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Health Educ Res. Jun 2010; 25(3): 478–488.
Published online Mar 26, 2010. doi:  10.1093/her/cyq019
PMCID: PMC2872615

Individual, social environmental and physical environmental barriers to achieving 10 000 steps per day among older women

Abstract

This study examined the determinants of attaining/not attaining 10 000 steps per day among older women. Methods: Daily step counts over 7 days were measured using accelerometry. Self-reported environmental characteristics, self-efficacy, social support and functional limitations were assessed in 128 older women. The presence of areas for activity within 1 km of each participant's residence was assessed using Geographic Information Systems. Multivariate analysis of variances were used to examine the degree to which these groups differed on measured constructs, and discriminant analysis was used to determine the profiles that discriminate among those who did not attain 10 000 steps per day and those who did. Results: Participants who did not attain 10 000 steps per day reported lower self-efficacy (P < 0.05), greater functional limitations (P < 0.05), had significantly fewer walking paths (P < 0.05) within 1 km of their home and reported significantly less street connectivity (P < 0.05) and safety from traffic (P < 0.05) than those who achieved 10 000 steps per day. Conclusion: Lack of perceived and actual environmental supports for walking, more functional limitations and lower self-efficacy are barriers to achieving 10 000 steps per day. The absence of these individual and environmental characteristics inhibits walking behavior in older women and should be considered in campaigns to promote a physically active lifestyle.

Introduction

The benefits of a physically active lifestyle extend to all segments of the population, including older adults [1]. Despite these known benefits, older adults continue to lead sedentary lifestyles, with older women in particular being the most inactive segment of the population [2]. Research has demonstrated that achieving 10 000 steps per day is associated with important health outcomes and congruous with public health recommendations for physical activity [3]. Previous studies aiming to increase physical activity behavior in older adults have largely focused on individual-level factors and have been met with limited success, particularly with respect to maintaining changes in physical activity following the cessation of the intervention [46]. In light of these trends, Satariano and McAuley [7] called for the implementation of a comprehensive research agenda, informed by social ecological models, and which examines the degree to which other important correlates of physical activity behavior such as social and environmental factors influence walking behavior in older adults.

Social ecological models of health behavior propose interplay between intraindividual, social and environmental factors to influence behavior. Specifically, a social ecological framework posits that efforts to promote physical activity targeted at the community level rely heavily on individual-level variables. Similarly, practices designed to encourage physical activity adoption and maintenance, which focus on the individual, are influenced by community-level variables, such as environmental characteristics. As Satariano and McAuley [7] cogently point out, adopting a social ecological perspective, in which these two approaches to promoting physical activity are viewed as complementary, holds great potential for translational research that addresses a comprehensive set of factors.

Among older adults, intra-individual factors including, though not limited to, functional limitations and self-efficacy have been consistently associated with physical activity [810]. Self-efficacy, reflective of an individual's belief in his/her ability to successfully complete a course of action, is the most consistent individual-level predictor of physical activity in older adults. Functional limitations, which reflect an individual's level of difficulty with daily activities, are both an important barrier to physical activity and a consequence of physical inactivity. Examining the role of compromised function on walking behavior in older women is an important avenue of exploration. Within the social environment, the degree of social support an individual receives has also demonstrated significant effects on activity behavior, with greater social support associated with increased physical activity participation [11, 12]. Importantly, the degree to which these factors determine the attainment of public health guidelines, as defined here relative to step counts, has yet to be examined in older adults. Moreover, the relative influence of each of these factors in the presence of other important social ecological factors remains to be examined.

An increasing number of studies have examined the role of environmental attributes such as access to services, street connectivity, safety and land use mix as correlates of physical activity behavior [13, 14]. Such studies have largely relied on self-report measures of perceived environmental attributes. Although such measures are clearly related to physical activity behavior [15], objective measures of environmental attributes, such as those assessed using Geographic Information Systems (GIS), have also demonstrated effects on physical activity behavior [16, 17], effects that differ from those reported among self-report measures [18, 19]. Moreover, there are some neighborhood attributes that are difficult to measure using only objective measures (e.g. aesthetics), and the same is also true relative to measures of individual perceptions. Indeed, an objective of Healthy People 2010 [20] was to increase the prevalence of objective data collection techniques such as GIS in studies of physical activity behavior determinants. The ability of GIS to measure the spatial characteristics of facilities and other resources for activity such as parks and walking paths and their proximity to individual homes provides researchers with valuable information relative to neighborhood accessibility. Few studies have assessed perceived and objective measures of environmental attributes synchronously [21], and fewer still have done so in older adults.

The purpose of this exploratory study was to use a social ecological model of walking behavior to examine the important question of why some older adults are able to achieve high levels of physical activity while others are not. Specifically, we sought to determine the social-cognitive, functional and environmental (both perceived and objective) characteristics that differentiated those who did not accumulate the recommended 10 000 steps per day from those whose daily step counts were at, or above, 10 000. Based upon previous research [22], we hypothesized that the individual, social and environmental factors specified in this study would be significantly associated with walking in this sample of older women. Specifically, we hypothesized that individual-level factors would be more strongly associated with walking behavior than would social and environmental factors. This preliminary analysis of relative influence has the potential to inform future efforts to bolster physical activity among older adults. Indeed, identifying in a hierarchical fashion those factors that discriminate individuals who are successful in meeting activity guidelines from those who are not has implications for future strategies adopted in individual- and community-level research, practice and policies aimed at promoting physical activity.

Methods

Participants

A convenience sample of older community-dwelling women (M age = 69.6, N = 128) were recruited from a prospective study of women's health [23] via an announcement in the project newsletter, which described this separate mail-based study. Inclusion criteria for the parent study were as follows: (i) female, (ii) race being Black or White, (iii) ethnicity being Non-Hispanic/Latina, (iv) no history of neurological disorder, (v) no history of physical disability that would prohibit an assessment of physical function and (vi) adequate mental status, as assessed by the Pfeiffer Mental Status Questionnaire [24]. Of the initial 249 women who received the newsletter, 153 expressed interest in participating in the study. Consent forms were mailed to all 153 individuals, of which 16 were not returned. Over the course of the study, nine participants withdrew from participation citing: (i) being too busy, (ii) personal illness or ill spouse and (iii) unwilling to complete the questionnaire packet and/or wear the activity monitor for 7 days.

Measures

Steps per day

Steps per day were measured with Actigraph accelerometers (Model 7165). This model of accelerometer assesses vertical acceleration to generate two forms of activity data: activity counts and step counts. The Actigraph's pedometer function records a step for any vertical acceleration of 0.30 g or above. For this analysis, only the step count data were used, as valid activity count cut-points to assess activity intensity have yet to be identified for older adults [25]. Participants were instructed to wear the monitor for 7 days to collect objective physical activity data. The total number of steps taken each day were summed and divided by the total number of days worn to arrive at an average of daily steps taken.

Perceived environmental attributes

Perceptions of the physical environment were assessed using the Neighborhood Environment Walkability Scale (NEWS) [26]. This measure assesses perceptions of nine environmental characteristics: residential density, land use diversity (presence and proximity of stores and facilities), access to services, street connectivity, walking/cycling areas, aesthetics, pedestrian safety from traffic, safety from crime and overall neighborhood satisfaction. All subscales, excluding the residential density and land use diversity scales, used a four-point Likert scale ranging from 1 (strongly disagree) to 4 (strongly agree). The total score for each scale was calculated by summing across all items and dividing by the number of scale items. High scores reflect favorable perceptions, whereas low scores reflect unfavorable perceptions of the environment. The residential density scale measures the prevalence of different residence styles in the neighborhood. The response items range from 1 (none) to 5 (all) and the mean value for all items serves as the total score. The land use diversity scale assesses the proximity of stores and facilities from the place of residence. Proximity was estimated by walking distance measured in minutes, using a scale from 1 (1–5 min) to 5 (31+ min); the total score for walking proximity was calculated as the mean across all items. High scores denote a greater proximity to facilities. Internal consistencies for these scales ranged from 0.53 to 0.94.

Objectively assessed environmental attributes

We used GIS to geocode each participant's address. A circular buffer of 1 km, a distance associated with foot travel, was created around each point. The presence or absence of schools, recreational areas (e.g. golf courses, recreation centers), parks, walking paths and exercise/gym facilities were identified, along with the prevalence of each variable in the neighborhood (i.e. 1 km buffer) of each participant.

Self-efficacy

The Barriers Self-Efficacy Scale [27] was used to assess an individual's belief in their ability to exercise three times per week for 40 min over the next 2 months in the face of commonly identified barriers to exercise (e.g. inclement weather, schedule conflicts). Confidence was rated on a scale of 0% (not at all confident) to 100% (highly confident), with 10-point increments. The total score was calculated as the average score across all items, resulting in a total score value of 0–100. Internal consistency for this scale was excellent (α = 0.96).

Social support

Social support was assessed using the Social Support and Exercise Survey [28]. This scale measures the degree to which friends and family demonstrate verbal and behavioral support for exercise behaviors in the previous 3 months. Participants rated the frequency for each of the 10 items on a 5-point Likert scale, ranging from 1 (never) to 5 (very often). Example items include ‘exercised with me’ and ‘gave me helpful reminders to exercise’. Support scores are created separately for friends and family. Internal consistencies for the friends (α = 0.91) and family (α = 0.92) subscales were excellent.

Functional limitations

Functional limitations were measured using the ‘Function’ component of the abbreviated Late Life Function and Disability Instrument (LL-FDI) [23]. This measure is comprised of 15 items that examine upper extremity function, basic lower extremity function and advanced lower extremity function in older adults. Participants indicated the level of difficulty experienced while performing an activity (e.g. walking a mile without stopping for rest) on a Likert scale ranging from 1 (none) to 5 (cannot do). Items are summed to arrive at a total score for function, resulting in a scale score ranging from 15 to 75. Higher scores indicate greater functional limitations. Internal consistency for the Function component of the LL-FDI was excellent (α = 0.88).

Procedures

All procedures were approved by the University of Illinois Institutional Review Board and informed consent was obtained from each participant prior to enrollment in the study. All measures were distributed and collected through the mail with the use of self-addressed pre-paid envelopes. Upon receipt of the signed consent form, each participant was mailed a questionnaire packet along with the accelerometer and instructions for wearing the monitor. Each participant was assigned a start and end date for wearing the monitor. Additionally, participants were asked to indicate dates and times when the monitor was on/off using the provided log. Approximately 3 days after the package was sent, a reminder call was made to each participant to ensure that all materials were received and to remind the participant when they were to start wearing their monitor. Any other questions were also answered at this time.

A second phone call was made to each participant 1 day prior to their requested finish date for wearing the monitor. The purpose of this call was to remind participants that they were approaching their final day and that they were to return the monitor, log and completed questionnaire packets to the laboratory using the provided envelope and postage. At this time, if participants indicated that they had omitted a day of wear, they were asked to wear the monitor for an additional day(s) so as to provide 7 complete days of data. Participants were paid $15 for their participation.

Data analysis

T-tests and χ2 tests were first run to examine the between-group differences on the demographic and health status factors. Next, we used a series of multivariate analysis of variance (MANOVAs) to examine the between-group differences among those who did not accumulate 10 000 steps per day and those who accumulated ≥10 000 steps per day on the nine NEWS subscales, objective environmental attributes, self-efficacy, social support and functional limitations, controlling for any demographic variables that demonstrated significant between-group differences in previous analyses. Those variables that demonstrated significant (P < 0.05) differences between the two groups in the MANOVAs were retained for subsequent analyses.

Given the exploratory nature of our primary research question, we used discriminant function analysis to examine the relative influence of each of these continuous variables on group membership. This analysis determined (i) whether the participants classified as taking ‘<10 000 steps per day’ or ‘≥10 000 steps per day’ presented different profiles on our set of variables and (ii) which combination of these independent variables (i.e. discriminant functions) best discriminated these groups. Thus, the functions classify participants as ‘<10 000 steps per day’ or ‘≥10 000 steps per day’ based solely on their continuous values of the significant independent variables. As only two groups were being compared, only one discriminant score was derived; discriminating <10 000 steps per day from the ≥10 000 steps per day.

The discriminant function was evaluated using a number of statistical tests. Wilks’ Lambda was used to determine whether the two groups had any difference in their mean scores for each independent variable. The canonical coefficient was used to measure the association between the discriminant score and the two groups, and the discriminant loadings were used to determine which variable contributed more to the differences between the groups. Finally, to assess the predictive ability of the function, the percentage of participants correctly classified into the two groups by the discriminant function was compared with the percentage of participants who could be classified correctly by chance (i.e. without the discriminating function). All analyses were performed using SPSS version 17 (PASW Inc.).

Results

Table I shows the characteristics of the overall sample, the proportions of <10 000 steps per day and ≥10 000 steps per day, and the characteristics of these two groups. Overall, the sample (N = 128) was comprised predominantly of married (54.8%) white women (84.4%%), and the majority of whom was retired (75.0%). The sample represented a broad spectrum of socioeconomic status (40.6% annual income >$40,000) and education level (44.5% ≥college degree). Although community dwelling, many of these women reported medical diagnoses of hypertension (37%), hyperlipidemia (28%) and functional impairment of the musculoskeletal system (85%). Recorded average daily step counts showed significant variation across the sample, ranging from 1616 to 21 919 steps per day (M steps per day = 8675).

Table I.
Sample characteristics

Mean scores for each of the independent variables for the entire sample and by group assignment are shown in Table II. Participants in this study were moderately efficacious, reported few functional limitations and reported moderate levels of social support from friends and family for exercise. Of the objectively assessed environmental attributes, parks were the most prevalent, followed by schools and walking paths. Very few recreation areas and exercise/gym facilities were identified within 1 km of participants’ residences. Relative to perceived environmental attributes, participants reported moderate/high levels of each of the nine characteristics.

Table II.
Comparison of characteristics of <10 000 steps per day and ≥10 000 steps per day groups

Results of the t-tests and χ2 tests (see Table I) indicated that individuals in the <10 000 steps per day group (n = 93) and individuals in the ≥10 000 steps per day group (n = 35) did not differ significantly (P < 0.05) on any of the demographic variables except for age. Participants reporting <10 000 steps per day were significantly older than participants reporting ≥10 000 steps per day (t(126) = 2.03, P < 0.05).

Results of the MANOVAs (see Table II) suggest that participants who recorded <10 000 steps per day had significantly fewer paths within 1 km of their home (F = 5.88, P = 0.02), more functional limitations (F = 6.96, P = 0.01), lower barriers self-efficacy (F = 9.48, P = 0.003), less street connectivity (F = 6.04, P = 0.02) and lower pedestrian/traffic safety ratings (F = 4.39, P = 0.04) than participants who recorded 10 000 steps per day or greater. No significant group differences were observed for any of the other study variables.

Next, a discriminant analysis was conducted using the 10 000 steps classification as the dependent variable and those variables that demonstrated significant between-group differences in the MANOVAs as covariates (e.g. age, functional limitations, self-efficacy, number of paths within 1 km of the residence, perceived pedestrian/traffic safety and perceived street connectivity). Table III summarizes the estimation of the discriminant function, showing how the inclusion of each variable changed Wilks’ Lambda, the F-value and the significance level of the function. The discriminant function was significantly different for those attaining 10 000 steps and those who did not (Wilks’ Lambda = 0.859, χ2 = 18.92, df = 4 and P = 0.001), and all of the independent variables contributed significantly to the discriminant function (P < 0.05). According to the discriminant function coefficients (see Table III), barriers self-efficacy was the strongest correlate of group assignment, followed by (in descending order) functional limitations, street connectivity, number of paths within 1 km, pedestrian/traffic safety and age. Overall, the discriminant function successfully predicted step behavior for 74.2% of cases with accurate predictions being made for 90.3% of those who failed to reach 10 000 steps and only 31.4% of those who reached 10 000 steps.

Table III.
Summary of the estimation of the discriminant function for <10 000 steps per day versus ≥10 000 steps per day

Discussion

Although much of the physical activity literature has focused upon individual-level correlates, social ecological model of physical activity behavior which emphasizes physical and social environmental factors along with intrapersonal variables have received increasing attention [6, 7]. The present study examined the relative influence of such factors on meeting public health recommendations to accumulate 10 000 steps per day among older community-dwelling women. Analyses indicated that women who walked <10 000 steps per day did indeed differ significantly from women who walked ≥10 000 steps per day on factors such as self-efficacy, functional limitations, access to walking paths within 1 km from the home, pedestrian/traffic safety, street connectivity and age. The percentage of individuals correctly classified by these characteristics was superior to those that could be obtained by chance. Indeed, 90.3% of those not meeting the public health guidelines of 10 000 steps per day were classified correctly using the profile identified by the discriminant analysis.

As hypothesized, the individual-level variables (i.e. self-efficacy to overcome barriers to physical activity and functional limitations) had the highest discriminatory power. Older women with low/moderate self-efficacy and women with greater functional limitations had greatest difficulty accumulating 10 000 steps per day. That self-efficacy to overcome barriers, a reflection of personal control, was the strongest factor is important, for it suggests two potential pathways for intervention to promote walking behavior: targeting the environment and targeting the individual. First, social ecological approaches may enhance personal control beliefs by reducing environmental barriers and improving accessibility of the environments and activity programs [7]. These adjustments to the environment are expected to lead to greater efficacy, which in turn would positively influence activity behavior. Second, efforts may target the individual's sense of control in an effort to enhance perceptions of the environment, thereby resulting in increased activity behavior. Individuals who are efficacious in their ability to overcome barriers to physical activity are more likely to take advantage of the opportunities that exist in the environment and are also less likely to be discouraged in the face of obstacles [29].

Clearly, self-efficacy plays a significant role in walking behavior in women, and interventions that target the sources of efficacy beliefs such as mastery experiences, vicarious experience of success among similar others, verbal persuasion that one possesses the necessary capabilities to succeed and judgments of physiological and affective readiness to participate [29] are critical to promoting activity behavior in this demographic. However, the extent to which the environment can be altered to reduce perceived barriers to physical activity and enhance efficacy beliefs has yet to be examined.

That functional limitations were inversely associated with meeting public health guidelines is consistent with previous literature in older adults [30]. However, given the cross-sectional nature of this study, we are unable to tease out what is largely believed to be a cyclical relationship, such that declines in one component perpetuate declines in the other. Further investigation to determine whether the relationship between functional limitations and walking behavior differs as a function of the type of limitations (e.g. upper body and lower body) or the presence of health comborbidities is warranted. Additionally, studies that examine the potential role for the environment to promote/inhibit physical activity among those with compromised function are needed.

Both the perceived and objective environment were also significantly associated with group membership. Specifically, having fewer paths within 1 km of one's home and reporting less street connectivity and less pedestrian safety from traffic were significantly associated with walking less than the recommended 10 000 steps per day, results which are consistent with previous research [31]. Previous research, however, suggests that the implications of these findings be considered carefully. Studies of walking trail use and proximity have reported that even when the objective distance to a walking trail was consistent between individuals, the absence or presence of psychosocial and neighborhood factors determined perceptions of proximity and individual use of the walking trail [32, 33]. Thus, although our results demonstrate that having access to walking trails is associated with obtaining 10 000 steps, increasing the prevalence of walking trails may not be sufficient and thus unlikely to result in significant increases in walking behavior. Instead, it may be that the integration of pathways which are not only accessible to older individuals but which also allows the completion of daily tasks (e.g. street connectivity for access to businesses) may be more apt to increase walking behavior in older women. Furthermore, our results underscore the importance of minimizing the degree to which pedestrians and motorized traffic coexist in areas designated for activity, an ideal perhaps best achieved through public policy and urban planning guidelines.

Somewhat surprisingly, women who walked <10 000 steps per day had similar access to parks, recreation areas or exercise/gym facilities within 1 km of their home as those women who walked ≥10 000 steps per day. These findings may be due, in part, to our definition of neighborhood, defined here as 1 km. Although previous research suggests that this distance is consistent with perceptions of walkability, a standardized definition of neighborhood as it relates to physical activity remains to be identified [34].

Additionally, no significant between-group differences were observed for social support from friends or family to exercise, with both groups reporting low/moderate ratings of social support. It is conceivable that this pattern of results may stem from properties of the scale. Six of 10 items appear to infer that the family/friends are also physically active (i.e. ‘offered to be physically active with me’ or ‘changed their schedule so we could be active together’), perhaps reflecting the frequency (i.e. ‘very often’, ‘rarely’) by which individuals exercised with friends and family as opposed to social support per se, which includes other elements, such as verbal persuasion and provision of resources. Contrary to previous studies reporting positive associations with physical activity [2, 14, 22, 35], perceptions of residential density, land use mix-diversity, land use mix-access, walking/cycling facilities, aesthetics, crime safety and neighborhood satisfaction did not differ significantly between groups.

It is important to note that our discriminatory function was markedly better at classifying those women who walked <10 000 steps per day, correctly classifying only one-third of those who accumulated ≥10 000 steps per day. Our results suggest that while greater efficacy to overcome barriers, fewer functional limitations, access to walking paths and greater street connectivity and safety from traffic may be necessary to promote activity, these characteristics, in and of themselves, do not reliably predict higher activity levels. Indeed, physical activity is a complex behavior, influenced by a series of interactions between individual- and environment-level variables [6, 15, 17]. As such, individual-level interventions to increase physical activity are likely to be more effective when the individual's neighborhood environment is supportive, with few barriers. Conversely, environment-level interventions to increase physical activity will likely be met with limited success when individual-level factors such as self-efficacy, motivation or perceived importance of physical activity are low.

The use of multi-level modeling techniques to account for factors at the individual and environment levels appears to be the next step in furthering our understanding of these associations and testing a truly ecological model of activity behavior [36]. To our knowledge, few studies have employed such a design to examine neighborhood-level effects on physical activity in older adults [5, 31, 37, 38]. Such research holds the potential to extend current physical activity research by adopting a comprehensive approach to examining both the impact of changes at the level of the individual as well as the effect of changes within the individual who resides in that neighborhood on physical activity.

Indeed, a fundamental characteristic of ecological models is using several measurement time points to examine causal inferences and potential mediators. Such research is imperative to further inform social ecological models and the application of these models to change physical activity behavior. Clearly, the cross-sectional design of the present study is a limitation, as we are unable to determine whether there is a minimally significant amount of change in these variables that is necessary to evoke change from the <10 000 steps per day to the ≥10 000 steps per day group. Furthermore, we do not address here the postulated interaction effects between these individual and environmental barriers; effects that are central to ecological models. Future research employing more complex longitudinal research designs that examine not only the influence of a given level of a mediator on behavior but also the implications that ‘changes’ in these variables have for physical activity are needed.

A strength of this study is our inclusion of both perceived and objective measures of the physical environment. However, we recognize that other environmental attributes such as population density and sidewalk conditions or street pattern and vehicular traffic that were not included in the present study may also be related to physical activity. Our use of both perceived and objective measures of the environment, however, allowed us to assess many more dimensions of the environment than either measure afforded alone and addresses a limitation of previous studies. Future studies using multiple geographic scales to define neighborhood and community (e.g. 0.5 km, 2 km) are needed.

Our relatively small sample size, although adequate for the methods used here, is also a limitation. These findings should be replicated in larger samples, other populations and with different modes of activity. That our study sample was limited to a convenience sample of older women limits our ability to generalize our findings to other populations; however, our ability to sample women residing in both rural and urban environments is a strength of the study.

Finally, the appropriateness of our physical activity outcome measure deserves consideration. Only 27% of our sample recorded an average of 10 000 steps per day, suggestive of a goal that may be difficult for older women to achieve, particularly in the presence of chronic conditions and functional declines. Although 10 000 steps per day is the recommended goal for adults, there is evidence that suggests that this step goal may not be appropriate for other groups, including older adults [3]. Future studies that examine different thresholds and modes (e.g. leisure and transportation) of activity in older adults are warranted. Moreover, the effect that car ownership has on walking behavior and environmental perceptions/use is also a point of interest for future research.

Physical inactivity, particularly among older women, is an important public health issue and these data suggest that restricted access to opportunities to be physically active, reflected here in low street connectivity and pedestrian safety and no/few proximal walking paths, is a risk factor for physical inactivity. In the presence of individual characteristics such as low self-efficacy and greater functional limitations, the effects of a prohibitive neighborhood environment on walking behavior in older women are magnified. To our knowledge, this is the first study to examine the relative influence of individual, social and environmental variables on walking behavior in older women. This study was designed to serve as an empirical evaluation of a social ecological model of physical activity behavior; the results of which have implications for both theory development and systematic application. Indeed, the results of this study suggest that some variables may be more important than others when it comes to walking behavior in older women and, as such, are prime targets for future efforts to increase activity behavior. Taken together, our results suggest that the absence of these specific individual and environmental characteristics inhibits walking behavior in older women and consequently should be considered by urban planners, traffic engineers and public health advocates in campaigns to promote physical activity among older adults.

Funding

National Institute on Aging (AG20188 to E.M.).

Conflict of interest statement

None declared.

Acknowledgments

This material is based upon work K.S.H. conducted at the University of Illinois.

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