# Converting WHO reference median to z-scores

This question was posted the Assessment and Surveillance forum area and has 5 replies.

### Bindi Borg

University of Sydney

Normal user

3 Apr 2019, 13:01

I sometimes see exclusion criteria in papers expressed as weight for length (WFL) < 75% or <80% of WHO reference median. I can't figure out how to convert this to z-scores, so can't figure out what subjects the paper is studying.

Apologies if this is an old question - I see some discussion on this some years back, but I haven't managed to find an answer.

Many thanks.

### Tamsin Walters

en-net moderator

Forum moderator

11 Apr 2019, 16:51

Dear Bindi,

We had a similar discussion previously on how to convert percentile estimates to WHO GS z-score, with the conclusion that it is probably not mathematically possible:

https://www.en-net.org/question/2888.aspx

If you are able to access the raw data, then the z-scores can be calculated.

Best wishes,

Tamsin

### Tamsin Walters

en-net moderator

Forum moderator

12 Apr 2019, 17:20

Hi Bindi,

Percentage of the median does not correspond precisely with z-scores as they are calculated differently. See these explanations from LSHTM: http://conflict.lshtm.ac.uk/page_123.htm.

However, in the past, percentage of the median was often used with the cut-offs you mention to admit children aged 6-59 months into acute malnutrition management programmes.

This article might be useful to understand the discrepancy between the measures and how they were used historically: https://www.ennonline.net/fex/1/practical

I hope this helps you a little in interpreting the papers you are reading.

Best wishes,

Tamsin

### Jay Berkley

Professor of Paediatric Infectious Diseases

Frequent user

13 Apr 2019, 17:44

Hi Bindi

How does percentage of median weight relate to weight-for scores?

There is not a direct translation between percentage of median and Z-scores, but we can use the LMS values given in the WHO tables for WFH to calculate the Z-score for individual length/height and weight measurement. For example, using the WHO WFH table for girls at https://www.who.int/childgrowth/standards/wfh_girls_2_5_zscores.txt we see that the median weight for a girl of height 79cm is 10.0Kg. Eighty percent of 10Kg is 8.0Kg, which is between -3 and -2 Z-scores:

Height L M S SD3neg SD2neg SD1neg SD0 SD1 SD2 SD3 75 -0.3833 9.2786 0.08996 7.2 7.8 8.5 9.3 10.2 11.2 12.3 75.5 -0.3833 9.3703 0.08989 7.2 7.9 8.6 9.4 10.3 11.3 12.5 76 -0.3833 9.4617 0.08983 7.3 8.0 8.7 9.5 10.4 11.4 12.6 76.5 -0.3833 9.5533 0.08976 7.4 8.0 8.7 9.6 10.5 11.5 12.7 77 -0.3833 9.6456 0.08969 7.5 8.1 8.8 9.6 10.6 11.6 12.8 77.5 -0.3833 9.7390 0.08963 7.5 8.2 8.9 9.7 10.7 11.7 12.9 78 -0.3833 9.8338 0.08956 7.6 8.3 9.0 9.8 10.8 11.8 13.1 78.5 -0.3833 9.9303 0.08950 7.7 8.4 9.1 9.9 10.9 12.0 13.2 79 -0.3833 10.0289 0.08943 7.8 8.4 9.2 10.0 11.0 12.1 13.3

We can use the standard formula to calculate the exact Z-score from a weight that is 80% of the median weight for a girl who is 79cm tall:

Z = (((WEIGHT/M) ^ L) -1) / (L*S)

Z = (((8/10) ^ -0.3833) -1) / (-0.3833*0.08943) = -2.60 Z-scores.

For 80% of median weight, the first term in the equation (Weight/M) will always be 0.8. But the L and S values are different for different heights. This means that at other values for height, a girl with a weight that is 80% of the median weight will have a different Z score.

I plotted Z score values for 80%, 75% and 70% of median weight for girls covered by this table, 2 to 5 years old across heights between 65cm and 120cm. For these girls, 80% of median weight varies around -2.6 to -2.4Z; 75% of median weight varies around -3.4 to -3.1Z; and 70% of median weight varies around -4.3 to -3.9Z.

Hope that's of some help.

All the best

Jay

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