Testing the Equality of Growth Curves of Independent Populations with Application on Egypt Case

Abstract

Problem statement: Numerous trials have been conducted to compare the body growth curves and hence growth rates relying on smoothing and modeling different growth curves using different parameter values for the same model. This study aimed to construct a test of the equality of two percentile growth curves and of a set of percentile growth curves from two independent populations regardless of the shape of these curves. Currently available tests allow us to make a decision on one group. Making a decision regarding the whole curve necessitates building new tests. Approach: This study developed two tests of the equality of two growth curves based on the concept of the precedence and the chi-square tests and a test of the equality of a set of growth curves. The Monte Carlo simulation technique was used to investigate the power of the three tests under a shift in the location parameter and under a shift in the scale parameter of the normal and gamma distributions. The tests were applied to the weight-for-age percentile growth curves of Egyptian regions. Results: The curve precedence test is more powerful than the curve chi-square test in testing the equality of growth curves under a shift in the location parameter of both the normal and gamma distributions. It is also more powerful than the curve chi-square test in testing the equality of growth curves under a shift in the scale parameter of the gamma distribution and in testing equality of growth curves with high ranks under a shift in the scale parameter of the normal distribution. Applying the new tests to the weight-for-age growth curves of the two Egyptian regions showed that the regions have different growth curves. Conclusion: The new tests are powerful in testing the equality of growth curves. According to them, the two Egyptian regions have different nutritional status.