This double counting is eliminated in the next row (labeled ties counts).
two values are tied) there is some double counting. The only problem is that when the ties count in bigger than 1 (i.e. Cells in this row (labeled preliminary ties counts) that are not zero correspond to time series values that are tied. To create the values in this range, first insert formula =COUNTIF(E3:$O3,D3) in cell D17 and then highlight range D17:N17 and press Ctrl-R. This is calculated based on the values shown in range D17:N19. Note that the ties correction used in the formula in cell R8 is based on the value in cell P19. Actually, if we had conducted a one-sided test we would reject the null hypothesis that there is either no trend or an upward trend, and conclude that there is a downward trend (the p-value for this test is half of the value shown in cell R10). The analysis shown in Figure 2 confirms that there is significant evidence for the claim that the data has a trend based on a two-sided test. This is consistent with the line chart of the time series data shown in Figure 3. Note that S = -44 (cell R7), which indicates the potential for a downward trend. In fact, the MK Test, based on this table is shown in Figure 2. S is now the sum of the elements in this table. Note that if S > 0 then later observations in the time series tend to be larger than those that appear earlier in the time series, while the reverse is true if S COLUMN(D4)-COLUMN($D4),SIGN($C4-D$3),””) , x n, the MK Test uses the following statistic: The null hypothesis for this test is that there is no trend, and the alternative hypothesis is that there is a trend in the two-sided test or that there is an upward trend (or downward trend) in the one-sided test. It does require that there is no autocorrelation. It does not require that the data be normally distributed or linear. The Mann-Kendall Test is used to determine whether a time series has a monotonic upward or downward trend.
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