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The practical implications of using z-scores: Concern's experience in Angola

by Beth Matthews, Maureen Billiet (Concern field staff Angola) Annalies Borrell (Concern chief nutritionist Dublin).

In children the three most commonly used anthropometric indices are weight for height, height for age and weight for age. These indices can be used to assess wasting, stunting and underweight respectively. For the purpose of this paper we are discussing wasting (weight / height), and where the term malnutrition is used it refers to this index.

When a child's "weight for height" is assessed, the child's weight is being compared to a reference weight for a child of the same height. The reference weights for each height are known as the NCHS/WHO reference values and are derived from the combination of two distinct data sets, which cover two age groups:

The reference values are used to assess or compare individual or population nutritional status. These reference values replaced the Harvard and Tanner standards and the recommendations to use the NCHS population, made by Waterlow et al (1977), were recognised and endorsed by WHO in 1983.

Though NCHS/WHO reference values are currently deemed the most appropriate for assessing the nutritional status of infants and young children, it is also recognised that they are not ideal. The WHO expert committee has recently recommended the development of a new reference conceming weight and height of infants and children.

The three methods by which a child or group of children is compared to the reference are known respectively as 'percentage of the median', 'percentiles' and 'z-scores' and are explained as follows:
  • percentage of median: the ratio of a child's weight to the median weight of a child of the same height in the reference data, expressed as a percentage, e.g., if the median weight of the reference data for a particular height is I Okgs then to say that a child is 80% weight for height means that the child is 8kgs
  • percentiles: the position of an individuals weight of a particular height in the reference values in terms of the percentage of values ex ceeded or equalled, e.g., if 10% of the refer ence population weigh less than the child being considered, then the child is in the 10th per centile.
  • z-scores: by describing how far in (units called standard deviations) a child's weight is from the median weight of a child at the same height in the reference data.

While 'percentage of median' is the most commonly used index for selection criteria for feeding programmes it has not been deemed an appropriate index for use with the NCHS/WHO reference values. It has the advantage of being easy to use and, more influential perhaps, of being easy to understand. But this ease of use is paid for in loss of accuracy. The method cannot take into account the fact that the variation in weight found in normal children at one height will be different to the variation found at a different height.

Percentiles are considered appropriate descriptors for malnutrition, using the NCHS/WHO reference values, but do not distinguish well between children who are in the 3rd percentile. It is difficult therefore to classify further these children into moderately and severely malnourished. Z-scores and percentage of the median can be used to further distinguish between severely and moderately malnourished.

Z-scores use an application of statistical theory to describe how far a child's weight is from the average (the median for the NCHS/WHO values) weight of a child of the same height in the reference data. This "distance" is called a z-score. It is expressed in multiples of the standard deviation and is derived as follows:

weight-for-height z-score = observed weight - median weight
standard deviation

where both the median weight and the standard deviation (how the different values are distributed about the mean) are those taken from the normalised growth curves derived from the NCHS /WHO reference values for the given height.

The z-score is a more sensitive descriptor than either percentiles' or 'percentage of the median'. The use of z scores has the advantage that it recognises that the spread of(or variation in) weights at one height may be different than that at a different height. Since the percentage of median' does not do this, its use may mean that children who are actually malnourished are not identified.

The table below illustrates how, as a child grows taller (older), s/he will be more likely tobe classified as malnourished by the use of z-score than by the use of percentage of the median.

Classifications of boy's weights (kgs) at different heights using percentage of median and z-scores:
height   -2   -1.5   -1
  80% z-score 85% z-score 90% z-score
65cm 5.7 5.7 6.0 6.0 6.3 6.4
115cm 16.4 16.9 17.3 17.8 18.1 18.6

For example a boy of 115 cms and 16.Skgs would not be admitted to supplementary feeding using percentage of median whereas using - 2 z-scores he would be selected.

Z-scores are useful in practice because they can:

Although there is substantial recognition that the z score is the most appropriate descriptor of malnutrition, health and nutrition facilities have been, in practice, reluctant to adopt its use as a means for individual assessment.

In programme use the practical requirements that a descriptor should fulfil are several. The descriptor should ensure the correct identification of malnourished children. It should allow estimation of absolute numbers of malnourished children through nutrition surveys. This would then lead to informed estimation of programme size and eventual programme coverage. Finally, the use of a particular descriptor should provide information on the relative seriousness of the nutritional situation, thus helping to identify the most appropriate type of intervention needed.

The use of z-scores in nutrition surveys

Concern, like many intemational agencies, analyses and reports nutrition survey results using z-scores. A comparison of the reported prevalence of malnutrition according to z-scores and 'percentage of the median' show that the two descriptors provide quite different results. See figure 1 below.

Figure 1

Figure 1: Comparison of prevalence of wasting as defined by z-score and percentage of median (Malange, Angola; 1995-96)
The difference in results has a significant impact in terms of programme planning and estimating food needs. In Malange (Angola), based on a population of 190,000 with a 17% under five population, the estimated programme sizes are described in the following table.

  Numbers based on z-scores Numbers based on percentage of the median
April '95 905 550
Oct '95 585 450
April '96 2620 1455
July '96 1230 875
Nov. '96 810 450

On average the use of the z-score selected an undemourished group which was 1.6 times greater than that selected by the use of the '80% of the median' method (range: 1.3 - 1.8). Similar differences were obtained from nutrition surveys carried out in other locations in Angola and in Sierra Leone.


Survey results with % of median: z-score ratios
    May '96 (ratio) Nov. 96' (ratio)
<-2 Z-score 9.0%   7.6%  
<80% of median 5.7% (1.6) 4.5% (1.7)
<-2 Z-score 9.6%   6.0%  
<80% of median 7.2% (1.4) 3.6% (1.6)
Kuito <-2 Z-score 5.1%   -  
<80% of median 2.7% (1.8) -  


Again, the use of z-scores selected a group which was between 1.4 and 1.8 times greater then that selected by the use of the 'percentage of the median' method.

The difference in the results obtained from z-scores and percentage of the median may become larger when proportionally more older stunted children are included in the survey; for example, when the selection criteria for measurement is 'less than 110cm' as opposed to 'less than 5 years' and the former includes more older stunted children.

Z-scores as selection criteria

Z-scores were introduced as admission criteria in May and June 1996 in five Concem nutrition centres in the provinces of Huambo and Bie in Angola. The programmes were all dry supplementary feeding programmes.

The rationale for implementing z-scores was:

The impact of using z-scores to define admission criteria was evaluated through monitoring standard nutrition centre performance indicators like the number of admissions, length of stay etc. The study did not aim to evaluate differences in risk of mortality, illness or child development between the two indicators as there was no follow-up of children following discharge.

Figure 2

Comparison of numbers eligible for admission using z-score and percentage of the median (Kuito, Angola: June - Dec. 1996)

Figure 3

Comparison of numbers eligible for admission using z-score and percentage of the median (Huambo, Angola: June - Dec. 1996)
The impact on length of stay was evaluated following the introduction of z-scores. The criteria for discharge was set at - 1 z-score (approximately equivalent to 90% of the median) since no z-score cards with a calculated weight for -1.5 z-score (approximately 85% of the median) were available at the time of implementation. Average length of stay increased considerably in Kuito province but remained almost unchanged in Huambo province. These results are described in the table below. The average daily weight gain decreased correspondingly.

Comparison of length of stay (in days) using percentage of median and z-score cut-offs
  January-June (% of the median) July-December (Z-Scores)
Kuito 67 91
Huambo 56 60

Since the use of z-scores was a new concept, co ordination difficulties periodically arose between Concern and other agencies over issues arising from its use.

WFP co-operated with Concern during the initial period that z-scores were implemented and provided the necessary additional increase in food requirements. However, problems arose during food shortages later on during the year since numbers of children registered in the programme remained unusually high. The concept of z-scores was difficult for WFP field level food-monitors and staff at headquarters in Luanda.

At field level, staff experienced difficulties during the referral procedure to therapeutic centre with those children falling below -3 z-scores but not less than 70% weight-for-height. These children remained in the Concern supplementary feeding programme.

The implementation of z-scores was supported by the nutrition department at the Ministry of Health and also by UNICEF and WHO. However, MoH nurses at field level had difficulties with understanding z-scores.

Using z-scores... what are the practical implications?

Z-score tables

The availability of z-score tables is essential for enabling staff to use the index in the field. Z-score cards are available and the methodology for using these cards is similar to that of the percentage median.

The calculation of individual z-scores

Sometimes rather than saying a child is between -2 and -3 z-scores we may wish to calculate the exact z-score value. This calculation involves three figures (see formula above); an observed weight, an expected weight and an associated standard deviation. In the calculation of z-scores based on the NCHS/WHO reference values there are two relevant standard deviations, a lower standard deviation which is used in the calculation of z-scores for children less than the median weight at a specific height and an upper standard deviation used to calculate z-scores for children greater than the median weight at a given height. It follows, that for selection purposes to feeding centres only the lower standard deviation is necessary. However, in situations where all children (those greater and less then the median weight at particular heights) require classification e.g. in the analysis of nutrition surveys, both lower and upper standard deviations should be provided for each height. Generally, field staff can learn the mechanical calculation but experience difficulties with the concept of z-scores.

Measurement of Child Progress

Nutritional deterioration and improvement of individuals can be monitored using z-scores as long as the median and the standard deviation for a given height are known. In circumstances where this is difficult alternative means for monitoring progress can be used, for example expected weight for a 5kg boy. This would be 15g/kg/day i.e. a total of 15g x 5kg x 7days = 525 grams per week.

Discharge criteria

The admission criteria are similar to those used in defining moderate and severe malnutrition in nutrition surveys (<-3 z-score for severe malnutrition etc.). The discharge criteria from therapeutic feeding programmes is >-2 z-score and from supplementary feeding programmes would normally be > - 1.5 z score. Staff who have been used to working with percentage of median' cut-offs may consider discharge too early at -1.5 z-score since this is almost equivalent to less than 85% for younger children. However, discharge at - 1 z-score may be considered inappropriate as it may prolong the length of stay in the nutrition programme. Using z-scores, selective feeding programmes will tend to include proportionally more older (stunted) children, therefore targeting those who are suffering acute or chronic malnutrition.

Compatibility between Surveys and Feeding programmes

Children can be referred during nutrition surveys since z-scores can be calculated by hand using a pocket calculator and z-score tables during the nutrition surveys. Coverage of the target group, as identified by the survey assessment, is more feasible since there is compatibility between surveys and programrnes.

Appropriate technology

Accurate results from nutrition surveys can be obtained from analysis by field staff without computers provided that the lower and upper standard deviations are given and calculations are sex-specific.

Programme assessment

The indicators for assessing the effectiveness of a nutrition centre, as established by MSF and other NGOs and based on 'percentage of the median' may be inappropriate for programmes using z-scores. Target weight gains and length of stay may be inappropriate, particularly where discharge is at -1 z-score.


Teaching z-scores is undoubtedly challenging. There is a need to address imaginative and interesting ways to teach z-scores using graphs, colours and scales.

Resource implications

A change in criteria to z-scores may have significant implications for food requirements for supplementary feeding programmes. Predicted estimates for food requirements based on survey findings may be one and a half times previous estimates. Furthermore, the actual food consumption could be more than double if length of stay increases (x 1.5) and the number of admissions increases (x 1.5). In many circumstances where food resources are limited, it may be necessary to alter the criteria for selection accordingly i.e. from -2 z-scoreto -1.8 or-l.5 etc.


Questions and Challenges

Show footnotes

1Gorstein J, Sullivan K, Yip R, de Onis Metal. Issues in assessment of nutritional status using anthropometry. Bulletin of the World Health Organisation 1994, 72:273 - 283
2de Onis M Habicht JP. Anthropometric reference data for international use. recommendations from a World Health Organisation expert Committee. Am. Journal of din. Nutrition. 1996, 64:650-658.
3WHO Technical Report No. 854. Physical Status. The use and interpretation ofAnthropometry pp.7-9 and pp. 219-224.

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Reference this page

Beth Matthews, Maureen Billiet, Annalies Borrell (1997). The practical implications of using z-scores: Concern's experience in Angola. Field Exchange 1, May 1997. p5.