P-values and laws of large numbers: Practicalinterpretation of significance in very large samples

Research in healthcare settings is often conducted using very large amounts of data.This typically leads to a limitation on the use of standard measures of statistical significance, such as p-values, as the related sampling distributions collapse in very large samples.However, while these probability-based calculations are of limited use, application of the laws of large numbers can be very useful in guiding the interpretation of very-large-sample-based results.In specific settings, this may lead to the continued use of the p-value as a tool for inference.In other very-large-sample settings, comparison of observed estimated population characteristics can be reported on a percent difference basis and can be related directly to practical outcomes such as increases in healthcare access or decreases in healthcare cost.These interpretations should be defined pre-experimentally within the context of each study protocol.