Computing the Z Score and Centiles for Cross‐sectional Analysis: A Practical Approach

Although Z scores have been reported in the literature, one of the problems for the nonstatistician is understanding the systematic approach used to compute the predicted mean and standard deviation, components of the Z score equation, which may vary as the independent variable changes over time (eg, gestational age). This review focuses on a step-by-step analysis using linear, quadratic, and fractional polynomials to compute the mean and standard deviation as a function of a continuous independent variable. Once the mean and standard deviation are computed, the Z score and centile can be derived and Z score calculators created that enable investigators to implement the results in the laboratory and/or clinical setting.