Change detection in hydrological records—a review of the methodology / Revue méthodologique de la détection de changements dans les chroniques hydrologiques <s> Wilcoxon-Mann-Whitney test/Mann-Whitney test/Mann-test/Rank-sum test <s> 1. Summarizing Data. 1.1. Characteristics of Water Resources Data. 1.2. Measures of Location. 1.3. Measures of Spread. 1.4. Measures of Skewness. 1.5. Other Resistant Measures. 1.6. Outliers. 1.7. Transformations. 2. Graphical Data Analysis. 2.1. Graphical Analysis of Single Data Sets. 2.2. Graphical Comparisons of Two or More Data Sets. 2.3. Scatterplots and Enhancements. 2.4. Graphs for Multivariate Data. 3. Describing Uncertainty. 3.1. Definition of Interval Estimates. 3.2. Interpretation of Interval Estimates. 3.3. Confidence Intervals For The Median. 3.4. Confidence Intervals For The Mean. 3.5. Nonparametric Prediction Intervals. 3.6. Parametric Prediction Intervals. 3.7. Confidence Intervals For Quantiles (Percentiles). 3.8. Other Uses For Confidence Intervals. 4. Hypothesis Tests. 4.1. Classification of Hypothesis Tests. 4.2. Structure of Hypothesis Tests. 4.3. The Rank-Sum Test as an Example of Hypothesis Testing. 4.4. Tests for Normality. 5. Differences Between Two Independent Groups. 5.1. The Rank-Sum Test. 5.2. The t-Test. 5.3. Graphical Presentation of Results. 5.4. Estimating the Magnitude of Differences Between Two Groups. 6. Matched-Pair Tests. 6.1. The Sign Test. 6.2. The Signed-Rank Test. 6.3. The Paired t-Test. 6.4. Consequences of Violating Test Assumptions. 6.5. Graphical Presentation of Results. 6.6. Estimating the Magnitude of Differences Between Two Groups. 7. Comparing Several Independent Groups. 7.1. Tests for Differences Due to One Factor. 7.2. Tests For The Effects of More Than One Factor. 7.3. Blocking - The Extension of Matched-Pair Tests. 7.4. Multiple Comparison Tests. 7.5. Presentation of Results. 8. Correlation. 8.1. Characteristics of Correlation Coefficients. 8.2. Kendall's Tau. 8.3. Spearman's Rho. 8.4. Pearson's r. 9. Simple Linear Regression. 9.1. The Linear Regression Model. 9.2. Computations. 9.3. Building a Good Regression Model. 9.4. Hypothesis Testing in Regression. 9.5. Regression Diagnostics. 9.6. Transformations of the Response (y) Variable. 9.7. Summary Guide to a Good SLR Model. 10. Alternative Methods to Regression. 10.1. Kendall-Theil Robust Line. 10.2. Alternative Parametric Linear Equations. 10.3. Weighted Least Squares. 10.4 Iteratively Weighted Least Squares. 10.5. Smoothing. 11. Multiple Regression. 11.1. Why Use MLR? 11.2. MLR Model. 11.3. Hypothesis Tests for Multiple Regression. 11.4. Confidence Intervals. 11.5. Regression Diagnostics. 11.6. Choosing the Best MLR Model. 11.7. Summary of Model Selection Criteria. 11.8. Analysis of Covariance. 12. Trend Analysis. 12.1. General Structure of Trend Tests. 12.2. Trend Tests With No Exogenous Variable. 12.3. Accounting for Exogenous Variables. 12.4. Dealing With Seasonality. 12.5. Use of Transformations in Trend Studies. 12.6. Monotonic Trend versus Two Sample (Step) Trend. 12.7. Applicability of Trend Tests With Censored Data. 13. Methods for Data Below the Reporting Limit. 13.1. Methods for Estimating Summary Statistics. 13.2. <s> BIB001 </s> Change detection in hydrological records—a review of the methodology / Revue méthodologique de la détection de changements dans les chroniques hydrologiques <s> Wilcoxon-Mann-Whitney test/Mann-Whitney test/Mann-test/Rank-sum test <s> Changes in streamflow volumes resulting from climatic change can affect the management of water resources. However, the detection of a statistically significant trend can be difficult because of the large interannual variability and the relatively short period of instrumental record. In this paper, five statistical tests are applied to the historical annual streamflow series of 30 unregulated Australian rivers, located in protected natural catchments, in order to detect trends or changes in the means. The Student t-statistic is also used to describe the relationship between interannual variability and the magnitude of change and length of data required to identify a statistically significant trend. The analysis indicates that, with the current data set, there is no clear evidence to suggest that the greenhouse effect is impacting on Australian streamflow volumes. The change required to identify a statistically significant change in the mean is directly proportional to the interannual variability, and less dependent on the length of data available. The interannual variability of Australian streams is twice that of Northern Hemisphere streams, therefore, a greater change is required in Australian flow volumes before a statistically significant change can be identified. The analysis of available historical records, however, indicates that statistically significant trends can be detected in the future flow volumes if the scenarios predicted by the G'CMs are realized. <s> BIB002
This is a rank-based test that looks for differences between two independent sample groups  WMO, 1988; BIB001 . It is based on the Mann-Kendall test statistic (see test 9 below), but is calculated for subsets of the series in order to detect the point of change in the mean BIB002 . In its basic form it assumes that the time of change is known. When the time of change is unknown, use of the median change-point test is recommended.