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"It has long been an axiom of mine that the little things are infinitely the most important" (Sherlock Holmes)

#### 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) SaddamIdiGeorgeTonyAbu 2428325158 83858590104 10.112.39.616.718.3

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.

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 SaddamIdiGeorgeTonyAbu − 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 165181192222211215217221232233238242245252257262264269284301 − 2.073 − 1.600 − 1.275 − 0.389 − 0.714 − 0.595 − 0.536 − 0.418 − 0.093 − 0.0640.0840.2020.2910.4980.6460.7930.8531.0001.4441.946 1521232427303132333537394649505859677282 − 1.460 − 1.133 − 1.024 − 0.969 − 0.806 − 0.643 − 0.588 − 0.534 − 0.479 − 0.370 − 0.261 − 0.1530.2290.3920.4470.8820.9371.3731.6452.190

#### 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}

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

#### Worked example

 Growth rate of five rodents in relation to their dominance rank Rank Month 1 2 3 4 Raw data Z-score Raw data Z-score Raw data Z-score Raw data Z-score 12345MeanSD 1053214.23.6 + 1.61+ 0.22 − 0.33 − 0.61 − 0.90 603525222533.415.7 + 1.69+ 0.10 − 0.54 − 0.73 − 0.54 706042453149.615.4 + 1.33+ 0.68 − 0.49 − 0.30 − 1.21 8 44314.02.6 + 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}

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.