Department of Materials Science and Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, Maryland, United States of America.
Johns Hopkins Institute for NanoBiotechnology, Baltimore, Maryland, United States of America.
PLoS One. 2023 Oct 31;18(10):e0289619. doi: 10.1371/journal.pone.0289619. eCollection 2023.
We present a simple, spreadsheet-based method to determine the statistical significance of the difference between any two arbitrary curves. This modified Chi-squared method addresses two scenarios: A single measurement at each point with known standard deviation, or multiple measurements at each point averaged to produce a mean and standard error. The method includes an essential correction for the deviation from normality in measurements with small sample size, which are typical in biomedical sciences. Statistical significance is determined without regard to the functionality of the curves, or the signs of the differences. Numerical simulations are used to validate the procedure. Example experimental data are used to demonstrate its application. An Excel spreadsheet is provided for performing the calculations for either scenario.
我们提出了一种简单的基于电子表格的方法，用于确定任意两条曲线之间差异的统计学显著性。这种改进的卡方检验方法适用于两种情况：在每个点处具有已知标准差的单个测量，或者在每个点处进行多次测量，然后取平均值以产生平均值和标准误差。该方法包括对小样本量测量中偏离正态性的重要修正，这在生物医学科学中很常见。统计显著性的确定不考虑曲线的功能或差异的符号。使用数值模拟验证了该程序。使用实验数据示例演示了其应用。提供了一个 Excel 电子表格，用于执行两种情况的计算。
