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Calculation of anthropometric Z-scores

Worked example

The table below gives some hypothetical data on age, height and weight of five boys between 2 and 5 years old.

Anthropometric data for 5 boys
Name Age (months) Height (cm) Weight (kg)
Saddam
Idi
George
Tony
Abu
24
28
32
51
58
83
85
85
90
104
10.1
12.3
9.6
16.7
18.3

If you have the WHO Anthro package you can use their anthropometric calculator to calculate Z-scores (and percentiles assuming a normal distribution) with the new WHO reference values. The figure below shows the output of this package for the data on Saddam - the mid-upper arm circumference input in this case was 14 cm.

anthro.gif

Epinut.gif

If you have the EpiInfo package, this gives Z-scores based on the old NCHS/WHO reference values. Note the results are rather different. The new reference values give Saddam a weight-for-height Z-value of − 1.28, whilst the old values give him a Z-value of − 0.91. These differences have caused some consternation amongst aid workers directly involved in assessing malnutrition (see references below), but should perhaps just serve as a warning that all such approaches have a large margin of error!

Results for weight for height, height for age, and weight for age for all five boys using the old NCHS/WHO reference values are given below:

Anthropometric data and Z-scores
Name Z-scores
Weight-for-height Height-for-age Weight-for-age
Saddam
Idi
George
Tony
Abu
− 1.48
+ 0.12
− 2.32
+ 2.35
+ 0.91
− 0.81
− 1.13
− 1.92
− 3.40
− 1.06
− 1.99
− 0.64
− 2.94
− 0.25
− 0.02

Remember the two key scores to look at are weight for height (for wasting) and height for age (for stunting). Weight for age shows the combined effects of these two processes. Clearly George is suffering from wasting, and Tony from stunting. Saddam is borderline for malnutrition when you consider the combined effects of stunting and wasting.

 

 

Comparison of distributions

Length and weight of sharks
Length (mm) Z-score Weight(g) Z-score
165
181
192
222
211
215
217
221
232
233
238
242
245
252
257
262
264
269
284
301
− 2.073
− 1.600
− 1.275
− 0.389
− 0.714
− 0.595
− 0.536
− 0.418
− 0.093
− 0.064
0.084
0.202
0.291
0.498
0.646
0.793
0.853
1.000
1.444
1.946
15
21
23
24
27
30
31
32
33
35
37
39
46
49
50
58
59
67
72
82
− 1.460
− 1.133
− 1.024
− 0.969
− 0.806
− 0.643
− 0.588
− 0.534
− 0.479
− 0.370
− 0.261
− 0.153
0.229
0.392
0.447
0.882
0.937
1.373
1.645
2.190

Worked example

The table below gives some data based (very loosely) on measurements done by Van Der Molen & Caille (2001) on the length and weight of juvenile smoothhound sharks.

The lengths were standardized by subtracting the sample mean (235.15 mm) and dividing by the sample standard deviation (33.84 mm). The weights were standardized by subtracting the sample mean (41.8 g) and dividing by the sample standard deviation (18.36 g).

Frequency polygons of the two distributions, each with a mean of 0 and a standard deviation of 1, are shown below. Whilst length approximates to a normal distribution, weight is right skewed.

{Fig. 1}
U05zscr2.gif

Note: standardizing measurements does not affect the shape of their frequency distribution; it simply puts them all on a common scale.

 

 

Standardization to remove effect of factor

Worked example

Growth rate of five rodents
in relation to their dominance rank
RankMonth
1234
Raw
data
Z-
score
Raw
data
Z-
score
Raw
data
Z-
score
Raw
data
Z-
score
1
2
3
4
5
Mean
SD
10
5
3
2
1
4.2
3.6
+ 1.61
+ 0.22
− 0.33
− 0.61
− 0.90
 
 
60
35
25
22
25
33.4
15.7
+ 1.69
+ 0.10
− 0.54
− 0.73
− 0.54
 
 
70
60
42
45
31
49.6
15.4
+ 1.33
+ 0.68
− 0.49
− 0.30
− 1.21
 
 
 8 
4
4
3
1
4.0
2.6
+ 1.54
   0.00
   0.00
− 0.39
− 1.15
 
 

The table gives some hypothetical data on the growth of rodents. The dominance hierarchy amongst five males was first established and then the growth rate recorded each month over 5 months. Because food availability varied from month to month, mean growth rate also varied considerably. Hence the measurements for each male in each month were standardized using the mean and standard deviation for that month.

Unstandardized and standardized growth rates ( SD) in relation to dominance rank are show below:

{Fig. 2}
U05zscr1.gif

Note that the standard deviations (relative to the mean values) are now much smaller, since the seasonal variation has been removed. The results from each month are now also weighted equally, rather than the results for month 2 and 3 having greater weight because of the higher growth rate.