The presence of bias in today's information retrieval (IR) systems has raised concerns on the social responsibilities of IR. Fairness has become an increasingly important factor when building systems for information searching and content recommendations. We investigated the top-k fairness ranking problem on search engines and proposed several topical diversity fairness ranking strategies to study the relationship between relevance and fairness in search results. Our experimental results show that different strategies perform differently with distinct datasets and under different utility metrics. To further investigate the relationship of data and fairness algorithms, we proposed a statistical framework that offered a novel perspective into the fairness optimization problem. Through a series of use cases, we demonstrated how our framework could be applied to associate optimization policies with data and provide insights to the multi-party fairness optimization. Our goal is to develop a general framework that is able to facilitate various analysis and decision making for addressing fairness in IR.