growth index =
= ((measure for child) - (mean measurement for group)) / (standard deviation for measure in group)
If the standard deviation is not known, but the 25th and 75th percentiles are known, then:
standard deviation =
= ((measure for 75th percentile) - (measure for 25th percentile)) / 1.36
where:
• 1.36 is the number of standard deviations between the 25th and 75 percentiles on a normal Gaussian distribution curve.
The growth index can then also be expressed as:
growth index =
= (1.36 * ((measure for child) - (mean measurement for group))) / ((measure for 75th percentile) - (measure for 25th percentile))
Since Z scores are simple linear functions of the original variable measures, the scale properties of the original measures are preserved under the transformation. Because weight, length, and head circumference are ratio level measures, their corresponding growth index (Z scores) can be meaningfully manipulate arithmetically (page 521, Karniski; Stevens).
