scholarly journals The modified Mann-Kendall test: on the performance of three variance correction approaches

Bragantia ◽  
2013 ◽  
Vol 72 (4) ◽  
pp. 416-425 ◽  
Author(s):  
Gabriel Constantino Blain
Keyword(s):  
Serial Correlation ◽  
Kendall Test ◽  
Trend Test ◽  
Climate Trends ◽  
Nominal Significance Level ◽  
Trade Off ◽  
Significance Level ◽  
Mk Test ◽  
Nominal Significance ◽  
Mann Kendall Test

The Mann-Kendall test has been used to detect climate trends in several parts of the Globe. Three variance correction approaches (MKD, MKDD and MKRD) have been proposed to remove the influence of serial correlation on this trend test. Thus, the main goal of this study was to evaluate the probability of occurrence of types I and II errors associated with these three approaches. The results obtained by means of Monte Carlo simulations and from a case of study allowed us to drawn the following conclusions: All approaches are capable of meeting the adopted significant level when they are applied to trend-free uncorrelated series. The approaches are as powerful as the original MK test when they are applied to uncorrelated series. Regarding serially correlated series it was verified that: (i) the performance of the MKDD and MKRD are comparable; (ii) both approaches may not be able to preserve the adopted significance level and (iii) although the MKD is capable of preserving the adopted significance level, it is less powerful than the MKDD and MKRD. Thus, there is a trade-off between the power of the three approaches and their capability of meeting the nominal significance level. Accordingly, we recommend the use of at least two approaches -MKD and MKDD(MKRD)- to evaluate the presence of trends in a given dataset.

scholarly journals Innovative Trend Analysis of Precipitation in the Lake Issyk-Kul Basin, Kyrgyzstan

Atmosphere ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 332 ◽  
Author(s):  
Yilinuer Alifujiang ◽  
Jilili Abuduwaili ◽  
Balati Maihemuti ◽  
Bilal Emin ◽  
Michael Groll
Keyword(s):  
Trend Analysis ◽  
Resource Planning ◽  
Kendall Test ◽  
Trend Test ◽  
Lake Basin ◽  
Positive Trend ◽  
Monthly Precipitation ◽  
Innovative Trend Analysis ◽  
Mann Kendall Test ◽  
Increasing Trends

The analysis of various characteristics and trends of precipitation is an essential task to improve the utilization of water resources. Lake Issyk-Kul basin is an upper alpine catchment, which is more susceptible to the effects of climate variability, and identifying rainfall variations has vital importance for water resource planning and management in the lake basin. The well-known approaches linear regression, Şen’s slope, Spearman’s rho, and Mann-Kendall trend tests are applied frequently to try to identify trend variations, especially in rainfall, in most literature around the world. Recently, a newly developed method of Şen-innovative trend analysis (ITA) provides some advantages of visual-graphical illustrations and the identification of trends, which is one of the main focuses in this article. This study obtained the monthly precipitation data (between 1951 and 2012) from three meteorological stations (Balykchy, Cholpon-Ata, and Kyzyl-Suu) surrounding the Lake Issyk-Kul, and investigated the trends of precipitation variability by applying the ITA method. For comparison purposes, the traditional Mann–Kendall trend test also used the same time series. The main results of this study include the following. (1) According to the Mann-Kendall trend test, the precipitation of all months at the Balykchy station showed a positive trend (except in January (Zc = −0.784) and July (Zc = 0.079)). At the Cholpon-Ata and Kyzyl-Suu stations, monthly precipitation (with the same month of multiple years averaged) indicated a decreasing trend in January, June, August, and November. At the monthly scale, significant increasing trends (Zc > Z0.10 = 1.645) were detected in February and October for three stations. (2) The ITA method indicated that the rising trends were seen in 16 out of 36 months at the three stations, while six months showed decreasing patterns for “high” monthly precipitation. According to the “low” monthly precipitations, 14 months had an increasing trend, and four months showed a decreasing trend. Through the application of the ITA method (January, March, and August at Balykchy; December at Cholpon-Ata; and July and December at Kyzyl-Suu), there were some significant increasing trends, but the Mann-Kendall test found no significant trends. The significant trend occupies 19.4% in the Mann-Kendall test and 36.1% in the ITA method, which indicates that the ITA method displays more positive significant trends than Mann–Kendall Zc. (3) Compared with the classical Mann-Kendall trend results, the ITA method has some advantages. This approach allows more detailed interpretations about trend detection, which has benefits for identifying hidden variation trends of precipitation and the graphical illustration of the trend variability of extreme events, such as “high” and “low” values of monthly precipitation. In contrast, these cannot be discovered by applying traditional methods.

scholarly journals Multi-annual analysis and trends of the temperatures and precipitations in West Anatolia

2017 ◽  
Vol 8 (3) ◽  
pp. 456-473 ◽  
Author(s):  
Turgay Partal
Keyword(s):  
Kendall Test ◽  
Temperature Data ◽  
Significance Level ◽  
Time Frequency ◽  
Pettitt Test ◽  
Frequency Representation ◽  
Mann Kendall Test ◽  
Scale Levels ◽  
Increasing Trends ◽  
Periodic Components

This study has been carried out to analyze the historical precipitation and temperature data for West Anatolia (Turkey) to understand the annual and multi-annual changes. The wavelet transform technique was used for time–frequency representation of the data. The trends in the data were estimated with the non-parametric Mann–Kendall test. A change point in the time series was determined by the Pettitt test. According to the wavelet analysis, some strong short-term periodical events at the scale levels of 1–4 were determined. The application of the Mann–Kendall test resulted with the identification of some decreasing trends in the observed annual precipitations and also in some periodic components, such as in 32 yearly periodic components. As well, 16 yearly periodic components of the temperature data showed very strong increasing trends at the 5% significance level.

Sample Size Reassessment in Non-inferiority Trials

2011 ◽  
Vol 50 (03) ◽  
pp. 237-243 ◽  
Author(s):  
T. Friede ◽  
M. Kieser
Keyword(s):  
Sample Size ◽  
Error Rate ◽  
Type I Error ◽  
Nuisance Parameters ◽  
Type I ◽  
Nominal Significance Level ◽  
Significance Level ◽  
Type I Error Rate ◽  
Planning Phase ◽  
Nominal Significance

SummaryObjectives: Analysis of covariance (ANCOVA) is widely applied in practice and its use is recommended by regulatory guidelines. However, the required sample size for ANCOVA depends on parameters that are usually uncertain in the planning phase of a study. Sample size recalculation within the internal pilot study design allows to cope with this problem. From a regulatory viewpoint it is preferable that the treatment group allocation remains masked and that the type I error is controlled at the specified significance level. The characteristics of blinded sample size reassessment for ANCOVA in non-inferiority studies have not been investigated yet. We propose an appropriate method and evaluate its performance.Methods: In a simulation study, the characteristics of the proposed method with respect to type I error rate, power and sample size are investigated. It is illustrated by a clinical trial example how strict control of the significance level can be achieved.Results: A slight excess of the type I error rate beyond the nominal significance level was observed. The extent of exceedance increases with increasing non-inferiority margin and increasing correlation between outcome and covariate. The procedure assures the desired power over a wide range of scenarios even if nuisance parameters affecting the sample size are initially mis-specified.Conclusions: The proposed blinded sample size recalculation procedure protects from insufficient sample sizes due to incorrect assumptions about nuisance parameters in the planning phase. The original procedure may lead to an elevated type I error rate, but methods are available to control the nominal significance level.

scholarly journals Removing the influence of the serial correlation on the Mann-Kendall test

2014 ◽  
Vol 29 (2) ◽  
pp. 161-170 ◽  
Author(s):  
Gabriel Constantino Blain
Keyword(s):  
Serial Correlation ◽  
Kendall Test ◽  
Temperature Data ◽  
Trend Test ◽  
Type I ◽  
Type Ii ◽  
Weather Station ◽  
Type I Errors ◽  
Serial Correlations ◽  
Type Ii Errors

The Pre-Whitening (PW), the Trend-Free Pre-Whitening (TFPW) and the Modified Trend-Free Pre-Whitening (MTFPW) were developed to remove the influence of serial correlations on the Mann-Kendall trend test. The main purpose of this study was to compare the performance of these algorithms for evaluating trends in auto-correlated series. The PW, TFPW and MTFPW were also applied to the monthly values of the rainfall (Pre), minimum (Tmin) and maximum (Tmax) air temperature data obtained from the weather station of Ribeirão Preto, State of São Paulo, Brazil. Sets of Monte Carlo simulations were carried out to evaluate the occurrence of the type I and the type II errors obtained from these three algorithms. The TFPW has the highest power. However, it also presented the highest occurrence of type I errors. The PW clearly limits the influence of serial correlation on the occurrence of type I errors. Nevertheless, this feature is accomplished at a cost of a great reduction of its ability to detect trends. The MTFPW leads to a better balance between the probabilities of both statistical errors. It was also concluded that the hypothesis of the presence of no climate change in the location of Ribeirão Pareto cannot be accepted.

scholarly journals Trend Analysis of Rainfall Data in Magelang District Using Mann-Kendall Test and Modification Mann-Kendall Variation

AGRIFOR ◽  
2018 ◽  
Vol 17 (2) ◽  
pp. 293 ◽  
Author(s):  
Joko Suryanto ◽  
Joko Krisbiyantoro
Keyword(s):  
Kendall Test ◽  
Significant Trend ◽  
Rainfall Data ◽  
Annual Rainfall ◽  
Partial Sums ◽  
Trend Test ◽  
Positive Trend ◽  
Mk Test ◽  
Rainfall Trends ◽  
Negative Significant Trend

The objective of the research was to analyzed rainfall trends from 6 rainfall stations Kajoran, Mendut, Muntilan, Ngablak, Salaman and Tempuran rainfall station in different time scales (monthly, 3-months periodicityand annual). Identification homogenity of the rainfall data period 1986-2016 for Magelang district using Rescaled Adjusted Partial Sums (RAPS) methode. The three non-parametric tests, Mann-Kendall (MK), modified Mann-Kendall (MMK), trend free prewhitening Mann-Kendall (TFPW-MK) and Sen’s slope wereemployed to assess significance of trends and detecting magnitude of trends.The results shows that monthly rainfall have no significant trend using MK, MMK, and TFPW-MK test at 0.05 level significance. Rainfall 3-month based January-February-March (JFM) period Kajoran station have negative significant trend with magnitude 19.4 mm/3-month. Mendut station have positive trend for April-May-June (AMJ) period with magnitude 6.75 mm/3-month. No significant trends at 0.05 level significance using MK trend test were detected in annual rainfall for 6 rainfall stations.

scholarly journals Changements historiques à long terme du débit écoulé dans le Haut bassin du fleuve Sénégal

2021 ◽  
Vol 384 ◽  
pp. 149-153
Author(s):  
Cheikh Faye
Keyword(s):  
River Basin ◽  
Confidence Level ◽  
Kendall Test ◽  
Hydraulic Structures ◽  
Trend Test ◽  
Upward Trend ◽  
Senegal River ◽  
Mann Kendall Test ◽  
Upstream Station ◽  
Senegal River Basin

Abstract. In this study, the flow trends on either side of the Manantali dam, in the upper Senegal River basin, were assessed. The assessment was carried out for the period 1970 to 2019 using the Sen slope and the Mann-Kendall test. The Mann-Kendall trend test was used to indicate the direction of the trends, while the Sen slope was used to assess the magnitude of the change. The results of the study showed that there was an upward trend in the flow of the Senegal River both annually and for every month upstream (Bafing-Makana station) and downstream (Bakel station) from the barrage. The strongest upward trend is noted in October on the upstream station with 4.12 m3/month and in September on the downstream station with 10.99 m3/month. In return, the weakest upward trend is observed in May on the upstream station with 0.07 m3/month and in August on the downstream station with 0.67 m3/month. The annual flow also showed a significant increase upstream (with a rate of 0.35 m3/year) and downstream (with a rate of 4.53 m3/year) with a confidence level of 99 %. The results of the study also showed that an increase in precipitation causes an increase in runoff, despite the construction of hydraulic structures.

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