I n national youth fitness tests and surveys, the 1-mile run/walk(MRW) has been the field test of choice for assessing maximal or peak aerobic power (˙VO_{2peak} ) in youth ^{(42)} . During the years of growth and development, MRW performance improves progressively with age ^{(37,38)} , but ˙VO_{2peak} expressed relative to body mass stays the same in boys and decreases in girls^{(1,24)} . This suggests that metabolic factors other than ˙VO_{2peak} account for the age-related improvement in distance running performance during the years of growth and development.

Age-related changes in running economy and in the percentage of˙VO_{2peak} (%˙VO_{2peak} ) utilized during the MRW could explain the age-related improvement in MRW performance. These metabolic variables improve with age and are related to running performance in youth^{(24,25,27)} . Krahenbuhl et al.^{(24)} found that longitudinal improvement in 9-min run performance in six boys studied at age 10 yr and again at age 17 yr were associated with improved running economy and in%˙VO_{2peak} used during the run, whereas ˙VO_{2peak} (ml·kg^{-1} ·min^{-1} ) did not change. Whether these data are representative of children in general is not known. McCormack et al.^{(27)} found that ˙VO_{2peak} , running economy, and%˙VO_{2peak} used accounted for over 90% of the variance in MRW performance among children 7-14 yr, but the relative importance of the metabolic variables differed in the young and older children. No analysis of how the age-related changes in the metabolic variables contributed to the age-related improvement in MRW performance was reported.

The primary purpose of this study was to determine the extent to which˙VO_{2peak} , ˙VO_{2econ} ,and%˙VO_{2peak} used during the MRW account for the age-related improvement in MRW performance in youth. We hypothesized that an improvement in running economy and an increase in%˙VO_{2peak} used during the MRW would account for the age-related improvement in MRW performance in youth. A secondary purpose was to determine the extent to which these results were altered by expressing˙VO_{2peak} and ˙VO_{2econ} relative to body mass raised to the optimal power function (determined by allometric scaling) in place of the traditional simple ratios. We hypothesized that use of the power function ratios in place of the traditional simple ratios would alter the relation of these variables to age and to MRW performance and change the portion of the age-related improvement in MRW performance explained by these variables.

METHODS
Subjects. The subjects for this study were 53 girls and 92 boys, 7-17 yr of age, recruited from local elementary, middle-school, and high schools of a university community. After a complete explanation of the testing procedures, written consent was obtained from each subject and a parent. Many of the subjects were active in sports, including soccer, football, swimming, and cross-country running. The physical characteristics of the subjects by gender and age group are summarized in Table 1 .

1-mile run/walk. The MRW test was administered on playground fields or on local running tracks using standardized instructions^{(18)} . Subjects were counseled on proper pacing and running strategy, and they performed at least one practive MRW prior to the day of the MRW test. The test was supervised by one or more of the investigators, and subjects were verbally encouraged throughout the test to maintain the fastest possible pace.

Metabolic measures. The three metabolic independent variables(˙VO_{2peak} , ˙VO_{2econ} , and%˙VO_{2peak} ) were measured during two treadmill runs at a single test session. First, following practice walking and running on the treadmill and a warm-up, the subjects ran for 4 min on the treadmill at 8 km·h^{-1} ·˙VO_{2} measured during the final minute was used as the measure of˙VO_{2econ.} Subjects then rested to recover. Second, following another warm-up the subjects ran on the treadmill at the average speed maintained during the 1-mile run/walk test (6-18 km·h^{-1} ) for 3 min. At the end of the 3-min interval and every minute thereafter, the grade on the treadmill was increased 2.5% until the subject could no longer continue. Verbal encouragement to run as long as possible was given. The˙VO_{2} during the third minute was used to calculate%˙VO_{2peak} utilized, and the highest ˙VO_{2} obtained on the test was accepted as ˙VO_{2peak} if ˙VO_{2} increased less than 2.1 ml·kg^{-1} ·min^{-1} with a 2.5% grade increase or if heart rate was within 10% of age-predicted maximum(220-age). Metabolic measures were assessed by open-circuit spirometry using a computer-automated system described previously ^{(27)} . The term ˙VO_{2peak} was used in place of ˙VO_{2max} because a definitive plateau was not attained on all tests.

Allometric scaling. Traditionally, ˙VO_{2peak} and˙VO_{2econ} have been expressed relative to body mass(ml·kg^{-1} ·min^{-1} ) to adjust for the influence of body size. However, these ratio expressions do not necessarily remove the influence of body mass in a group, and it has been argued that˙VO_{2peak} and ˙VO_{2econ} should be adjusted using regression analysis or allometric scaling to avoid problems of spurious correlations with other variables^{(19,46,48)} . Others have maintained that traditional (i.e., simple) ratio expressions are meaningful^{(9,20)} . Therefore, to explore the effect of the mode of expression of these metabolic variables on age-related changes in MRW performance, ˙VO_{2peak} and ˙VO_{2econ} were expressed relative to body mass and relative to body mass raised to the optimal power function determined by allometric analysis.

To determine the optimal power functions, the natural log of˙VO_{2peak} and ˙VO_{2econ} (l·min^{-1} ) were regressed on the natural log of body mass using linear regression analysis. Analyses were performed separately for boys and girls. The resulting regression equations predicting log_{e} (˙VO_{2peak} ) in boys and girls were Y = 0.94X - 2.72 and Y = 0.91X - 2.77. The corresponding equations predicting log_{e} (˙VO_{2econ} ) were Y = 0.75X - 2.39 and Y = 0.70X - 2.31. The equations for boys and girls were not significantly different so the common regression coefficients (0.93 and 0.74) were used as the exponents in calculating ˙VO_{2peak} and ˙VO_{2econ} expressed relative to the optimal power function of body mass (power function ratio scores) for boys and girls.

Statistical analysis. Simple linear regression analysis was used to describe the relation of the metabolic measures to age and to MRW performance in boys and girls. Differences between the regression lines for boys and girls were tested using the method described by Pedhazur^{(32)} . Multiple linear regression analysis was used to determine the extent to which the metabolic measures accounted for the age-related change in MRW performance. Age and gender were entered into the multiple regression model first. Metabolic measures were successively added one-by-one and in combination, and change in the regression coefficient for age used to evaluate the extent to which the metabolic variables accounted for the effect of age on MRW performance. An alpha level of 0.05 was used for all significance tests.

RESULTS
The means and standard deviations of the metabolic variables and MRW time by gender and age group are presented in Table 2 . Scatter plots of the relationships of ˙VO_{2peak} and ˙VO_{2econ} expressions to body mass are shown in Figure 1 .˙VO_{2peak} and ˙VO_{2econ} (L· min^{-1} ) were strongly related to body mass in boys (r = 0.94, 0.95, P < 0.05) and girls (r = 0.89, 0.92, P < 0.05). Weak inverse relationships existed between ˙VO_{2peak} (ml·kg^{-1} ·min^{-1} ) and body mass in boys (r = -0.24,P < 0.05) and girls (r = -0.23, P > 0.05), whereas the corresponding correlations for ˙VO_{2econ} (ml·kg^{-1} ·min^{-1} ) were moderately strong (r = -0.73 and -0.70, P < 0.05). There were no significant relationships in boys or girls of ˙VO_{2peak} (r = -0.03 and 0.00) and˙VO_{2econ} (r = 0.01 and 0.04) expressed relative to the optimal power function with body mass. Correlations among the variables used in the regression analysis are presented by gender in Table 3 .

Scatter plots of the relationships of MRW performance and the metabolic variables to age are presented in Figure 2 . MRW time decreased significantly (improved) with age in boys and girls. The slopes (b) of the regression lines (-0.47 min·y^{-1} in girls and - 0.62 min·y^{-1} in boys) were not significantly different, but the y-intercept was significantly lower in boys by 2.8 min (seeFig. 2 caption for regression equations).˙VO_{2peak} (ml·kg^{-1} ·min^{-1} ) did not change with age in boys or girls, but values at a given age were systematically higher in boys by 9.2 ml·kg^{-1} ·min^{-1} . Similar nonsignificant relations were found when ˙VO_{2peak} was expressed relative to body mass^{0.93} . ˙VO_{2econ} (ml·kg^{-1} ·min^{-1} ) decreased significantly with age in boys and girls. The slopes of the regression lines were not significantly different between girls (-1.1 ml·kg^{-1} ·min^{-1} ·y^{-1} ) and boys (-0.94 ml·kg^{-1} ·min^{-1} ·y^{-1} ), but the y-intercept was higher in boys by 0.6 ml·kg^{-1} ·min^{-1} . Expressing ˙VO_{2econ} relative to body mass ^{-0.74} eliminated the relation with age.%˙VO_{2peak} increased with age in boys and girls. Neither the slopes (1.3%·y^{-1} in girls and 1.6%·y^{-1} ) nor the y-intercepts were significantly different between boys and girls.

Scatter plots between the MRW and the metabolic variables in boys and girls are presented in Figure 3 . As expected, MRW time was negatively related to ˙VO_{2peak} (ml·kg^{-1} ·min^{-1} ) (r = -0.27 in boys and -0.38 in girls, P < 0.05) and%˙VO_{2peak} (r = -0.83 and -0.74,P < 0.05), and positively related to ˙VO_{2econ} (ml·kg^{-1} ·min^{-1} ) (r = 0.48 and 0.34, P < 0.05). The corresponding partial correlations, holding the effects of age and gender constant, were -0.47, -0.72, and -0.08. When expressed relative to body mass raised to the optimal power, simple correlations with˙VO_{2peak} were stronger (r = -0.40 and r = -0.54, P < 0.05), but those with ˙VO_{2econ} were eliminated (0.04 and -0.02,P > 0.05). The slopes of regression lines were not different in boys and girls for any of the relations, but the y-intercepts were higher in girls for the relations of MRW time with ˙VO_{2econ} and%˙VO_{2peak} (see Fig. 3 caption for regression equations).

Multiple regression analysis was used to determine the extent to which the association of age with MRW performance was accounted for by the metabolic variables (Table 4) . Age and gender were entered into the multiple regression model first (equation 1). The regression coefficient for age indicated that on average MRW performance decreased 0.52 min for every 1 yr increase in age in boys and girls. Addition of%˙VO_{2peak} alone(equation 4) or in combination with either of the two other metabolic variables expressed relative to body mass (equations 6 and 7) reduced the regression coefficient for age to -0.29 or -0.30, indicating that changes in%˙VO_{2peak} accounted for approximately 42% of the age-related increase in MRW performance. Addition of ˙VO_{2peak} or˙VO_{2econ} (ml·kg^{-1} ·min^{-1} ) alone(equations 2 and 3) did not reduce the effect of age on MRW; but in combination there was a small reduction to -0.45. Inclusion of all three metabolic variables in the regression model reduced the regression coefficient for age -0.14, indicating that approximately 73% of the age-related improvement in MRW performance was accounted for by the combination of the three metabolic variables. When ˙VO_{2peak} and ˙VO_{2econ} were expressed relative to body mass raised to the optimal power, the results of the analyses were similar except that the regression coefficient for age did not decrease with the addition of ˙VO_{2econ} to age, gender, and˙VO_{2peak} or these variables plus%˙VO_{2peak} . With all three metabolic independent variables in the model, the regression coefficient for age was higher (-0.23).

DISCUSSION
The MRW is a widely-used field test ^{(42)} with established reliability and concurrent validity as a measure of˙VO_{2peak} (ml·kg^{-1} ·min^{-1} ) in samples of youth of limited age range ^{(12)} . This implies that MRW scores can be used to reflect ˙VO_{2peak} . Consequently, with the exception of the Fitnessgram test, MRW scores are not converted to a predicted˙VO_{2peak} in interpreting the results of youth fitness tests. Raw MRW scores are compared with percentile norms or criterion referenced standards for interpretation. However, the improvement in MRW performance in the population or in an individual child over several years may be mistakenly interpreted as reflecting an improvement in ˙VO_{2peak} despite the fact that ˙VO_{2peak} (ml·kg^{-1} ·min^{-1} ) does not increase with age. In youth heterogenous in age, the MRW has acceptable predictive validity as a measure of ˙VO_{2peak} only if the effects of age and gender on the relation of MRW performance to ˙VO_{2peak} are considered ^{(13)} . Understanding the physiologic basis for the age-related increase in MRW time is needed to properly interpret developmental changes on this field test.

The primary purpose of this study was to determine the extent to which˙VO_{2peak} , ˙VO_{2econ} , and%˙VO_{2peak} used during the MRW account for the age-related improvement in MRW performance in youth. These three metabolic variables were selected for study because in theory they should account for virtually all of the variance in MRW performance if it is assumed that performance is limited by the highest rate of steady-state˙VO_{2} that can be maintained and that differences in the extent to which anaerobic metabolism is used are small. The latter assumption is not unreasonable because in a run-test lasting between 6 and 16 min in which a maximal effort is given, anaerobic metabolism would be expected to supply between 10 and 25% of the energy used ^{(3)} . In a study on young adults, anaerobic metabolism supplied less than 10% of the energy used in performing a MRW test, and test performance was unrelated to measures of anaerobic energy utilized and capacity ^{(44)} . Anaerobic power and capacity in youth are less than in adults ^{(5)} and probably have less effect on performance. Therefore, no effort was made to quantify variability in anaerobic metabolism or capacity in this study. As explained below, however, because of the way it is calculated, variation in%˙VO_{2peak} could reflect, in part, effects of variation in these anaerobic measures on MRW performance.

The principal finding of this study is that the age-related improvement in MRW performance in youth is unrelated to ˙VO_{2peak} and is explained in terms of measures of aerobic metabolism by an increase in the%˙VO_{2peak} used during the MRW and by an improvement in˙VO_{2econ} (ml·kg^{-1} ·min^{-1} ). This outcome, based on cross-sectional data of a moderately large sample of boys and girls 7-17 yr, is the same as that of a longitudinal study of six boys by Krahenbuhl et al. ^{(21)} . The finding that the age-related improvement in MRW performance does not reflect an underlying change in˙VO_{2peak} indicates that year-to-year changes in MRW performance should not be used to infer changes in ˙VO_{2peak} during the years of growth and development. To more accurately assess individual or group changes in ˙VO_{2peak} with age, MRW scores at a given age should be converted into ˙VO_{2peak} ^{(13)} to take into account the age-linked change in the relation of ˙VO_{2peak} to MRW.

In the sample of youth used for this study, MRW time decreased with increasing age by an average of 0.52 min (31 s) per year in boys and girls. This rate of change is the same or greater than that reported in youth fitness surveys based on national probability samples for boys and girls^{(33,37,38)} . The greater rate of change in MRW time with age in the present sample was probably related to a tendency for the level of fitness, as judged by the percentile ranking on the MRW, to improve across age, particularly in the girls.

The aim of this study was to gain an understanding of the relative importance of several metabolic measures as determinants of the improvement in MRW performance with age. The importance of a metabolic measure in accounting for age-related change in MRW performance depends on (a) its change with age and (b) its relation to MRW performance. ˙VO_{2peak} was related to MRW performance but did not change with age. Thus, it did not contribute to improved MRW performance with age (Fig. 4) . Running economy improved (˙VO_{2econ} in ml·kg^{-1} ·min^{-1} decreased) with age and was related to MRW performance if variation in ˙VO_{2peak} was taken into account. Therefore, it contributed to improved MRW with age. A decrease in oxygen cost reduces the relative metabolic strain (%˙VO_{2peak} ) of running at a given speed because ˙VO_{2peak} is stable across age. With increasing age, a faster pace can be maintained at a given ˙VO_{2} or%˙VO_{2peak} . Finally, the relative metabolic strain(%˙VO_{2peak} ) that can be sustained during the MRW increased with with age and was related to MRW performance. Thus, it also contributed to improved MRW performance. The increased%˙VO_{2peak} used during the MRW increases the highest average rate of ˙VO_{2} that can be sustained during the run. With increasing age, the combination of an increased rate of ˙VO_{2} that can be sustained during the run and a reduced oxygen cost of running provide the extra oxygen required to sustain a higher average running speed.

˙VO_{2peak} in ml·kg^{-1} ·min^{-1} did not change across age in boys or girls. The lack of change across age is typical for boys but unusual for girls. ˙VO_{2peak} (ml·kg^{-1} ·min^{-1} ) in girls usually decreases with age after age 10 ^{(1,2,24)} . The˙VO_{2peak} of younger girls who volunteered for the present study was slightly lower, and the ˙VO_{2peak} of the older girls was slightly higher than is typical. The mean ˙VO_{2peak} of the boys was higher than in girls by approximately 9 ml·kg^{-1} ·min^{-1} , regardless of age. This difference is greater than that normally observed for younger children but representative of the usual gender difference for older adolescents. The lack of change in ˙VO_{2peak} (ml·kg^{-1} ·min^{-1} ) across age in boys and girls means that it was not an important determinant of the age-related change in MRW.

The increase across age in the%˙VO_{2peak} used during the MRW, from an average of approximately 84% at age 7 yr to approximately 97% at age 17 yr, increased the average ˙VO_{2} sustained during the MRW by 6-7 ml·kg^{-1} ·min^{-1} in boys and girls, independent of changes in ˙VO_{2peak} and ˙VO_{2econ} . This change accounted for a significant portion of the age-related decrease in MRW time. In the multiple regression analyses, holding constant the effect of the%˙VO_{2peak} used during the MRW decreased the regression coefficient for age from -0.52 to -0.30 (44%). This finding is in agreement with the logitudinal study of Krahenbuhl et al. ^{(21)} . They found that in six boys tested at age 9.9 yr and again 7 yr later at age 16.8 yr, who did not engage in any regular run training between the two tests, the estimated%˙VO_{2peak} used during a 9-min run increased from 85.8% to 99.5%. Based on the regression equation describing the relation of%˙VO_{2peak} to age in the present study (Fig. 2) , the estimated%˙VO_{2peak} of boys increased from 87.2% to 98.3% between the same ages. The change in girls was similar. The correspondence between the two types of data is striking and suggests that the longitudinal changes observed by Krahenbuhl et al. in a very limited number of boys are quite representative.

Development changes in behavioral and physiological factors could contribute to the increase in the%˙VO_{2peak} used during the MRW with age. Because the MRW time was used to establish the speed at which the average˙VO_{2} during the MRW was measured, everything that affected MRW performance other than ˙VO_{2peak} and ˙VO_{2econ} affected the estimate of the%˙VO_{2peak} used. Therefore, behavioral changes such as an increase in the effort given on the test or an improvement in pacing may have been partly responsible for the increase in the%˙VO_{2peak} with age. This may result, in part, simply from practice in taking tests such as the MRW. Physiological changes such as an increase in anaerobic capacity or in the lactate threshold may have also contributed to the increase. Based on measures of glycolytic enzyme activities, peak blood lactate in the blood following exhaustive exercise, and peak oxygen deficit, anaerobic capacity, and power appear to increase with age during childhood and adolescence^{(5,7,16,17,34)} . Lactate or ventilatory threshold, which can vary from approximately 40 to 90%˙VO_{2peak} , may increase ^{(31)} or decrease slightly ^{(4,5,10)} with age. It also is possible that the state of training of the older youth was greater than the younger youth tested for this study. Training can increase the lactate threshold, anaerobic capacity, and other physiological determinants of the%˙VO_{2peak} used during the MRW ^{(3)} .

˙VO_{2econ} (ml·kg^{-1} ·min^{-1} ) decreased progressively as a function of age in boys and girls. This finding agrees with other cross-sectional ^{(2,25,26)} and longitudinal ^{(14,15,21,43)} data. The slopes from regression equations relating the rate of change in˙VO_{2} during submaximal running at a standard speed to age in boys(-0.94) and girls (-1.1) were slightly greater than those calculated from the graphical mean data of Astrand ^{(2)} (-0.70 for boys and-0.85 in girls). Despite considerable research on the topic, the reason for the improvement in running economy (decrease in ˙VO_{2econ} ) with age is unknown ^{(25,40)} .

Allometric scaling indicated that ˙VO_{2econ} (l·min^{-1} ) did not increase in direct proportion to body mass in this cross-sectional sample but rather in proportion to body mass^{0.74} . Body mass increased proportionately faster than ˙VO_{2econ} (l·min^{-1} ). This finding is consistent with data on adults^{(6)} and youth ^{(35)} .˙VO_{2econ} in ml·kg^{-0.74} ·min^{-1} did not change with age. Similar findings based on longitudinal data were reported by Sjodin and Svedenhag ^{(43)} . Why ˙VO_{2econ} (L·min^{-1} ) does not develop in proportion to body mass is not clear ^{(35,40,43)} . Regardless of the mechanism responsible, it appears the disproportionate rate of increase in body mass relative to ˙VO_{2econ} (l·min^{-1} ) during growth and development may be responsible for the decrease with age in the˙VO_{2} (ml·kg^{-1} ·min^{-1} ) required to run at a given speed.

Despite the quite large improvement in running economy (decrease in˙VO_{2econ} in ml·kg^{-1} ·min^{-1} ) across age, it did not explain the group age-related decline in running performance independent of other variables. When added to age and gender in predicting MRW time in the multiple regression analysis, the regression coefficient for age did not decrease. This was because with age and gender held constant there was no relation of ˙VO_{2econ} to MRW time (partial correlation = -0.08). Likewise, no decrease occurred when ˙VO_{2econ} was added to the regression model with age, gender, and%˙VO_{2peak} already in the model. However, when added to the regression model with age, gender, and˙VO_{2peak} or age, gender, ˙VO_{2peak} and%˙VO_{2peak} already in the model, the regression coefficient for age decreased substantially. In the latter case, the 0.31 change from -0.45 to-0.14 is a 60% reduction of the regression coefficient for age with age and gender in the model (-0.52). Holding constant%˙VO_{2peak} and˙VO_{2peak} in addition to age and gender strengthens the relation between ˙VO_{2econ} and MRW time (partial correlation = 0.5). This means that in a group heterogeneous in ˙VO_{2peak} and%˙VO_{2peak} , there is little relation between ˙VO_{2econ} and MRW time because of the strong confounding effects of these two variables. Therefore, even though ˙VO_{2econ} decreases with age, this has little effect on the MRW performance of the group because offsetting changes in the other variables have a bigger effect on MRW time. The lack of relation between˙VO_{2econ} (ml·kg^{-1} ·min^{-1} ) and MRW or other distance run test performances is in agreement with results of most^{(22,23,27,40)} , but not all^{(41)} , cross-sectional studies on children. This finding is also consistent with studies on adults that have found that˙VO_{2econ} is not an important predictor of distance run performance in groups heterogeneous in ˙VO_{2peak} ^{(11,45)} .

On the other hand, the decrease in the regression coefficient for age when˙VO_{2econ} was added to age, gender, and ˙VO_{2peak} or these variables plus%˙VO_{2peak} indicates that if variation in˙VO_{2peak} is held constant, then improvement in running economy does explain a portion of the age-related decrease in MRW. This finding is consistent with longitudinal studies that have reported associations between individual changes in running economy and changes in distance running performance in youth whose ˙VO_{2peak} (ml·kg^{-1} ·min^{-1} ) did not change^{(14,15,21)} . It is also consistent with studies on adults that have found running economy is quite strongly associated with distance running performance in groups homogenous in ˙VO_{2peak} ^{(8,28)} . Thus, the improvement in running economy with age is an important determinant of the age-related decrease in MRW time in an individual or group only if considered in conjunction with the change in˙VO_{2peak} , or changes in ˙VO_{2peak} and%˙VO_{2peak} used during the MRW. The combination of improved running economy and increased%˙VO_{2peak} used during the MRW, taking into account information on ˙VO_{2peak} , accounted for almost three-quarters of expected decrease in MRW time across age.

Use of allometric scaling to adjust ˙VO_{2peak} (l·min^{-1} ) for the influence of body mass, instead of the˙VO_{2peak} /body mass ratio, had little effect on the results of this study. The body mass scaling factors (0.94 for boys and 0.91 for girls) were not significantly different from 1.0, indicating that the simple ratio scores provided a valid correction for body size ^{(30)} . Scaling factors for body mass of approximately 1.0 have been found in a number of other cross-sectional ^{(10)} and longitudinal^{(31,39,43)} studies on growing children. Others have found scaling factors significantly less than 1.0^{(1,36,47)} . Based on principles of dimensional analysis, ˙VO_{2peak} should scale as a function of body mass^{0.67} ^{(3)} . Nevill ^{(29)} has suggested that mass exponents higher than 0.67 reported in studies on growing children may result from a changing relation of ˙VO_{2peak} to body mass with age because of an increasing proportion of leg muscle in relation to body mass. He suggested incorporating body height as a covariate to control for changing muscle size. When we performed the analysis described by Nevill, the scaling factor for body mass dropped to 0.65 in boys and 0.43 in girls. This confirms his suggestion that altered body dimensions affect the relation of ˙VO_{2peak} (L· min^{-1} ) to body mass. Adding body height did not significantly reduce the residual variance in predicting˙VO_{2peak} for boys or girls, however, and therefore, it did not provide a better adjustment for body size.

In contrast to ˙VO_{2peak} , use of allometric scaling to adjust˙VO_{2} (l·min^{-1} ) during submaximal running at 8 km·h^{-1} for the influence of body mass, instead of using the˙VO_{2} /body mass ratio, had considerable effect on the interpretation of results for running economy. The body mass scaling factors (0.75 for boys and 0.70 for girls) were significantly less than 1, which is consistent with other studies on youth and young adults^{(6,35,36)} . Thus, there was not a proportional relation between the numerator and denominator assumed in the use of simple ratio scores, and therefore they did not provide an adequate adjustment of ˙VO_{2econ} for the effect of body mass. This was evidenced by moderately strong negative relationships between˙VO_{2econ} (ml·kg^{-1} ·min^{-1} ) and body mass(Fig. 1) . Expression of ˙VO_{2econ} relative to the body mass raised to the optimal power function (mass^{0.74} ) instead of as the simple ratio to body mass eliminated the influence of body mass on˙VO_{2econ} , and eliminated the decrease of ˙VO_{2econ} with age. We interpret these data to mean that the change with age in˙VO_{2econ} expressed as a simple ratio variable(ml·kg^{-1} ·min^{-1} ) is a result of the slower rate of increase with age in ˙VO_{2} (l·min^{-1} ) compared with body mass. Use of simple ratio scores that assume a proportional rate of increase to compare ˙VO_{2econ} in children of different ages undercorrects for the influence of body mass in lighter children and overcorrects in heavier children. These findings and their interpretation agree with those of others^{(6,43,35,36)} .

When ˙VO_{2peak} and ˙VO_{2econ} were expressed as power function ratios, neither changed systematically with age. Thus, the%˙VO_{2peak} used during the run, which increased systematically with age, was the only metabolic variable of the three that could explain the age-related improvement in MRW performance. This was reflected in the multiple regression analyses by the failure of ˙VO_{2econ} to explain any of the age-related decrease in MRW time. This finding indicates that the contribution of running economy to the age-related decrease in MRW time is dependent on its expression as a simple ratio variable and on the differential rate of increase in ˙VO_{2econ} (l·min^{-1} ) and body mass during growth and development. In addition, when ˙VO_{2peak} and˙VO_{2econ} were expressed as power function ratios, somewhat less of the age-related decrease in MRW time was explained (regression coefficient for age not decreased as much in the multiple regression analysis). Thus, use of power function ratio scores did not help explain the age-related decrease in MRW performance, but it did provide insight into the interpretation of the age-related improvement in running economy.

We conclude that age-related improvement in MRW performance in youth is explained primarily by an increase in the%˙VO_{2peak} used during the MRW and an improvement in running economy. Improvement in ˙VO_{2econ} helps explain the decrease in MRW time only if considered together with information on ˙VO_{2peak} (ml·kg^{-1} ·min^{-1} ) and if expressed as a simple ratio variable to body mass (in ml·kg^{-1} ·min^{-1} ). ˙VO_{2peak} (ml·kg^{-1} ·min^{-1} ) does not change systematically with age and therefore does not explain the age-related decrease in MRW time. Age-related changes in MRW time should not be used to infer changes in˙VO_{2peak} .

Figure 1-Scatter plots of ˙VO2peak(l·min-1) (girls: Y = 0.02X -0.37; boys: Y = 0.02X -0.01),˙VO2peak (ml·kg-1·min-1) (girls: -0.10X+ 50.00; boys: -0.07X + 56.73), ˙VO2peak(ml·kg-0.93·min-1) (girls: 0.0X + 63.68; boys:-0.01X + 67.61), ˙VO2econ (l·min-1) (girls: 0.02X + 0.36; boys: 0.03X + 0.42), ˙VO2econ(ml·kg-1·min-1) (girls: -0.25X + 44.18; boys:-0.17 + 44.16), and ˙VO2econ(ml·kg-0.74·min-1) (girls: 0.03X + 99.76; boys: 0.00X + 92.24) to body mass. Figure 2-Scatter plots of ˙VO2peak(ml·kg-1·min-1) (girls: Y = 0.037X + 45.3, r = 0.02, SEE = 5.8 ml·kg-1·min-1; boys: Y = -0.113X + 54.5, r = -0.07, SEE = 5.6 ml·kg-1·min-1),˙VO2peak (ml·kg-0.93·min-1) (girls: Y = 0.66X + 56.2, r = 0.23, SEE = 7.8 ml·kg-0.93·min-1; boys: Y = 0.27X + 63.5, r = 0.13, SEE = 7.0 ml·kg-0.93·min-1),˙VO2econ (ml·kg-1·min-1) (girls: Y =-1.1X + 46.5, r = -0.70, SEE = 3.3 ml·kg-1·min-1; boys: Y = -0.94X + 47.1, r = -0.68, SEE = 3.3 ml·kg-1·min-1), ˙VO2econ(ml·kg-0.74·min-1) (girls: Y = -0.09X + 102.0, r = 0.03, SEE = 9.4 ml·kg-0.74·min-1); boys: Y = 0.03X+ 92.1, r = 0.01, SEE = 7.9 ml·kg-0.74·min-1),%˙VO2peak (girls: Y = 1.3X + 74.9, r = 0.42, SEE = 8.0%; boys: Y = 1.6X + 71.4, r = 0.53, SEE = 8.5%), and MRW (girls: Y = -0.62X + 17.3, r =-0.74, SEE = 1.6 min; boys: Y = -0.47X + 14.5, r = -0.67, SEE = 1.7 min) to age. Figure 3-Scatter plots of MRW to ˙VO2peak(ml·kg-1·min-1) (girls: Y = -0.16X + 17.4, r =-0.38, SEE = 2.2 min; boys: Y = -0.11X + 14.5, r = -0.27, SEE = 2.2 min),˙VO2peak (ml·kg-0.93·min-1) (girls: Y =-0.16X + 20.4, r = -0.54, SEE = 2.0 min; boys: Y = -0.13X + 17.4, r = -0.40, SEE = 2.1 min), ˙VO2econ(ml·kg-1·min-1) (girls: Y = 0.16X + 4.31, r = 0.34, SEE = 2.3 min; boys: Y = 0.25X - 0.22, r = 0.48, SEE = 2.0 min),˙VO2econ (ml·kg-0.74·min-1) (girls: Y =-0.05X + 15.2, r = 0.19, SEE = 2.3 min; boys: Y = 0.01X + 7.4, r = 0.04, 2.3 min), and% ˙VO2peak (girls: Y = -0.20 + 28.15, r = -0.74, SEE = 1.6 min; boys: Y = -0.19 + 26.1, r = -0.83, SEE = 1.3 min). Figure 4-Diagram illustrating the metabolic adaptations that contribute to improvement in MRW performance with age in boys and girls. Improved running economy with age (decreased oxygen cost of running at a given speed; ˙VO2econ in ml·kg-1·min-1) reduces the metabolic strain (% ˙VO2peak) of running at a given speed if ˙VO2peak does not change, making possible an increase in the speed of running that elicits the same relative metabolic strain. An increase in the relative metabolic strain (average% ˙VO2peak) that can be sustained during the MRW increases the average sustainable˙VO2 and average MRW speed. ˙VO2peak does not contribute to improved MRW performance with age. REFERENCES
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