Runs Test: Large Sample Size Given that we have a time series with observations and > 20, define the number of runs, R, as the number of sequences above or below the median We want to test the null hypothesis He: the series is random The distribution of the number of runs under the null hypothesis can be approximated by a normal distribution. It can be shown that under the null hypothesis (14321 has a standard normal distribution. This result provides a test for randomness. The following tests have significance level a. 1. If the alternative hypothesis is positive association between adjacent ob- servations, the decision rule is as follows: roject, 114.331 4-1) 2. If the alternative is a two-sided hypothesis of nonrandomness, the deci- sion rule is as follows: Text Hz > 114.341 Hur 18 Analysis of Categorical Data u36 Example 14.17 Analysis of Sales Data (Runs Test: Large Sample Size) You have been asked to determine if 30 weeks of sales follow a random pattern from one observation to the next in a time series. The data are stored in the data file Weekly Sales