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• Tau = Kendall's Rank Correlation Tau, which is based on the Mann-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 words, 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 refecting Ho 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 196, as shown on Table A 1 of Nonparametric Statistical Methods With an a • of 0.05, 95 percent (1 - (x, called the confidence level) of the area under the normal curve hes between -Z.= -1 96 and Z,= 196 A positive (negative) value of Z can indicate an upward (downward) trend With an a value of 0 05, any Z value above 196 signifies an upward trend, and any value below -196 signifies a downward trend In such cases, Ho of no trend would be rejected. For values which fall between -1 96 and 196, 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 196 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 sAON VJn794\279410001 CS-98\pzusmer6 E moon D-3 Rev 0 7/22/98