedentary Transition Probability (ASTP) were previously calculated in the MACS sleep substudy using ARC tools (https://github.com/martakarass/arctools), and these values were transferred to this secondary analysis.

Algorithms for Pure and Total Movement Dispersion.

The following definitions and calculations for pure and total movement dispersion were previously published in the original development of the algorithms (Klamm et al. 2022). The algorithms were first developed and tested in a small pilot study involving school-age children; however, the measure itself remains unchanged when applied to different age groups or populations. Total movement dispersion reflects the intensity of motion by incorporating both the magnitude of the acceleration vector and the temporal distribution of movements. Specifically, it accounts for acceleration magnitudes across different time steps, allowing intensified movements to be represented by larger acceleration values—thereby increasing the overall dispersion. In contrast, pure dispersion excludes the magnitude component and focuses solely on the spread of movement, capturing the distribution pattern without regard to intensity.

The dispersion between two movement values (magnitude of the acceleration vector) at different time steps, t_i and t_j, can be defined as P_ij = C₁ * (VM_i * VM_j) * |Δt|^p.

Here, C₁ and p are constants used to control the total quantities, ${\text{VM}}_i$, ${\text{VM}}_j$ are the acceleration magnitudes at t=t_i and t_j respectively, and Δt= t_i - t_j. To eliminate the white noises and invalid movements, a limiter - ${\text{VM}}_{\mathit{\text{limiter}}}$ can be introduced. Thus, the modified acceleration magnitudes can be obtained as follows (Equation 1):

$${\text{VM}}_i=\left\{\begin{array}{cc}{\text{VM}}_i-{\text{VM}}_{\mathit{\text{limiter}}}& if{\text{VM}}_i\ge {\text{VM}}_{\mathit{\text{limiter}}}\\ 0\hfill & if{\text{VM}}_i<{\text{VM}}_{\mathit{\text{limiter}}}\end{array}\right.$$ 1.

For the total dispersion of the movement data over a period of time (time steps from t=t₁ to t=t_n), we define it as (Equation 2):

$$D_t={\sum }_{\text{i}=1}^{\text{n}}{\sum }_{\text{j}=\text{i}+1}^{\text{n}}{\text{P}}_{\text{ij}}={\sum }_{\text{i}=1}^{\text{n}}{\sum }_{\text{j}=\text{i}+1}^{\text{n}}{C}_1*({\text{VM}}_i^{\prime }*{\text{VM}}_j^{\prime })*{\left|\Delta \text{t}\right|}^p$$ 2.

To exclude the influence of the movement magnitude and only evaluate the dispersion from the distribution, a pure movement dispersion is defined as (Equation 3):

$$D_p={\sum }_{\text{i}=1}^{\text{n}}{\sum }_{\text{j}=\text{i}+1}^{\text{n}}{C}_1*\alpha *{\left|{\text{t}}_i-{\text{t}}_j\right|}^p\text{where}\alpha =1\text{if}{\text{VM}}_i*{\text{VM}}_j\ne 0.$$ 3.

Furthermore, for the comparison between data from different groups, dimensionless forms of the total and pure dispersions are derived through dimension analysis (Equations 4 and 5),

$$D_t^{*}=\frac{D_t}{{\overline{VM}}_{sum}*\Delta t^p*N^{p+1}}$$ 4.

And

$$D_p^{*}=\frac{D_p}{\Delta t^p*N^{p+2}}$$ 5.

Here, ${\overline{VM}}_{sum}$ is the mean value of the sum of the vector magnitudes from all the samples.

Raw data conversion to movement dispersion variables.

The participants’ accelerometer data (motion acceleration in all directions and its magnitude) were recorded at regular intervals (10s) for seven consecutive days. We divided individual participant data into separate days, running from midnight to midnight, but used only the 6 am to 10 pm period for each day. A data preprocessing step first removes discontinuous or abnormal data. A limiter VM_limiter (see equation 1) is used to filter the white noises or the values caused by accidental small movements. In this study, we set VM_limiter to 100, based on the magnitude scale of the accelerometer data. We then treat each day as a cycle and calculate each participant’s pure and total dispersion for each day using equations 4 and 5 above. In this study, we set p = 2, C1 = 1.0, and t_i to be the time in seconds from the beginning of the day.

Statistical Tests

To evaluate the relationships between pure and total movement dispersion and other established measures of PA and SB (MVPA minutes, MVPA bouts, SB minutes, SB bouts, ASTP, and SATP), Spearman’s rank correlation coefficients were computed. This nonparametric test was selected because of the non-normal distributions of the PA variables. Log transformation was applied to non-normally distributed variables; however, this transformation still did not achieve normality. Therefore, the authors continued with Spearman’s rank correlations for this study to evaluate the relationships between pure and total movement dispersion and traditional measures of PA and SB. Additional Spearman’s rank correlations were run within age groups to assess for differences. The statistical analysis was conducted using SAS 9.4 with the level of significance set a priori at p < .05.

Results

The accelerometer data received from MWCCS for 638 sleep substudy participants were assessed for completeness, and a total of 594 participants (93%) were included in this analysis after removing 44 participants for inadequate wear time. The minimum sample size was calculated to be 488, based on a power analysis using a medium effect size (0.3), 95% power, and an a priori significance level set at p < .05. Therefore, the sample for this secondary analysis exceeded the necessary sample size to achieve the desired power. The sample included 62% white, 27% black, and 15% Hispanic, with 55% of all participants being HIV positive. The average age of the participants was 58.1 years (SD = 11.4; range = 26–86). Participants were included if their accelerometer data met the requirements for wear time as described above. On average, the accelerometer data covered 6.1 days per participant. The average and standard deviations for all the measures of PA and SB among the sample are detailed in Table 1. Several of the measures were skewed even after log transformation, so nonparametric tests were used for analyses. The medians and interquartile ranges are also reported to reflect the values utilized in the following nonparametric statistical tests. A statistically significant difference (p < .05) was noted between age groups (<40 years old, 40–60 years old, and >60 years old) for all variables of interest, except for the active-to-sedentary transition probability. Therefore, Spearman correlations were run for the total group and repeated for each age group to assess associations between pure and total movement dispersion and other established measures of PA and SB.

Table 1.

Sample Comparisons of the Measures of PA and SB

Measures	Total n=594		<40 yrs. old n=51		40–60 yrs. old n=269		>60 yrs. old. n=274		p
	M (SD)	Mdn (IQR)	M (SD)	Mdn (IQR)	M (SD)	Mdn (IQR)	M (SD)	Mdn (IQR)
MVPA min./day	71.5 (37.2)	65 (43)	95 (45.6)	88 (49)	79.3 (38.9)	71 (41)	60.6 (29.7)	54 (36)	<.001
SB min./day	765 (106.8)	766 (144)	710.5 (117.3)	703 (217)	763.2 (115.9)	757 (154)	776.2 (93.2)	779 (123)	.0011
MVPA bout (min.)	3.6 (.9)	3.5 (.9)	4 (.8)	4 (.7)	3.7 (.8)	4 (.8)	3.5 (1)	3 (.8)	<.001
SB bout (min.)	102 (51.6)	89.8 (44)	86.2 (29.1)	77 (41)	94.5 (41)	86 (38)	111.3 (60.5)	97 (46)	<.001
SATP	.11 (.03)	.1 (.03)	.12 (.03)	.11 (.04)	.11 (.03)	.11 (.04)	.1 (.02)	.1 (.03)	.0003
ASTP	.22 (.05)	.21 (.07)	.22 (.06)	.21 (.08)	.22 (.06)	.21 (.07)	.22 (.05)	.21 (.05)	.9453
Pure Movement Dispersion	.037 (.013)	.035 (.019)	.04 (.013)	.04 (.02)	.038 (.014)	.04 (.02)	.035 (.012)	.03 (.01)	.0006
Total Movement Dispersion	92.5 (52.9)	79.5 (61)	116.9 (60.8)	106 (68)	101.9 (58)	89 (73)	80.3 (43.1)	68 (45)	<.001

Note: min.=minutes; M=mean; SD=standard deviation; Mdn = median; IQR=interquartile range; MVPA=moderate to vigorous physical activity; SB=sedentary behavior; SATP=sedentary to active transition probability; ASTP=active to sedentary transition probability

Table 2 presents the Spearman rank correlation coefficients between pure and total movement dispersions and other standard measures of PA and SB among the participants as a whole. This analysis aims to assess the convergent validity of these new PA variables by examining how pure and total movement dispersion relate to standard measures of PA and SB.

Table 2.

Relationship between Pure and Total Movement Dispersion and Established Measures of PA and SB among the Overall Sample

Established Measures	Pure Movement Dispersion		Total Movement Dispersion
	r s	p	r s	p
MVPA minutes	.4056	<.0001	.5719	<.0001
SB minutes	−.0853	.0377	−.2183	<.0001
MVPA bout length	.1708	<.0001	.2844	<.0001
SB bout length	−.382	<.0001	−.5039	<.0001
SATP	.5011	<.0001	.3964	<.0001
ASTP	−.3837	<.0001	−.4707	<.0001

Note: r_s = Spearman correlation coefficient; SATP = Sedentary-to-Active Transition Probability; ASTP = Active-to-Sedentary Transition Probability

For pure movement dispersion, which does not include movement intensity, there are positive correlations with MVPA minutes, MVPA bout length, and Sedentary-to-Active Transition Probability. This finding suggests that higher pure movement dispersion is associated with more moderate-vigorous physical activity minutes, longer moderate-vigorous physical activity bouts, and a higher probability of transitioning from sedentary to active behavior. In contrast, pure movement dispersion shows negative correlations with SB minutes, SB bout length, and Active-to-Sedentary Transition Probability, indicating that increased movement dispersion corresponds to reduced sedentary time, shorter length of sedentary behavior bouts, and a decreased probability of transitioning from active to sedentary behavior. For total movement dispersion, which includes the intensity of movement, there are positive correlations with MVPA minutes, MVPA bout length, and Sedentary-to-Active Transition Probability. At the same time, there are negative correlations with SB minutes, SB bout length, and Active-to-Sedentary Transition Probability, with higher correlations in all comparisons except for Sedentary-to-Active Transition Probability. These relationships are further demonstrated through scatter plot correlations (Online Resource 1). Pure movement dispersion exhibited a best-fit with SATP (R² = .273); whereas, total movement dispersion showed the strongest fit with average minutes in MVPA (R² = .437) and ASTP (R² = .206).

The relationships between pure and total movement dispersion and these established measures of PA and SB were examined further within age groups (<40 years old, 40–60 years old, and >60 years old) to detect any changes in the convergent validity. Table 3 shows these relationships among the participants under 40 years old. The relationship between pure movement dispersion and SB minutes (p = .2174) and MVPA bout length (p = .0829) was no longer significant in this subgroup. Additionally, the relationship between total movement dispersion and MVPA bout length (p = .0692) was not significant. All other measures remained significant with pure and total movement dispersion among individuals under 40 years of age.

Table 3.

Relationship between Pure and Total Movement Dispersion and Established Measures of PA and SB among Participants Under 40 years old (n=51)

Established Measures	Pure Movement Dispersion		Total Movement Dispersion
	r s	p	r s	p
MVPA minutes	.5214	<.0001	.6279	<.0001
SB minutes	−.1758	.2174	−.3067	.0286
MVPA bout length	.2451	.0829	.2565	.0692
SB bout length	−.451	.0009	−.5215	<.0001
SATP	.5162	.0001	.2958	.0351
ASTP	−.3178	.023	−.5585	<.0001

Note: r_s = Spearman correlation coefficient; SATP = Sedentary-to-Active Transition Probability;

ASTP =Active-to-Sedentary Transition Probability

Table 4 examines the same relationships among participants aged 40–60 years. The relationship between pure movement dispersion and SB minutes (p = .5835) was no longer significant in this subgroup. The MVPA bout length (p = .0541) approached significance. However, the relationship between total movement dispersion and MVPA bout length (p = .0692) returned to significance within this subgroup. All other measures remained significant with pure and total movement dispersion among individuals between 40 and 60 years of age.

Table 4.

Relationship between Pure and Total Movement Dispersion and Established Measures of PA and SB among Participants 40–60 years old (n=269)

Established Measures	Pure Movement Dispersion		Total Movement Dispersion
	r s	p	r s	p
MVPA minutes	.4954	<.0001	.6511	<.0001
SB minutes	−.0348	.5835	−.1912	.0023
MVPA bout length	.1217	.0541	.2415	.0001
SB bout length	−.4648	<.0001	−.5497	<.0001
SATP	.504	<.0001	.3948	<.0001
ASTP	−.453	<.0001	−.524	<.0001

r_s = Spearman correlation coefficient; SATP = Sedentary-to-Active Transition Probability; ASTP = Active-to-Sedentary Transition Probability

Table 5 shows the relationships between pure and total movement dispersion and the established measures of PA and SB among participants over 60 years old. In this subgroup, only the average minutes of SB were not significantly related to pure movement dispersion. All other measures remained significant among individuals aged 60 years and older.

Table 5.

Relationship between Pure and Total Movement Dispersion and Established Measures of PA and SB among Participants Over 60 years old (n=274)

Established Measures	Pure Movement Dispersion		Total Movement Dispersion
	r s	p	r s	p
MVPA minutes	.2995	<.0001	.4602	<.0001
SB minutes	−.0996	.0893	−.2112	.0003
MVPA bout length	.1353	.0207	.2258	<.0001
SB bout length	−.2799	<.0001	−.4248	<.0001
SATP	.4689	<.0001	.367	<.0001
ASTP	−.344	<.0001	−.4455	<.0001

Note: r_s = Spearman correlation coefficient; SATP = Sedentary-to-Active Transition Probability; ASTP = Active-to-Sedentary Transition Probability

Discussion

Implications

Other approaches for quantifying the daily patterns of PA have focused more on the number or proportion of bouts or the probability of moving from sedentary to active behavior or vice versa (Chastin and Granat 2010; Schrack et al. 2019). The derived variables of pure and total movement dispersion provide a novel method for quantifying the spread of PA across the day on a more granular level that accounts for the space between individual epochs of activity during the day. For example, an individual may be able to see a change in patterns of PA in a daily graph, but these derived variables make it possible to determine if the change was significant or not (Welsch et al. 2021). To the best of the authors’ knowledge, no similar variables have been established in the literature to quantify the pattern of accumulating PA across the day in this way. The development of pure and total movement dispersion provides an opportunity to examine movement and intensity distributions across the day in relation to a variety of health outcomes, such as cardiovascular risk, to inform health promotion messages about daily PA.

The comparison to measures of PA and SB that account for various aspects of movement (intensity, time, and transition) supports the utilization of pure and total movement dispersion to capture multiple measures of movement behavior. Both variables demonstrated significant positive correlations with average total minutes and bout lengths in MVPA and significant negative correlations with average total minutes and bout lengths of SB among the overall group, with total movement dispersion showing a stronger relationship due to its inclusion of intensity. When examined further by age group, pure movement dispersion was not significantly related to minutes of SB or the average length of MVPA bouts among individuals aged 40 years or less or 60 years or older. Additionally, individuals under 40 did not show a significant relationship between total movement dispersion and the average length of MVPA bouts. However, the other relationships with pure and total movement dispersion remained strong across the age groups. The changes in relationships with SB minutes and MVPA bout length among the youngest group may be due to the smaller sample size (n = 51), as the other two age groups were over five times larger in number (40–60, n = 269; >60, n = 274). Additionally, the younger groups demonstrated higher average minutes of MVPA, with weaker correlations, suggesting that these measures have weaker convergent validity among more active individuals. Future studies will further investigate this aspect.

These findings support the ability of pure and total movement dispersion to capture the intensity and length of PA. Both pure and total movement dispersion were significantly correlated with Sedentary-to-Active Transition Probability, which measures the transitions from sitting or lying down to movement. Pure movement dispersion had a stronger correlation due to its focus on any movement, regardless of intensity. Additionally, both had significant negative correlations with Active-to-Sedentary Transition Probability, which measures the transitions from movement to sitting or lying down. The total movement dispersion had a stronger correlation, which may be due to a shift in intensity when activity stops and transitions into sedentary behavior. The relationship with Sedentary-to-Active Transition Probability and Active-to-Sedentary Transition Probability demonstrates the ability of pure and total movement dispersion to measure the change in PA from sedentary to active and vice versa. Pure and total movement dispersion introduce an additional dynamic by accounting for intensity, which enables further exploration into the importance of the combination of movement and intensity, or the benefits of movement alone.

When pure and total movement dispersion are added along with the established measures of PA and SB, a more complete picture of an individual’s daily patterns of movement can be determined. These derived variables are not intended to replace current measures of PA and SB, but rather to add another tool to the arsenal, aiding PA researchers in quantifying a different aspect of movement beyond total minutes. For example, PA researchers could report total minutes of MVPA to determine whether individuals meet the recommended levels (Piercy et al. 2018) and add pure and total movement dispersion to describe how PA was distributed. In addition, the derived values of pure and total movement dispersion could be used by the public to guide individuals in the management of their PA and SB throughout the day once optimal levels of these metrics are identified in future work. If an individual receives their pure and total movement dispersion scores along with an explanation and optimal ranges, they would be shown the need to infuse more movement into their day, which could lead to decisions to set reminders during workdays to get up and walk or be mindful to add activity such as playing basketball or walking with family on the weekends.

Future applications

A future application of this novel approach to measuring PA behaviors may include examining the relationships with numerous objective health outcomes to provide a preliminary perspective on causal relationships and guide the development of interventions focused on infusing PA across the day. Furthermore, it will be important to determine if pure and total movement dispersion have a linear or U-shaped relationship with these health outcomes. If it is U-shaped, then an optimal range could be identified to inform its implementation as a metric for improved health in future studies. Other applications include measuring the impact on health outcomes to determine whether pure and total movement dispersion have a different or equal effect on health compared to total minutes of MVPA alone. Incorporating these derived variables of objectively measured pure and total movement dispersion may help determine whether an intervention focused on infusing PA throughout the day is effective. Additionally, these variables can be translated into intervention components that participants can readily interpret. For example, if participants are made aware of their baseline movement score, intervention strategies can include promoting more movement and less sitting, aiming to improve these scores over time. Currently, the calculations for pure and total movement dispersion rely on a supercomputer; however, future plans include creating an RStudio Shiny app to make these calculations easier to use in studies and to disseminate them to the general scientific community for wider applications.

Strengths and Limitations

This study is a significant contribution to the PA literature, as it continues to explore innovative methods for measuring the daily patterns of PA and SB to benefit health behaviors and, consequently, public health. The use of a large sample utilizing accelerometers for objective measurement of activity allows for powerful comparisons to several established and newer measures of PA and SB, as well as additional insights about the role of movement, intensity of movement, and the length of bouts of SB. This secondary analysis was conducted for the purpose of measuring sleep and PA in a cohort consisting only of sexual minority men, some with and some without HIV. Activity levels may differ among the general population, including women; however, the convergent validity of the measures would not be expected to be influenced by such differences. The different cohort sites had clear protocols for administering this study, so it is anticipated that the data are reliable regardless of site; however, this was not observed by the authors of the current study. In addition, no similar measure exists to allow comparison with a grounded truth and determine validity at the one-to-one level, or to enable other statistical measures to be run.

Conclusion

The results of this validation study support the ongoing utilization of pure and movement dispersion as innovative methods for quantifying an individual’s daily movement behaviors. Both derived variables demonstrate a strong relationship with other measures that capture the amount and intensity, as well as the transition, of PA and SB, which supports the convergent validity of pure and total movement dispersion in representing all these aspects together. Pure and total movement dispersion provide a method and variables that can be utilized to describe samples, PA outcomes, and the effectiveness of PA interventions. Researchers focused on encouraging more PA and less SB, in alignment with the Move More, Sit Less campaign, may find great value in incorporating these movement dispersion algorithms and variables in their studies to measure daily movement patterns and encourage individual PA behavior changes.