v15 Runs Test: Small Sample Size First we consider a time series of n observations with n = 20. We denote observations above the median with + signs and observations below the median with - signs. These signs are used to define the sequence of observations in the series. Runs Test: Small Sample Size Let R denote the number of runs in the sequence of n observations with n 20. The null hypothesis is that the series is a set of random variables. Appendix Table 14 gives the smallest significance level at which this null hypothesis can be rejected against the alternative of positive association between adjacent observations, as a function of R and n. If the alternative is the two-sided hypothesis on nonrandomness, the signifi- cance level must be doubled if it is less than 0.5. Alternatively, if the significance level read from the table is greater than 0.5, the appropriate significance level for the test against the two-sided alternative is 2(1 - a). Example 14.16 illustrates a time series with n = 16 daily observations on an index of the volume of shares traded on the New York Stock Exchange. If this series were random, then the volume traded on one day would be independent of the volume traded on any other day. In particular, a high-volume day would be no more likely to be followed by another high-volume day than would any other day. Example 14.16 New York Stock Exchange (Runs Test: Small Sample Size) A series of 16 daily observations on an index of the volume of shares traded on the New York Stock Exchange is shown in Table 14.20. Test the null hypothesis of random- ness. Data are stored in the data file Shares Traded