A Comprehensive Guide for Selecting Appropriate Statistical Tests: Understanding When to Use Parametric and Nonparametric Tests

Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Knowing how to select an appropriate test can lead to more accurate results. Invalid results and misleading conclusions may be drawn from a study if an incorrect statistical test is used. Therefore, to avoid these it is essential to understand the nature of the data, the research question, and the assumptions of the tests before selecting one. This is because there are a wide variety of tests available. This paper provides a step-by-step approach to selecting the right statistical test for any study, with an explanation of when it is appropriate to use it and relevant examples of each statistical test. Furthermore, this guide provides a comprehensive overview of the assumptions of each test and what to do if these assumptions are violated.

A Comprehensive Guide for Selecting Appropriate Statistical Tests: Understanding When to Use Parametric and Nonparametric Tests

Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Knowing how to select an appropriate test can lead to more accurate results. Invalid results and misleading conclusions may be drawn from a study if an incorrect statistical test is used. Therefore, to avoid these it is essential to understand the nature of the data, the research question, and the assumptions of the tests before selecting one. This is because there are a wide variety of tests available. This paper provides a step-by-step approach to selecting the right statistical test for any study, with an explanation of when it is appropriate to use it and relevant examples of each statistical test. Furthermore, this guide provides a comprehensive overview of the assumptions of each test and what to do if these assumptions are violated.

Investigation into Recent Temperature and Rainfall Trends in Mali Using Mann-Kendall Trend Test: Case Study of Bamako

Rainfall and temperature variability analysis is important for researchers and policy formulators in making critical decisions on water availability and use in communities. The Western Sahel, which comprises Mali is considered as one of the vulnerable regions to climate change, and also encountered the challenges of climatic shocks such as flood and drought. This research therefore sought to investigate climate change effects on hydrological events and trends in Sahelian rainfall intensity using Bamako (Mali) as a case study from 1991 to 2020, as limited data availability did not allow an extended period of study. Monthly observed data provided by MALI-METEO was used to validate daily rainfalls data from African Rainfall Climatology Version 2 (ARC2) satellite-based rainfall product on monthly basis. The validated model performance used Nash-Sutcliffe Efficiency (NSE) and Percent Bias (PBAIS) and gave results of 0.904 and 1.0506 respectively. Trends in annual maximum temperatures and rainfalls were analyzed using Mann-Kendall trend test. The result indicated that the trend in annual maximum rainfalls was decreasing, while annual total rainfall was increasing but not significant at 5% significance level. The rate of increase in annual total rainfalls was 0.475 mm/year according to the observed annual rainfall series and decreased to 0.68 mm/year in annual maximum. The analysis further found that annual maximum temperatures were increasing at the rate of 0.03°C/year at 5% significance level. To provide more accurate climate predictions, it is recommended that further studies on rainfall and temperature with data sets spanning 60 - 90 years be carried out.

Wavelet Analysis and Nonparametric Test for Climate Change in Tarim River Basin of Xinjiang During 1959-2006

Using wavelet analysis,regression analysis and the Mann-Kendall test,this paper analyzed time-series(1959-2006) weather data from 23 meteorological stations in an attempt to characterize the climate change in the Tarim River Basin of Xinjiang Uygur Autonomous Region,China.Major findings are as follows:1) In the 48-year study period,average annual temperature,annual precipitation and average annual relative humidity all presented nonlinear trends.2) At the 16-year time scale,all three climate indices unanimously showed a rather flat before 1964 and a detectable pickup thereafter.At the 8-year time scale,an S-shaped nonlinear and uprising trend was revealed with slight fluctuations in the entire process for all three indices.Incidentally,they all showed similar pattern of a slight increase before 1980 and a noticeable up-swing afterwards.The 4-year time scale provided a highly fluctuating pattern of periodical oscillations and spiral increases.3) Average annual relative humidity presented a negative correlation with average annual temperature and a positive correlation with annual precipitation at each time scale,which revealed a close dynamic relationship among them at the confidence level of 0.001.4) The Mann-Kendall test at the 0.05 confidence level demonstrated that the climate warming trend,as represented by the rising average annual temperature,was remarkable,but the climate wetting trend,as indicated by the rising annual precipitation and average annual relative humidity,was not obvious.

A method to predict rockburst using temporal trend test and its application

Rockbursts have become a significant hazard in underground mining,underscoring the need for a robust early warning model to ensure safety management.This study presents a novel approach for rockburst prediction,integrating the Mann-Kendall trend test(MKT)and multi-indices fusion to enable real-time and quantitative assessment of rockburst hazards.The methodology employed in this study involves the development of a comprehensive precursory index library for rockbursts.The MKT is then applied to analyze the real-time trend of each index,with adherence to rockburst characterization laws serving as the warning criterion.By employing a confusion matrix,the warning effectiveness of each index is assessed,enabling index preference determination.Ultimately,the integrated rockburst hazard index Q is derived through data fusion.The results demonstrate that the proposed model achieves a warning effectiveness of 0.563 for Q,surpassing the performance of any individual index.Moreover,the model’s adaptability and scalability are enhanced through periodic updates driven by actual field monitoring data,making it suitable for complex underground working environments.By providing an efficient and accurate basis for decision-making,the proposed model holds great potential for the prevention and control of rockbursts.It offers a valuable tool for enhancing safety measures in underground mining operations.

New Nonparametric Rank-Based Tests for Paired Data

We propose a new nonparametric test based on the rank difference between the paired sample for testing the equality of the marginal distributions from a bivariate distribution. We also consider a modification of the novel nonparametric test based on the test proposed by Baumgartern, Weiβ, and Schindler (1998). An extensive numerical power comparison for various parametric and nonparametric tests was conducted under a wide range of bivariate distributions for small sample sizes. The two new nonparametric tests have comparable power to the paired t test for the data simulated from bivariate normal distributions, and are generally more powerful than the paired t test and other commonly used nonparametric tests in several important bivariate distributions.

Calculation of Two-Tailed Exact Probability in the Wald-Wolfowitz One-Sample Runs Test

The objectives of this paper are to demonstrate the algorithms employed by three statistical software programs (R, Real Statistics using Excel, and SPSS) for calculating the exact two-tailed probability of the Wald-Wolfowitz one-sample runs test for randomness, to present a novel approach for computing this probability, and to compare the four procedures by generating samples of 10 and 11 data points, varying the parameters n0 (number of zeros) and n1 (number of ones), as well as the number of runs. Fifty-nine samples are created to replicate the behavior of the distribution of the number of runs with 10 and 11 data points. The exact two-tailed probabilities for the four procedures were compared using Friedman’s test. Given the significant difference in central tendency, post-hoc comparisons were conducted using Conover’s test with Benjamini-Yekutielli correction. It is concluded that the procedures of Real Statistics using Excel and R exhibit some inadequacies in the calculation of the exact two-tailed probability, whereas the new proposal and the SPSS procedure are deemed more suitable. The proposed robust algorithm has a more transparent rationale than the SPSS one, albeit being somewhat more conservative. We recommend its implementation for this test and its application to others, such as the binomial and sign test.

Study on Key Biological Indicators of Diabetes Based on Statistical Tests

Normality testing is a fundamental hypothesis test in the statistical analysis of key biological indicators of diabetes.If this assumption is violated,it may cause the test results to deviate from the true value,leading to incorrect inferences and conclusions,and ultimately affecting the validity and accuracy of statistical inferences.Considering this,the study designs a unified analysis scheme for different data types based on parametric statistical test methods and non-parametric test methods.The data were grouped according to sample type and divided into discrete data and continuous data.To account for differences among subgroups,the conventional chi-squared test was used for discrete data.The normal distribution is the basis of many statistical methods;if the data does not follow a normal distribution,many statistical methods will fail or produce incorrect results.Therefore,before data analysis and modeling,the data were divided into normal and non-normal groups through normality testing.For normally distributed data,parametric statistical methods were used to judge the differences between groups.For non-normal data,non-parametric tests were employed to improve the accuracy of the analysis.Statistically significant indicators were retained according to the significance index P-value of the statistical test or corresponding statistics.These indicators were then combined with relevant medical background to further explore the etiology leading to the occurrence or transformation of diabetes status.

农村税费改革视角下的中部地区农民收入增长趋势分析——基于Mann-Kendall非参数检验模型

采用中部地区6省份1993-2010年农民收入面板数据,运用Mann-Kendall非参数检验法,分析了农村税费改革前后农民纯收入及工资性收入、家庭经营收入、财产性收入和转移性收入的增长趋势。结果显示,农村税费改革后,以工资性收入和家庭经营收入来源为主的中部地区农民收入增加较为显著,但人均纯收入与中国大陆地区平均水平的绝对差距有所扩大,相对差距逐步缩小,表明农村税费改革基本实现了阶段性目标。据此,提出了继续稳定家庭经营,不断扩大农民家庭经营收入范围;有序引导农民非农就业,积极拓展劳务收入增长空间;推进农村综合改革,提高中部地区农民财产性收入水平;加大对农村地区的财政扶持,提高对农民的转移支付水平等进一步实现中部地区农民收入较快增长的对策建议。

A Nonparametric Model Checking Test for Functional Linear Composite Quantile Regression Models

This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model.A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectation under the null model.The proposed test statistic has an asymptotic standard normal distribution under the null hypothesis,and tends to infinity in probability under the alternative hypothesis,which implies the consistency of the test.Furthermore,it is proved that the test statistic converges to a normal distribution with nonzero mean under a local alternative hypothesis.Extensive simulations are reported,and the results show that the proposed test has proper sizes and is sensitive to the considered model discrepancies.The proposed methods are also applied to two real datasets.

Detecting Global Vegetation Changes Using Mann-Kendal(MK) Trend Test for 1982–2015 Time Period

Vegetation is the main component of the terrestrial ecosystem and plays a key role in global climate change. Remotely sensed vegetation indices are widely used to detect vegetation trends at large scales. To understand the trends of vegetation cover, this research examined the spatial-temporal trends of global vegetation by employing the normalized difference vegetation index(NDVI) from the Advanced Very High Resolution Radiometer(AVHRR) Global Inventory Modeling and Mapping Studies(GIMMS) time series(1982–2015). Ten samples were selected to test the temporal trend of NDVI, and the results show that in arid and semi-arid regions, NDVI showed a deceasing trend, while it showed a growing trend in other regions. Mann-Kendal(MK) trend test results indicate that 83.37% of NDVI pixels exhibited positive trends and that only 16.63% showed negative trends(P < 0.05) during the period from 1982 to 2015. The increasing NDVI trends primarily occurred in tree-covered regions because of forest growth and re-growth and also because of vegetation succession after a forest disturbance. The increasing trend of the NDVI in cropland regions was primarily because of the increasing cropland area and the improvement in planting techniques. This research describes the spatial vegetation trends at a global scale over the past 30+ years, especially for different land cover types.

Nonparametric TOA estimators for low-resolution IR-UWB digital receiver

Nonparametric time-of-arrival（TOA） estimators for impulse radio ultra-wideband（IR-UWB） signals are proposed. Nonparametric detection is obviously useful in situations where detailed information about the statistics of the noise is unavailable or not accurate. Such TOA estimators are obtained based on conditional statistical tests with only a symmetry distribution assumption on the noise probability density function. The nonparametric estimators are attractive choices for low-resolution IR-UWB digital receivers which can be implemented by fast comparators or high sampling rate low resolution analog-to-digital converters（ADCs）,in place of high sampling rate high resolution ADCs which may not be available in practice. Simulation results demonstrate that nonparametric TOA estimators provide more effective and robust performance than typical energy detection（ED） based estimators.

基于R/S和Mann-Kendall的天山北坡气候变化趋势预测

以新疆天山北坡昌吉州和石河子地区为例,结合该区1959-2006年的年平均气温和降水量资料,通过R/S分析方法揭示其分形特征,并利用Mann-Kendall非参数检验分析其突变性和单调性。结果如下:通过Mann-Kendall非参数检验,研究区温度、降水量序列的突变点分别发生在1986和1993年,依此为依据对其时间序列进行分割。在R/S分析中,利用分割后两个时间段的气象数据,根据温度(1986-2006年)和降水量(1993-2006年)序列的Hurst指数预测,在2006年后的一段时间内研究区的温度和降水量可能仍将保持上升趋势,气候向暖湿性转变。

Surface air temperature change in the Wuyi Mountains,southeast China

Detecting changes in surface air temperature in mid-and low-altitude mountainous regions is essential for a comprehensive understanding of warming trend with altitude.We use daily surface air temperature data from 64 meteorological stations in Wuyi Mountains and its adjacent regions to analyze the spatio-temporal patterns of temperature change.The results show that Wuyi Mountains have experienced significant warming from 1961 to 2018.The warming trend of the mean temperature is 0.20℃/decade,the maximum temperature is 0.17℃/decade,and the minimum temperature is 0.26℃/decade.In 1961-1990,more than 63%of the stations showed a decreasing trend in annual mean temperature,mainly because the maximum temperature decreased during this period.However,in 1971-2000,1981-2010 and 1991-2018,the maximum,minimum and mean temperatures increased.The fastest increasing trend of mean temperature occurred in the southeastern coastal plains,the quickest increasing trend of maximum temperature occurred in the northwestern mountainous region,and the increase of minimum temperature occurred faster in the southeastern coastal and northwestern mountainous regions than that in the central area.Meanwhile,this study suggests that elevation does not affect warming in the Wuyi Mountains.These results are beneficial for understanding climate change in humid subtropical middle and low mountains.

非参数CD-CAT题库Q矩阵优化设计

开展非参数CD-CAT题库Q矩阵的优化设计,并将它用于指导题库题目编制或选择,且它无需模型参数估计,这对于促进非参数CD-CAT进入课堂评价至关重要.受p-优化的启发,该文提出比例法生成优化Q矩阵,同时将已有的参数化模型题库设计方法推广到非参数化题库Q矩阵的优化设计.模拟研究结果显示:比例法和推广的融合法都有较好表现,而且当题库量较少时比例法更有优势.

AVWC－test在生命科学研究中应用效果的评估

ＡＶＷＣ－ｔｃｓｔ是新近发展起来的生物统计方法，它能把非参数资料转变成参数资料进行定量统计分析。本研究进一步从国内外刊物上公开发表的学术论文中精选出了一定数量的研究数据，用ＡＶＷＣ－ｔｅｓｔ方法进行统计处理，并与传统的非参数统计方法和计量资料统计方法进行同源自身对照，研究了其统计效能。结果清楚地表明：ＡＶＷＣ－ｔｅｓｔ方法是一种应用面广，精确、灵敏、方便的生物统计分析方法，能更好地发掘科学资料的信息，提高研究效率。

Spatiotemporal changes in sunshine duration and its influential factors in Chongqing,China from 1961 to 2020

The surface solar radiation in most parts of the world has undergone a phenomenon known as global dimming and brightening,characterized by an initial decrease followed by an increase.As a result,the sunshine duration(SD)has decreased in the past 60 years.Against the backdrop of global dimming and brightening,SD has decreased to varying degrees in many regions of China.Using the observed data of SD,cloud amount(total cloud amount and low cloud amount,abbreviated as TCA and LCA),precipitation,and relative humidity(RH)from 34 meteorological stations in Chongqing during the period of 1961-2020,along with a digital elevation model(DEM)with a resolution of 90 m,this study analyzed the spatiotemporal variations and influencing factors of SD.The analysis employed methods such as linear regression,Mann-Kendall test,wavelet transformation,and DEM-based possible SD distributed model.The results showed that the annual SD in Chongqing has significantly decreased over the last 60 years,with a decreasing interannual trend rate(ITR)of 40.4 h/10a.Except for no obvious trend in spring,SD decreased significantly in summer,autumn and winter at the ITR of 21.1 h/10a,8.5 h/10a and 7.5 h/10a,respectively.An abrupt decrease in the annual SD was found in 1979.The difference before and after the abrupt decrease was 177.7 h.The difference before and after the abrupt decrease was 177.7 h.The annual SD possessed the oscillation period of 11a.The spatial heterogeneity of the mean annual SD during the last 60 years was obvious.The distribution of SD in Chongqing is high in the northeast and low in the southeast.In addition,about 73%of the total area in Chongqing showed a significant and very significant decreasing trend.The regions with significant changes are mainly concentrated in the regions with altitudes of 200~1000 m.The increasing LCA was the main cause of the decrease of the annual SD in the regions with 200-400 m altitude decreased the most and changed the most.Increasing LCA is the primary cause of the reduction in annual SD,showing a strong negative correlation coefficient of-0.7292.In Chongqing,PM2.5 concentration showed a significant decrease trend in annual,spring,autumn and winter during 2000-2020,but the significant correlation between PM2.5 concentration and SD was only in autumn and reached an extremely significant level.

南昌市NDVI时空演化特征及其气候驱动因子分析

揭示南昌市植被覆盖的演化特征和确定影响其变化趋势的主要气候驱动因子,为其长期稳定、良性发展和积极应对后续的气候变化提供指导。采用2000—2020年南昌市的NDVI月度数据、气温、降水和气压等10个气象驱动因子,利用单样本K-S(Kolmogorov-Smirnov)检验、弗里德曼检验、肯德尔和谐系数检验法等非参数检验法和随机森林分析方法,对不同驱动因子的重要性进行研究。结果表明,1)在2000—2020年南昌市的NDVI呈波动下降趋势,该峰值出现在2000年,谷值则在2010年;2)城市整体植被覆盖呈现四周高中间低的空间分布规律,北部和西部地区的NDVI值相对较高且下降速率缓慢,中部的东湖区和青山湖区等NDVI值相对较低且有明显下降趋势;3)植被覆盖的极大平均值出现在每年8月,受温度的影响最显著,而风向的影响最不显著,降水的影响有一定的时滞性,植被覆盖变化应结合多要素的共同驱动作用来决定。

改进邻域漂移的多假设检验点云降噪

在获得三维点云数据时,由于仪器、环境、算法等原因,不可避免地会使获得的点云数据带有噪声,而点云数据所携带的噪声将影响后续的点云处理效果。为了抑制三维点云数据中的噪声,同时保留其不同程度的特征,提出一种改进邻域漂移的多假设点云降噪方法。首先,利用邻域点和法向双张量投票法进行特征描述;接着,利用非参数估计构建转移概率函数,并使用核回归方法对新的采样点进行权重计算,在此基础上运用粒子滤波实现邻域漂移,经过多次迭代得到非局部邻域;然后,通过多假设检验法确定不同特征点处的多个法向,并通过加权平均获得最终法向;最后,采用多假设检验的方法分别对特征点和非特征点进行滤波,产生多个候选点并使用目标函数进行优化,从而对点云模型进行降噪。利用所提方法与RIMLS、EAR、L1、PointNet方法对相同噪声模型进行恢复,并对恢复模型与原模型进行误差分析,结果表明,所提方法的平均降噪精度相比RIMLS、EAR和L1方法分别提高了38.1%、41.3%和12.4%,与PointNet相比约降低2.9%,但是所提方法无须进行数据库训练且可调参。

三峡水库干流含沙量对不同形态磷浓度的影响分析

磷是水环境质量评价和污染控制考核的重要指标,其在天然水体中以溶解态、颗粒态等形态存在。研究水中含沙量的改变对不同形态磷浓度的影响,对磷污染控制有着重要意义。选取三峡水库干流为研究对象,采用Mann-Kendall非参数检验法和Pearson相关系数分析了该河段含沙量变化对总磷、溶解磷、颗粒磷等不同形态磷浓度的影响。结果表明:①2003~2019年三峡水库干流的平均流量无明显变化,含沙量则明显减少。②总磷浓度在2003~2012年间起伏波动、缓慢上升,2013~2019年则持续下降;溶解磷浓度呈先上升后下降的趋势,各断面峰值出现在2013、2014年;颗粒态磷浓度呈波动下降趋势。③与2003~2012年浓度均值相比,2013~2019年浑浊水样磷浓度、沉降水样磷浓度以及颗粒磷浓度分别下降了40%,25%和65%;溶解磷浓度则出现明显上升,库尾朱沱断面、变动回水区寸滩断面上升约60%,常年回水区清溪场和万县断面分别上升约20%和12%;溶解磷/沉降水样磷的比值快速上升,2013~2019年溶解磷/沉降水样磷均达到68%以上。④在新水沙条件影响下,三峡水库干流不同形态磷浓度已发生明显改变,最易被浮游生物利用的溶解磷已成为三峡水库干流磷的主要存在形式。研究成果可为三峡库区营养盐控制和治理提供科学依据。