Measurement Toolkit - Percentiles and Z-scores (2024)

Percentiles

In clinical practice, growth percentiles are commonly derived by manual plotting of the child’s growth measurement against their age on a sex-appropriate paper growth chart to visually indicate their approximate percentile position or band (e.g. “between 85^th to 97^th”) (see Figure 1).

Alternatively, percentiles can be more precisely converted from Z-scores (see section below).

Figure 1 WHO Child Growth Standards Weight-for-age: Birth to 5 years percentiles chart for girls.
Source: http://www.who.int/childgrowth/standards/chts_wfa_girls_p/en/

Z-scores

A Z-score is calculated using the formula (assuming a normal distribution):

Measured value – Average value in the reference population

Standard Deviation of the reference population

Average values and standard deviations for various reference populations are available adjusted for age and sex and indicating the appropriate transformation to achieve a normal distribution (see below).

Calculation of Z-scores by hand is laborious. Fortunately, several computer programs are available and data can be entered either one child at a time or using spreadsheets for large numbers of children (e.g. http://www.who.int/childgrowth/software/en/).

It is very important to note the units of measurement required by each of the programs. For example: weight in kg; height/length in cm; age in decimal years, months or days; and sex as M for male and F for female.

Percentiles and Z-scores are easily interchangeable using a table of Z-scores and their associated areas (percentile = the area from infinity to Z) or a calculator.

In Microsoft Excel: To convert Z-scores to percentiles, use the Norm.Dist function with the settings: mean=0; SD=1; cumulative=TRUE.

Which growth reference?

It is important to select the reference population carefully, with consideration of the aim of the assessment or study. For example, older growth reference data might be appropriate if analysing data from an historical study or survey, or to assess secular trends in growth.

Some countries (e.g. UK, USA, and several other European countries) have growth reference data based on their national population (see below). Such growth references are representative of children in those populations. Hence, these percentiles and Z-scores tell you where a measured child lies in relation to that population, but they do not imply that a normal growth value or pattern is healthy.

WHO International Growth Standards and Growth References

The World Health Organisation (WHO) provides international growth standards for children aged 0-5 years and international growth references for children and adolescents aged 5-19 years. While both are intended to be used for children of any nationality, there is an important distinction between standards and references.

1. The WHO Child Growth Standards 0-5 years are based on data from the WHO’s large prospective Multinational Growth Reference Study (MGRS), which followed children growing in optimal environmental and health conditions in six countries. Growth standards describe an optimally healthy growth pattern that steers a middle-ground between undernutrition and overnutrition. They do not necessarily provide a good statistical fit to each country, e.g. in an ‘overnourished’ population the large majority of children may lie above the 50^th percentile for weight and BMI.

1. The WHO Growth Reference for 5-19 years is a reconstruction of 1977 national US growth data. It is intended for use in populations who do not have appropriate national growth data.

Preterm infants

Birth weight and birth length reference data are available for preterm infants born from 24 weeks gestation onwards. For example, the INTERGROWTH-21^stgrowth references.

For assessments of postnatal growth, prematurity needs to be taken into account. Age-adjustment is for children born before 37 weeks gestation. For example, if an infant is born 6 weeks early (at 34 weeks gestation), he/she will have a corrected age of 6 weeks less than his/her actual age since birth (compared to 40 weeks of gestation).

Many growth computer softwares will adjust for gestational age. When manually plotting measurements onto a chart, their measurements should be plotted at their actual age, with a horizontal line drawn back to their corrected age. The adjustment should continue to be made until the child is one year old.

The Preterm Postnatal Growth Standardsare particularly suitable formonitoring postnatal growth in preterm babies after 32 weeks’ postmenstrual age and may be used for the assessment of preterm infants until 64 weeks’ postmenstrual age (6 months “corrected” age), the time at which they overlap, without the need for any curve adjustment, with the WHO Child Growth Standards for term newborns.

Growth categories based on percentiles and Z-scores

To identify individuals with unhealthy growth: the WHO recommends cut-off values of +/- 2 Z-scores, which roughly correspond to the 2^nd and 98^th percentiles (Table 1).

Table 1 WHO classification of growth and nutritional status.

¹ Z-score and percentile equivalence: 3SD=0.1%; 2SD=2.3%; 1SD=15.9%; +1SD=84.1%; +2SD=97.7%; +3SD=99.9%.
Adapted from: http://ebook.ecog-obesity.eu/chapter-growth-charts-body-composition/world-health-organization-reference-curves/

To assess and monitor the prevalence of overweight and obesity in populations:

As shown in Figure 2, the (UK) National Child measurement programme (NCMP) and some other national organisations use the BMI-for-age 85^th and 95^th percentiles cut-offs (equivalent to Z-scores of +1.04 and 1.65, respectively).

Figure 2 Individual and population cut-off values for BMI-for-age percentiles used in the UK.