The time series we studied in the current article is the log-transformed daily returns of the Shenzhen composite index from December 25, 1995 to December 31, 2010. The Shenzhen composite was created with April 3, 1991 as the base of 100. In computing the composite index, all listed companies in the Shenzhen Stock Exchange are weighted by their volume. That is, the composite index =100*total value of the day/total value on April 3, 1991. In this article, we apply several popular nonparametric statistical tools to assess the normality of the log-transformed daily returns and test the day of the week effect. The data set contains 3636 observations from trading days during the study period (http://www.szse.cn/main/marketdata/tjyb_front/). In Section 2, we briefly review the three nonparametric statistical tests of normality we used and report our results from these tests. All three tests rejected the null hypothesis of normality for the log-transformed daily returns. In Section 3, we summarize the results from the Skillings–Mack test [14], which is an extension of the Friedman’s test [15]. Some concluding remarks are given in Section 4. Our results from nonparametric analysis indicated that there existed a negative Thursday effect on the Shenzhen composite index, which was consistent with the results from parametric models based on GARCH in Bai et al. [3]. A good understanding of the behavior of stock markets including the day of the week effect would not only provide investors sound strategy in buying and selling assets, but also enable regulatory agencies in promoting healthy economic activities.