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