the sequence. A nonparametric test has been devised to test the hypothesis of 

 zero autocorrelation.'" The random variable IV is approximately normally distri- 

 buted with mean 



S,^ - S, 



and variance 



S,' - S, S/ - 4S,^ S, + AS, S3 + S,^ - 2S, 



Ow = 



"' ~ N-1 (N-1) (N-2) 



-M, 



where 





The X's are the sequence of /3o's. For Scripps Pier, N = 40, and 

 X4, = X,. Calculations yield IV = 149.184, M„,. = 145.850, and ctj^ = 2.25, so that 

 t = {^ -M^^) /a^fj = 1.48. For / a standard normal variable, the 5 percent critical 

 value is 1.64, since the alternative hypothesis is \'^>M^. Since 1.48<1.64, the 

 null hypothesis IV = M\f/ is not rejected, and again it is concluded that no trend 

 exists in the sequence of /3o's. 



Since no trend was detected in the Scripps Pier data, it is of interest to 

 go one step further into the question of randomness and examine the empirical 

 distribution of certain statistics obtained from the analysis of the 40 individual 

 years. Figure 7A is a histogram of the same set of /So's that were tested for 

 trend. The normal curve with the sample mean of 16.912 and sample standard 

 deviation of 0.613 is also shown in the figure. Even though the histogram is 

 skewed, a chi-square, goodness-of-fit test leads to an acceptance of normality 

 at the 5 percent probability level. 



The purpose of this study is not one of making goodness-of-fit tests, 

 and no further use is made of this technique. Rather it is included to point out 

 that, on the basis of tests for trend and the histogi'am above, quantities such as 

 j8o used to characterize sea-surface temperatures for an entire year behave 

 exactly as one expects independent random variables to behave. This is not to 

 deny the existence of real year-to-year differences in the ocean, but rather to 

 emphasize that these differences are not unexpected to an oceanometrician. 



As a test for year-to-year differences in the /So's, table 7 displays an 



25 



