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A relatively large negative number of -19 is shown in the <br />example; therefore, a downward trend is likely. <br />Tau = Kendall's Rank Correlation <br />Tau, which is based on the Mann -Kendall statistic (S), is a <br />measure of correlation. When tau = 0, the x and y vari- <br />ables are considered independent of one another. The <br />closer tau is to —1 or 1, the stronger the correlation is. If <br />tau > 0, then x and y are positively associated. Here, tau <br />is < 0; thus, x and y are negatively associated. In other <br />words, concentrations of 1,1-dichloroethane decrease as <br />time increases. <br />Z = The test statistic Z, which takes into account the variance <br />of the Mann -Kendall statistic (S), is used in the normal <br />approximation test when N is greater than 40. It may also <br />be used for N as small as 10, unless there are many tied <br />data values. If the null hypothesis of no trend is true, the <br />test statistic Z is considered to have a standard normal <br />distribution. <br />To test for either an upward or downward trend (a two - <br />tailed test), an alpha (a) level of significance must first be <br />chosen. In this case, a was chosen at 0.05, which is the <br />probability of rejecting Ho of no trend when it is actually <br />true (Type I error). The split probability of a Type I error <br />for a two -tailed test is 0.025 or a/2. The Z value associ- <br />ated with 0.025 is 1.96, as shown on Table A.1 of Non- <br />parametric Statistical Methods. With an a of 0.05, <br />95 percent (1 - a, called the confidence level) of the area <br />under the normal curve lies between -Za = -1.96 and <br />Za = 1.96. <br />A positive (negative) value of Z can indicate an upward <br />(downward) trend. With an a -value of 0.05, any Z value <br />above 1.96 signifies an upward trend, and any value <br />below -1.96 signifies a downward trend. In such cases, H <br />of no trend would be rejected. For values which J, <br />between -1.96 and 1.96, it cannot be determined with sta- <br />tistical significance that a trend exists; if the null hypothe- <br />sis of no trend is true, the test statistic Z is considered to <br />have a standard normal distribution. <br />In this example, Z = -2.048 (corrected for ties), which is <br />less than -1.96. Therefore, a downward trend of <br />1,1-dichloroethane is occurring in MW -3A at a 95 percent <br />confidence level. <br />pjb\b02\bO20104j A - 3 Rev. 0 September 25, 1991 <br />