Recent techniques for fault localization statistically analyze coverage information of a set of test runs to measure the correlations between program entities and program failures. However, coverage information cannot identify those program entities whose execution affects the output, which weakens the aforementioned correlations. Thus, this paper proposes a novel statistical fault localization approach to address this problem. Our statistical approach utilizes program slices of a set of test runs to capture the influence of a program entity's execution on the output, and uses statistical analysis to measure the suspiciousness of program entities to be faulty. In addition, this paper presents a new slicing approach called approximate dynamic backward slice to balance the size and accuracy of a slice, and applies this slice to our statistical approach. The experimental results on two standard benchmarks show that our statistical approach significantly outperforms eight representative fault localization techniques.