# The Suitability of Arm Span as a Substitute Measurement for Height

Abstract

Comment by dmbarton2: Introduction

Many anthropometric equations rely on individual height. Accurate height is not obtainable when various skeletal abnormalities exist. Arm span is proposed as a possible substitute for height. Twenty six subjects’ arm span and height were measured. The Pearson R for arm span and height was 0.518 (p<0.05). The independent t-test for mean differences in arm span width between males and females was t(24)=3.70, p=0.001 Results of this study show that arm span and height are moderately correlated and arm span can be used as a predictor of height. Also male arm span is significantly greater than female arm span. Comment by dmbarton2: Methods Comment by dmbarton2: Conclusion

**Introduction**

Comment by dmbarton2: Foundation

In many medical, physiological, and human performance measurements the height of human subjects is used as a predictive and/or classification variable. Equations predicting Body Mass Index, pulmonary function, caloric expenditure, and body fat percentage are just a few of the many equations using height as a predictive variable.1 However, spinal curvature conditions such as kyphosis, scoliosis, lordosis, and kyphoscoliosis make it difficult to determine the correct height of the individual and thereby necessitating the need to identify a substitute anthropometric measurement.2 Comment by dmbarton2: Need

The need for an anthropometric measurement to serve as a substitute for height has long been recognized. One possible substitute measurement is arm span, that is – the distance from the left middle finger tip to the right middle fingertip of outstretched arms parallel to the ground.

Comment by dmbarton2: Purpose statement

The purpose of this cross-sectional observational study was to determine if there was a significant relationship between arm span and height to determine if an arm span could serve as a valid and reliable substitute for height. Also to be determined is whether or not male and female arm span differs significantly.

**Methods**

Sample:

A convenience sample of 26 high school seniors was be used.

Equipment:

Task Force Hand Tools 25 foot tape measure.

Measurements:

Each subject height (with shoes off) was determined with the subject standing flat footed and with erect posture.

The arm span was taken with arms outstretched, parallel to the ground, from the tip of the right middle finger to the left middle finger across the back.

All measurements were recorded to the nearest ½ inch.

Statistical Procedures:

Mean, median, standard deviation, minimum and maximum and measures of data distribution normality were calculated for the sample. Data were examined for outliers.

Statistical correlation was used to determine the magnitude and significance of the relationship between arm span and height. Comparison of mean arm span measurement was employed to determine if males and females arm spans differed significantly.

Hypotheses tested:

Null Hypothesis: ρ (rho) =0 There is no significant relationship between arm span and height.

Alternative Hypothesis: ρ (rho) ≠0 There is a significant relationship between arm span and height.

Null Hypothesis: μ(mu) male – μ(mu) female =0 There is no significant difference between mean width of male and female arm span.

Alternative Hypothesis: μ(mu) male – μ(mu) female ≠0 There is a significant difference between mean width of male and female arm span.

Hypotheses tested at the 0.05 level of significance.

**Results**

Descriptive statistics for male and female arm span are shown in Table 1.

*Table 1. Male and female Arm Span Statistics*

Descriptives |
|||||

Gender | Statistic | Std. Error | |||

Arm_Span | Male | Mean | 68.1429 | .62772 | |

95% Confidence Interval for Mean | Lower Bound | 66.7867 | |||

Upper Bound | 69.4990 | ||||

5% Trimmed Mean | 68.1587 | ||||

Median | 68.0000 | ||||

Variance | 5.516 | ||||

Std. Deviation | 2.34872 | ||||

Minimum | 64.00 | ||||

Maximum | 72.00 | ||||

Range | 8.00 | ||||

Interquartile Range | 3.25 | ||||

Skewness | .092 | .597 | |||

Kurtosis | -.287 | 1.154 | |||

Female | Mean | 65.0000 | .55048 | ||

95% Confidence Interval for Mean | Lower Bound | 63.7884 | |||

Upper Bound | 66.2116 | ||||

5% Trimmed Mean | 65.0000 | ||||

Median | 65.0000 | ||||

Variance | 3.636 | ||||

Std. Deviation | 1.90693 | ||||

Minimum | 62.00 | ||||

Maximum | 68.00 | ||||

Range | 6.00 | ||||

Interquartile Range | 3.50 | ||||

Skewness | .000 | .637 | |||

Kurtosis | -1.269 | 1.232 |

Descriptive statistics for male and female height are shown in Table 2.

*Table 2. Male and female Height Statistics*

Descriptives |
|||||

Gender | Statistic | Std. Error | |||

Height | Male | Mean | 68.2143 | .66447 | |

95% Confidence Interval for Mean | Lower Bound | 66.7788 | |||

Upper Bound | 69.6498 | ||||

5% Trimmed Mean | 68.1825 | ||||

Median | 68.0000 | ||||

Variance | 6.181 | ||||

Std. Deviation | 2.48623 | ||||

Minimum | 64.00 | ||||

Maximum | 73.00 | ||||

Range | 9.00 | ||||

Interquartile Range | 3.25 | ||||

Skewness | .311 | .597 | |||

Kurtosis | .006 | 1.154 | |||

Female | Mean | 65.0000 | .67420 | ||

95% Confidence Interval for Mean | Lower Bound | 63.5161 | |||

Upper Bound | 66.4839 | ||||

5% Trimmed Mean | 65.0556 | ||||

Median | 65.0000 | ||||

Variance | 5.455 | ||||

Std. Deviation | 2.33550 | ||||

Minimum | 61.00 | ||||

Maximum | 68.00 | ||||

Range | 7.00 | ||||

Interquartile Range | 3.00 | ||||

Skewness | -.514 | .637 | |||

Kurtosis | -.284 | 1.232 |

Results from the tests for normality are shown in Table 3.

*Table 3. Tests of Normality.*

Tests of Normality |
|||||||

Gender | Kolmogorov-Smirnova | Shapiro-Wilk | |||||

Statistic | df | Sig. | Statistic | df | Sig. | ||

Height | Male | .177 | 14 | .200* | .968 | 14 | .853 |

Female | .168 | 12 | .200* | .898 | 12 | .149 | |

Arm_Span | Male | .167 | 14 | .200* | .960 | 14 | .717 |

Female | .200 | 12 | .200 | .935 | 12 | .439 | |

*. This is a lower bound of the true significance. | |||||||

a. Lilliefors Significance Correction |

Distribution of arm span and height data are shown in Figures 1 and 2. *(Note from Dr. Barton: Histograms may be used in place of box plots)*

Figure 1. Distribution of male and female height data

*Figure 2. Distribution of male and female arm span data.*

Comment by Dr. Barton: Whether or not a parametric or non-parametric test is used for the HLTH 511 research report will depend on whether or not the data in the ResearchReportData is normally distributed.

The data appear normally distributed therefore Pearson correlation is employed for the correlation analysis and an independent t-test is employed for the comparison of male and female mean arm span measurements.

Correlation between arm span and height are shown in Table 4.

*Table 4. Correlation of Arm Span and Height*

Correlations |
|||

Height | Arm_Span | ||

Height | Pearson Correlation | 1 | .518** |

Sig. (2-tailed) | .007 | ||

N | 26 | 26 | |

Arm_Span | Pearson Correlation | .518** | 1 |

Sig. (2-tailed) | .007 | ||

N | 26 | 26 | |

**. Correlation is significant at the 0.01 level (2-tailed). |

Scatterplot of arm span and height is shown in Figure 3.

*Figure 3. Scatterplot of Arm Span and Height*

Results of independent t-test comparing male and female arm span measurement is shown in Table 5.

*Table 5. Results of Independent T-Test of Male and Female Arm Span Measurement*

Independent Samples Test |
||||||||||

Levene’s Test for Equality of Variances | t-test for Equality of Means | |||||||||

F | Sig. | t | df | Sig. (2-tailed) | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference | |||

Lower | Upper | |||||||||

Arm_Span | Equal variances assumed | .034 | .854 | 3.703 | 24 | .001 | 3.14286 | .84875 | 1.39112 | 4.89460 |

Equal variances not assumed | 3.764 | 23.946 | .001 | 3.14286 | .83490 | 1.41950 | 4.86622 |

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**Discussion**

Comment by dmbarton2: Summary statement

In an effort to determine whether or not a significant correlation between arm span and height, and male/female differences in arm span – measurements were obtained from 26 “normal” subjects.

Skewness and kurtosis results in Tables 1 and 2 indicate arm span and height data are normally distributed. The non-significant p values for the Shapiro-Wilk test shown in Table 3 also indicate the data are normally distributed. Figures 3 and 4 substantiate this conclusion as there are no outliers visible in the box plots. Therefore all data were included in the statistical analyses and parametric statistical tests are appropriate.

Results of the correlation analysis in Table 4 indicate a significant (p<0.05) moderate positive (r=0.518) correlation between arm span and height. This strength and direction of the correlation is further demonstrated by the scatterplot shown in Figure 3.

Results if the independent t-test comparing male and female arm span measurements shown in Table 5 indicate a significant mean difference t(24)=3.70, p=0.001 (Equal variances assumed) between male and female arm span measurements. As shown in Table 1 male arm span (68.13) is greater than female (65.00). This difference is further illustrated in Figure 2.

Comment by dmbarton2: Final conclusions

The results of this study indicate arm span measurement can be used as a substitute for height in normal subjects with caution and that male arm span is significantly greater than female arm span. Comment by dmbarton2: Limitations of the study

Limitations of this study include the small sample size, narrow range of arm spans and height, and the fact that all subjects were healthy and had no observable spinal curvature. Caution must be exercised in generalizing these results to populations other than described above.

Comment by Barton, David M: At least one reference required.

Use of anthropometric measures to assess weight loss;George A. Bray,4 M.D., Frank L. Greenway,5 M.D., Mark E. Molitch,6 M.D., William T. Dahms,7 M.D., Richard L. Atkinson,8 M.D., and Kare

The use of arm span as a predictor of height: A study of South Indian Women *SP Mohanty, S Suresh Babu and N Sreekumaran Nair* *Kasturba Medical College and Hospital, Manipal, Karnataka, India*