This paper presents a method for assessing whether algorithmic decision making induces disparate impact in online retailing. The proposed method specifies a statistical design, a sampling algorithm, and a technological setup for data collection through web crawling. The statistical design reduces the dimensionality of the problem and ensures that the data collected are representative, variation-rich, and suitable for the investigation of the causes behind any observed disparities. Implementations of the method can collect data on algorithmic decisions, such as price, recommendations, and delivery fees that can be matched to website visitor demographic data from established sources such as censuses and large scale surveys. The combined data can be used to investigate the presence and causes of disparate impact, potentially helping online retailers audit their algorithms without collecting or holding the demographic data of their users. The proposed method is illustrated in the context of the automated pricing decisions of a leading retailer in the United States. A custom-built platform implemented the method to collect data for nearly 20,000 different grocery products at more than 3,000 randomly-selected zip codes. The data collected indicates that prices are higher for locations with high proportions of minority households. Although these price disparities can be partly attributed to algorithmic biases, they are mainly explained by local factors and therefore can be regarded as business necessities.