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Tau, which is based on theMann-Kendall statistic (S), is a measure of correlation. When tau = 0, the x and y variables are considered independent of one another. The closer tau is to -1 or 1, the stronger the correlation is. If tau < 0, then x and y are negatively associated. Here, tau is > 0; thus, x and y are positively associated. In other v.-ords, concentrations of chloride increase as time increases. Z-Value = The test statistic Z, which takes into account the variance of the Mann-Kendall statistic (S), is used in the normal approximation test when N is greater than 40. It may also be used for N as small as 10. unless there are many tied data values. If the null hypothesis of no trend is true, the test statistic Z is considered to have a standard normal distribution. To test for either an upward or downward trend (a two-tailed test), an alpha (a) level of significance must first be chosen. In this case, a was chosen at 0.05, which is the probability of rejecting He of no trend when it is actually true (Type I error). The split probability of a Type I error for a two-tailed test is 0.025 or a/2. The Z value associated with 0.025 is 1.96, as shown on Table A.1 of Nonparametric Statistical Methods. With an a of 0.05, 95 percent (1 - a, called the confidence level) of the area under the normal curve lies between -Za = -1.96 and Za=1.96. A positive (negative) value of Z can indicate an upward (downward) trend. With an a value of 0.05, any Z value above 1.96 signifies an upward trend, and any value below -1.96 signifies a downward trend. In such cases, Ho of no trend would be rejected. For values which fall between -1.96 and 1.96, it cannot be determined with statistical significance that a trend exists; if the null hypothesis of no trend is true, the test statistic Z is considered to have a standard normal distribution. In this example, Z = 2.439 (corrected for ties), which is greater than 1.96. Therefore, an upward trend of chloride is occurring at a 95 percent confidence level. # ties = A tie occurs when two data points are equivalent to one another. The computer software corrects the tau and Z values for tied groups. Unless there are no tied groups for a particular parameter, the Z values corrected for ties are used to evaluate correlations between time and constituent concentrations. P-Value = Probability that an observed pattern of increases or decreases over time is not a trend. To reject He, the probability corresponding to the Z value(corrected for ties) must be less than the specified a value. The smaller the probability value, SAC/pjM3M390011.8at-94 Ifc:9 C-3 Rev.0,October 28, 1994