Sample Data Time 1 2 3 4 Data 10 17 13 19 Slope Est = ½(1.5+3) = 2.25 The confidence interval of the slope is calculated from the same array of ordered slopes Qi using indexes M1 and M2. where and Using tabulated Z values for cumulative normal distribution, the 99% and 95% confidence intervals are calculated using and , respectively. Seasonal Analysis For seasonal (monthly) analysis, the data are divided by season and ordered by year within each season. The trend test is first done on the individual seasons. For data points in the season ni ith there are data pairs, where = These data pairs are identified as increasing, Ni Ni ni(ni-1)/2. Ni decreasing, or unchanging over time. The Mann-Kendall statistic for the season, is just the Si, number of increasing pairs minus the number of decreasing pairs. is calculated for each season. The individual season values are then summed across the seasons. K The test statistic is calculated from Z VAR(S’) This value is compared to a probability table to test for either upward or downward trend (a Z two-tailed test) just as in the annual analysis. The trend is significant at the if the absolute α-level value of the calculated is greater than found in the table. Z Z1-α/2
Sample Data Time Data 1 10 2 17 3 13 4 19 Slope Est = ½(1.5+3) = 2.25 The confidence interval of the slope is calculated from the same array of ordered slopes Qi using indexes M1 and M2. where and Using tabulated Z values for cumulative normal distribution, the 99% and 95% confidence intervals are calculated using and , respectively. Seasonal Analysis For seasonal (monthly) analysis, the data are divided by season and ordered by year within each season. The trend test is first done on the individual seasons. For ni data points in the ith season there are Ni data pairs, where Ni = ni(ni-1)/2. These Ni data pairs are identified as increasing, decreasing, or unchanging over time. The Mann-Kendall statistic for the season, Si, is just the number of increasing pairs minus the number of decreasing pairs. is calculated for each season. The individual season values are then summed across the K seasons. The test statistic Z is calculated from VAR(S’) This Z value is compared to a probability table to test for either upward or downward trend (a two-tailed test) just as in the annual analysis. The trend is significant at the α-level if the absolute value of the calculated Z is greater than Z1-α/2 found in the table.
TrendAnalysis.docx