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BASIC SCIENCES: Original Investigations

How Many Days of Pedometer Use Predict the Annual Activity of the Elderly Reliably?


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Medicine & Science in Sports & Exercise: June 2008 - Volume 40 - Issue 6 - p 1058-1064
doi: 10.1249/MSS.0b013e318167469a
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Habitual physical activity is an important behavior related to the incidence of coronary artery disease, obesity, osteoporosis, and other significant contributors to morbidity and mortality in elderly individuals (6,11). Walking is a convenient method of filling this health need in older people, and several studies in family practice have indicated that pedometers offer a simple and motivational means of augmenting habitual physical activity (13).

The spontaneous physical activity of free-living humans is influenced by many factors, both endogenous and exogenous. Trost et al. (15) have noted the effects of demographic and biologic characteristics, psychologic, cognitive, and emotional influences, behavioral attributes and skills, sociocultural influences, and characteristics of the physical environment. In consequence, patterns of physical activity show substantial intra- and/or interindividual variance. A previous study that evaluated habitual physical activity by measuring uniaxial accelerometer counts during waking hours (4) and a questionnaire estimate of 24-h physical activity (5) both emphasized that the day-by-day intraindividual variance must be considered before examining interindividual differences in physically active behavior; this recommendation seems equally important when using other types of personal activity monitors. Knowing the extent of intraindividual variance is critical to appropriate data sampling, whether monitoring individual patterns of physical activity or exploring the determinants of physical activity.

When deciding on the pattern of data collection needed to obtain a reliable estimate of an individual's physical activity in the face of such external determinants as day of the week and season (4,5,17,19), previous investigators have had only limited information on the extent of day-by-day variations. Some investigators have accepted the arbitrary recommendation of the International Biological Programme (1 wk, including the weekend, and repeated once, e.g., in summer and in winter) (10). Intraindividual variations in physical activity are likely to be particularly marked in an elderly population, where schedules are no longer governed by requirements of schooling or employment. There is also a need to clarify characteristics of the residual variance, considered as white noise in some previous studies (4,5). In what we think is a unique study, we have recently had opportunity to collect detailed physical activity measurements on a substantial healthy elderly population during an entire year. We here apply the techniques of variance analysis and Fourier transformation to examine patterns of variability of daily step counts within the individual and within our test population; this has allowed us to make mathematical estimates of the number of days of sequenced, randomly timed, and seasonally timed observations needed to predict the annual habitual physical activity in healthy elderly people during a 365-d period. We have applied a modification of the classic Spearman-Brown measure (12) to make two estimates of reliability: the number of days of observation required so that between-subjects variations would account for 80% and 90%, respectively, of the total variance. Our primary hypothesis was that systematic sampling (on the basis of season and day of the week) or sampling distributed randomly throughout the year would yield the required levels of reliability with substantially fewer days of observation than sequenced sampling.


Subjects and study location.

Our subjects were a convenience sample of 37 men (age 71 ± 4 yr, height 1.57 ± 0.06 m, body mass 58 ± 9 kg [mean ± SD]) and 44 women (age 71 ± 4 yr, height 1.47 ± 0.06 m, body mass 51 ± 8 kg), free-living and healthy elderly Japanese volunteers. All gave their written informed consent to participate in this institutionally approved study, after the protocol, stresses, and possible risks had been fully described to them. They lived in Nakanojo, a medium-sized residential town (with a population of 18,321 in 2001) with level terrain, situated approximately 150 km northwest of Tokyo. Mean daytime summer and winter temperatures were 26 and 4°C, respectively, and the annual rainfall was approximately 1.3 m in 2001. There were few significant accumulations of snow during our period of observation. On the basis of their annual medical examination, all study participants were judged free of chronic conditions that might limit their physical activity during the observation period. None were still employed. Twenty-one men and 32 women were engaged in regular sport or other forms of deliberate exercise. These individuals were classed as "habitual exercisers."


An electronic physical activity monitor [modified Kenz Lifecorder, Suzuken Co., Ltd, Nagoya, Aichi, Japan (14)] was used throughout. The device is small (62.5 × 46.5 × 26.0 mm3), light (40 g), and relatively inexpensive (approximately US $250 per unit). It can accumulate data for a maximum of 36 d. The mechanism comprises a uniaxial piezoresistive accelerometer and amplifier that measures vertical accelerations of the trunk. The device can be used to measure both step counts and 11 intensities of physical activity, although for the purpose of this study, the focus was simply on the step count. In brief, a central processing unit detects both digitized accelerations >0.15g and the number of shifts in digitized acceleration from under to over the detection threshold during each 2-min interval. A proprietary algorithm then determines which accelerations are true steps rather than incidental movement. The monitor has essentially the same characteristics as the unmodified version (Kenz Lifecorder) that has received detailed appraisal from several investigators (1,8,9). The step counts of adults when walking around an outdoor track are determined with an intramodel reliability of 0.998, the 95% confidence limits of estimate being ±3% relative to the actual number of steps taken (9). In the present study, data were stored for subsequent computer retrieval and analysis. The monitor is fitted with an event marker. Subjects were instructed to push the button when recording began and when the device was removed for such reasons as bathing, showering, or dressing. Normally, they met this requirement scrupulously. When no step counts were recorded during a 2-min interval, we noted whether the digitized acceleration exceeded 0.06g, a value much less than the acceleration caused by a step. This criterion distinguished periods when there was slight incidental body movement from those when there was none.

Experimental protocols.

The activity monitor was attached to a waist belt, worn uniformly on the left side of the subject's body. A previous study (1) established that results were uninfluenced by the side of attachment. Subjects were instructed to wear the monitor throughout each 24-h period, only removing it while bathing, showering, or dressing. Recording continued between July 2001 and June 2002. Monthly visits to the Public Health Center in Nakanojo allowed data retrieval and battery replacement in the space of a few minutes.

Immediate analyses of physical activity data.

Data were analyzed continuously during each 24-h period from midnight to the following midnight. By recording throughout both day and night, we avoided introducing variance related to the times of fitting and removal of the device. A computer program scanned all records to detect any consecutive intervals during waking hours (as determined by questionnaire) when there were neither recorded body movement nor event stamps. In the few intervals of this type lasting >2 h, we concluded that the subject had forgotten to wear the device. Such intervals were encountered on <5% of measurement days [6 ± 4 d (0-17) of 365 d], the cumulative duration amounting to <0.2 ± 0.2% of the total monitoring period. To avoid a possible systematic underestimation of daily physical activity, data for such intervals were arbitrarily replaced by values estimated by a linear interpolation from scores obtained immediately before and after the period of inadequate data recording (14), this approach being preferred to the alternative option of excluding the corresponding 24 h of data.

To evaluate components of overall variance previously dismissed as "white" or random noise, a computer program randomly resequenced the original day-by-day data from each subject, thus giving information equivalent to the sampling of step counts on randomly selected days. Individual data were also checked for the effects of season and day of the week, and residuals from those effects were estimated. Seasonal classifications were made using arbitrary quarterly cut points (summer: July 1-September 30; autumn: October 1-December 31; winter: January 1-March 31; spring: April 1-June 30); these cut points correspond closely with those selected in several previous studies (5,16).

Mathematical and statistical analyses.

To estimate the power spectrum density for original and randomly resequenced data and the sequence of residuals from the effects of season and day of the week, we first extracted from each subject's entire data set 10 time-shifted, equally overlapping subsets of 256 data points. A fast Fourier transformation was then applied to each of these subsets. Finally, results for the 10 subsets were averaged for frequency. Transformation from the time to the frequency domain enabled us to analyze the periodicity of peaks in the time series.

Total variances for original and randomly resequenced data were each separated into between-subjects and within-subject components. We then applied a modification of the classic Spearman-Brown calculation (12), estimating the intraclass reliability coefficient (R) as the proportion of total variance attributable to between-subjects variance:

where σB2 is the between-subjects variance and {σW(n)}2 is the within-subject variance for n days of moving averaged data. The log-log plot of {σW(n)}2 versus n shows a slope of −1.0 for white noise. R(n) can be estimated from σB and σW(1), using the original Spearman-Brown calculation (12). To examine the effects of season and day of the week on the intraclass reliability coefficient, the original day-by-day data from each subject were resequenced in regular fashion:

where ai is the ith number of data in the original sequence. From these resequenced data, we calculated the intraclass reliability coefficient for n = 4k days. Any 4k consecutive values of the resequenced data include an equal number of observations for each season and for all days of the week when k ≥ 2. This tactic allows us to take maximum account of both season and day of the week when selecting sampling days fewer than 28 which is the lowest common multiple of 4 (season) and 7 (day of the week). The upper limit of n was determined as R(n) > 0.9 in all data sets.

Differences in daily step counts between sexes, between days of the week or seasons, and intra- and interindividual differences in the effect of day of the week and season were assessed using both multifactor repeated-measures ANOVA and multiway ANOVA, applying an appropriate Bonferroni correction to post hoc data. Differences for main effects were considered significant when the adjusted P was <0.05.


The average daily step counts for our data covering the 1-yr period were 7120 ± 2561 in men and 6443 ± 2662 in women (P = 0.248). Essentially similar values were found for averages calculated after excluding days with missing data (step counts of 7134 ± 2571 and 6458 ± 2671, respectively). Although step counts tended to be lower in women, there was a considerable overlap between sexes. Table 1 summarizes the average physical activity by day of the week, and Table 2 by season of the year. When analyzed by repeated-measures ANOVA, there was no significant main effect attributable to day of the week, although there was a significant day × subject first-order interaction (P < 0.05; Table 1); the greatest interindividual differences in physical activity were seen on Saturdays in men, and on Tuesdays in women. Analysis by season showed a significant main effect (P < 0.05) and a significant season × subject first-order interaction (P < 0.05; Table 2). Interindividual differences in physical activity were larger in women than in men; moreover, in men, interindividual differences of activity tended to be larger in the spring, when some men increased their physical activity, whereas in women, differences were smaller in winter, when many subjects undertook little physical activity. Analysis by day × season showed a significant first-order interaction in both sexes (P < 0.05) and a significant day × season × subject second-order interaction only in women (P < 0.05).

Daily step count for each day of the week.
Daily step count for each quarter of the year.

Figure 1 depicts normalized power spectral densities averaged for men and women, as calculated by fast Fourier transformation of individual data. Narrow peaks of variance with periods of 2.3, 3.5, and 7.0 d are seen (Fig. 1). There are no distinct peaks at lower frequencies, but powers in this range are greater than peak values at the higher frequencies (Fig. 1). These particular characteristics are related neither to the individual's sex (Fig. 1) nor to exercise habits (Fig. 2). However, the low frequency variance is eliminated if the analysis is repeated using randomly resequenced data (Fig. 1). The spectra of residuals from the effects of season and day of the week show narrow peaks with a period of around 2.3 d and powers in the lower frequency range, which are again higher than in the higher frequency range (Fig. 1).

Log-log plots of normalized power spectral density (PSD, ratio of observed power to the total integrated spectral power) for the original data, the randomly resequenced data, and the residuals for individual effects of season and day of the week in men and women. PSD values for the original data, the randomly resequenced data, and the residuals have been offset vertically using multiplication coefficients of 2.4, 0.3, and 0.7, respectively, for clarity of presentation. Values are means ± SD. The SD values are almost identical across all frequencies, so are shown only for the lowest frequency.
Log-log plots of normalized PSD for original data on nonexercisers and habitual exercisers. PSD for the nonexercisers has been offset vertically by a multiplication coefficient of 2.5 for clarity of presentation. Values are means ± SD. The SD values are almost identical across all frequencies, so are shown only for the lowest frequency.

These characteristics of our data are reflected in plots of within-subject variance for n consecutive days (Fig. 3). The log-log plot of variance versus cumulative days of observation shows a slope of almost −1.0 for the randomly resequenced data set, a steeper slope than for the original data (Fig. 3). The slope for the regularly resequenced data set on the basis of season and day of the week is also steeper than that for the original data, although less steep than that for randomly resequenced data (Fig. 3).

Log-log plots of mean ± SD within-subject variance for n consecutive days for the original data, the randomly resequenced data, and the regularly resequenced data on the basis of season and day of the week in men and women. Values are normalized by variance for n= 1 of each data set.

Figure 4 indicates the number of consecutive days of observation needed to reach the specified confidence levels when estimating the annual habitual physical activity of a single individual from our elderly population. At least 25 and 8 consecutive days of data collection are required to reach 80% reliability in men and women, respectively (Fig. 4). To reach 90% reliability, at least 105 and 37 consecutive days of observation are needed (Fig. 4). By adopting the alternative tactic of sampling days on a random basis (as mimicked by our randomly resequenced data set), the monitoring periods in both sexes can be reduced to 4 d for 80% reliability, and to 11 and 9 d for 90% reliability in men and women, respectively (Fig. 4). On using a pattern of sampling that considers the effects of season and day of the week (as mimicked by our regularly resequenced data set on the basis of season and day of the week), the respective monitoring periods for men and women can be reduced to 8 and 4 d (i.e., 2 and 1 consecutive days every 89 d, respectively) for 80% reliability and to 16 and 12 d (i.e., 4 and 3 consecutive days every 89 d, respectively) for 90% reliability (Fig. 4).

Reliability coefficients for the original, the randomly resequenced, and the regularly resequenced data on the basis of n consecutive days of assessment in men and women.


Habitual physical activity bears an important relationship to many causes of morbidity and mortality (11,18). Errors in the estimation of an individual's physical activity weaken epidemiological associations between such data and population health. In population terms, this problem can be largely countered by increasing the number of subjects and spreading the timing of observations in random fashion during an entire year. However, such an approach cannot be adopted when dealing with the individual; accurate determinations of daily physical activity for an individual require either many days of continuous monitoring or a careful selection of appropriate sampling days on the basis of the predetermined time characteristics of physical activity. The day of the week (4,5,16,17) and the season of the year (5,14,16,20) have already been identified as periodic factors that commonly influence habitual physical activity (although our data show significant interindividual differences in both day of the week and seasonal effects in elderly Japanese). Supporting our findings, observations obtained in the US through application of a 24-h physical activity recall questionnaire five times per year accounted for only 14% and 22% of total 12-month variance in 60- to 70-yr-old male and female subjects, respectively (5). In the study of Matthews et al. (5), seasonal factors accounted for a further 11% and 9% of variance in men and women, respectively. These authors classified the remainder of the intraindividual variance (49% and 61% in men and women, respectively) as random (white) noise, pending clarification of its nature and origins (5). Tudor-Locke et al. (16) have looked at physical activity patterns for 365 d but on a very small and selected sample of subjects, with only a limited analysis of variations. The present study is the first to look in detail at patterns of physical activity during an entire 365-d period. Spectral analysis of these data describes the distribution of variability in relation to frequency; this is an important step in finding a previously unremarked periodicity and in deciding whether the residual variance should be considered as random noise that can be ignored when determining overall physical activity levels for a specific period.

In our study, the daily step count showed no consistent pattern with respect to days of the week when averaged over individuals (Table 1); others have also seen minimal overall effects of day of the week in men and women aged 60-79 yr (4). However, power spectra of individual daily step counts for both men and women showed a distinctive peak with a periodicity of around 7 d (Fig. 1), indicating that the effect of day of the week differs between subjects. The implication is that intraindividual variations during a 7-d period may be larger than previously inferred from studies on the basis of group-averaged data (3-5), and this is confirmed by the significant first-order day of the week × subject interaction term in our repeated-measures ANOVA. The Fourier analysis of step counts also showed clear peaks with periods of approximately 2.3 and 3.5 d in both men and women (Fig. 1). The peak with a period of 2.3 d was still observed in the residuals from the effects of season and day of the week (Fig. 1). The origins of these 2.3- and 3.5-d cycles have yet to be identified clearly; possibly, the 3.5-d cycle may be harmonic components of 7-d (weekly) variation and the 2.3 d may reflect endogenous or exogenous effects that have yet to be identified.

The residual variance does not show the characteristics of random noise as previously anticipated. In our observations, the power spectra of variations in physical activity for both men and women were greater at low frequencies; the data were like a power-law function of the type (1/fβ, where f is the frequency and β is the spectral component) (2,7). Non-white noise would show a linear relationship between the log of spectral power and the log of frequency with a slope of β > 0; in contrast, the observed spectrum was flat (β = 0) in the randomly resequenced data set (Fig. 1). Looking at the data for residuals from the effects of season and day of the week, the power spectrum was still not flat despite removing peaks with periods of 256 and 128 d (Fig. 1); this indicates that an artifact of Fourier analysis caused by seasonal effects was not the main source of the power-law function variance. A power-law dependence of human temporal behavior has also been reported in a hospital environment (2,7) and at home in the elderly (21). Due account must be taken of these various characteristics when deciding on appropriate sampling tactics to estimate the annual physical activity of an elderly person.

Previous studies of reliability coefficients for accelerometers (4), pedometers (17), and questionnaires (5) proposed the minimum numbers of days needed to obtain reliable estimates of an individual's physical activity without detailed mathematical consideration of methods to optimize data collection. The number of days of observation suggested in some of these studies (4,5,17) was estimated on the erroneous basis that much of the variability in daily physical activity was a form of "white noise." However, we have plotted actual within-subject variance against the number of days of observation and thus determined the precise number of days of consecutive, random, or seasonally selected sampling needed to attain specified reliability coefficients. As the number of days of observation is increased, the within-subject variance decreases more slowly in consecutive than in randomly resequenced data (Fig. 3), with a corresponding influence on the number of days of observation needed to obtain acceptable estimates (Fig. 4). When sampling was planned to consider season and day of the week, the within-subject variance decreased much faster than for consecutive sampling (Fig. 3), although more slowly than for the randomly resequenced data (Fig. 3). Thus, the data support our primary hypothesis; the sampling period must be substantially longer for continuous than for random or seasonally distributed observations. To select days randomly for sampling, for example, researchers can pick days from randomly shuffled cards on which each date for a 1-yr period has been written. However, if the sample size is substantial, it is easier to use a computer program to select days on a random basis.

The reliability coefficient that we have chosen for our study is on the basis of the relative magnitudes of between- and within-subject variance. Our results may thus be unique to a particular sample of elderly Japanese society living in a medium-sized town at the beginning of the 21st century. Application of similar methods of analysis to data sets from other populations with differing between- and/or within-subject variance may well reveal some differences of sampling requirements in these populations. However, like most elderly people in developed countries, our subjects no longer had any formal employment. This allowed us to focus on nonoccupational activities that show greater and more "natural" [i.e., aperiodic (Fig. 1)] variability than occupational activity (4,5). Despite some potential differences in other communities, we anticipate that a repetition of our work will demonstrate a similar need for extended periods of observation when making a precise determination of physical activity patterns in an individual. Plainly, further yearlong studies are required, where a similar methodology is applied to determine how far appropriate sampling patterns differ between populations. Such studies should include those of working age and those living in larger cities and in rural areas. Our results also emphasize that future research should adopt statistical techniques that take account of the supposedly "natural" variations in physical activity, previously dismissed as "white noise."

In conclusion, our results support the hypothesis that the numbers of observation days needed to obtain reliable estimates of an elderly individual's annual physical activity are fewer if observations are distributed by day of the week and season or randomly rather than consecutively. From the practical viewpoint of increasing a person's physical activity, it may also be helpful to focus motivational efforts on the season when activity for a given individual is at its lowest.

The authors thank the expert technical assistance of the research and nursing staffs of the Tokyo Metropolitan Institute of Gerontology, The University of Tokyo, and the Nakanojo Public Health Center. We also thank the subjects whose participation made this investigation possible. This study was supported in part by a grant from the Japan Society for the Promotion of Science. This research was undertaken as part of the longitudinal interdisciplinary study on the habitual physical activity and health of elderly people living in Nakanojo, Gunma, Japan (the Nakanojo Study).


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