Scripps Pier: 



BB A B AAA B AAA BB A B AA B AAAAA BBB A BBBBBB A BB AAA 

 B (19 runs) 



Langara Island: 



AAAA BB A BBBBB A BBB AAAA (7 runs) 

 Triple Island: 



AAA B AA BBBBBB A BBB AAAA (7 runs) 

 Cape St. James: 



AA BB AAAA BBBBBB A BB AAA (7 runs) 



If the ^o's are randomly distributed with respect to time, a fairly large 

 number of runs is expected. If a trend exists in a sequence of ^o's, only a few 

 runs are expected. The theoretical distribution and the critical values of the 

 number of runs can be determined. « The critical number of runs at the 5 percent 

 probability level for the 40 observations at Scripps Pier is 15, the null hypothesis 

 of no trend being rejected if there are 15 or fewer. Since the observed number of 

 runs is 19, the null hypothesis is not rejected, and it is concluded that no long- 

 term trend exists in the /So's for the 40 years of data for Scripps Pier. 



Langara Island, Triple Island, and Cape St. James each have 7 runs in 20 

 observations, the median /3o being omitted for Triple Island. The probability of 7 

 or fewer runs arising by chance in 20 observations is 0.051, so the 7 runs are not 

 quite significant at the 5 percent level. It is concluded that no trend exists in 

 the records for any of the three locations. 



It should be pointed out that once a time series of 20 to 40 years in 

 length is selected for analysis, runs as long as 5 or 6 years, among those ob- 

 served, are reasonable and expected. For example, a slightly different test of 

 hypothesis using runs is based on the length of the longest run." For the longest 

 run to be significant at the 5 percent level, it must be at least length 7 in 20 

 observations or length 9 in 40 observations. The longest runs obtained in this 

 analysis are of length 6, and are not significant for either series length. 



An alternate test for randomness is the autocorrelation coefficient with 

 lag 1, or more simply the statistic 



N 



=1 



If a set of observations is ordered with respect to time, and if time is irrelevant, 

 no correlation would be expected to exist between successive pairs of values of 



24 



