Analyzing Deficient Response Summaries from Designed Experiments

All too often statisticians do not have access to raw experimental data. These scenarios require additional methodology to properly account for the missing information. In this article, we demonstrate a technique for analyzing averages of lifetime data collected at various experimental conditions that provides inference for factor effects. To handle these summaries, we use some numerical techniques to calculate the probability density function of the average of n independent and identically distributed lognormal random variables. We illustrate our method with an example from the literature and provide some R code that implements a Bayesian analysis. We also provide recommendations for more informative summary statistics than lifetime averages for lognormal data.