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Converting WHO reference median to z-scores

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

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Anonymous 24

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

Anonymous 24

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 Parediatric 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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