In this study, to power comparison test, different univariate normality testing procedures are compared by using new algorithm. Different univariate and multivariate test are also analyzed here. And also review effici...In this study, to power comparison test, different univariate normality testing procedures are compared by using new algorithm. Different univariate and multivariate test are also analyzed here. And also review efficient algorithm for calculating the size corrected power of the test which can be used to compare the efficiency of the test. Also to test the randomness of generated random numbers. For this purpose, 1000 data sets with combinations of sample size n = 10, 20, 25, 30, 40, 50, 100, 200, 300 were generated from uniform distribution and tested by using different tests for randomness. The assessment of normality using statistical tests is sensitive to the sample size. Observed that with the increase of n, overall powers are increased but Shapiro Wilk (SW) test, Shapiro Francia (SF) test and Andeson Darling (AD) test are the most powerful test among other tests. Cramer-Von-Mises (CVM) test performs better than Pearson chi-square, Lilliefors test has better power than Jarque Bera (JB) Test. Jarque Bera (JB) Test is less powerful test among other tests.展开更多
In 2023,a multivariate normality test based on a chi-square approximation was developed.This method assumes independence among Gaussian random variables,and defines the test statistic,denoted by Q,as the sum of square...In 2023,a multivariate normality test based on a chi-square approximation was developed.This method assumes independence among Gaussian random variables,and defines the test statistic,denoted by Q,as the sum of squared values.This study aims to develop R scripts that implement the Q-test for mul-tivariate normality using either the Shapiro-Wilk W statistic(QSWa)or the Shapiro-Francia W’statistic(QSFa).A bootstrap version of the Q-test(QSWb and QSFb),which does not assume independence,is also included.Addition-ally,it incorporates Royston’s H-test.The use of the scripts is illustrated with a sample of 50 participants assessed on a variable across four yearly admin-istrations.The sampling distribution generated by the bootstrap method dif-fers from the chi-square distribution and corresponds to a generalized chisquare distribution-namely,the distribution of a sum of squares of correlated variables.This distribution is less peaked and has a heavier right tail than the chi-square distribution.It is concluded that the bootstrap approach is con-servative under the null hypothesis of multivariate normality;however,it is theoretically more appropriate than the chi-square approximation.To ap-proximate the distributions of the two versions of the Q-test,it is recom-mended that the z or z’values set to zero in the calculation of the Q statistic not be subtracted when determining the degrees of freedom in the chi-square approximation.Moreover,a significance level of 10%is suggested for the bootstrap approach,rather than the conventional 5%.展开更多
Epiphytic plant species are an important part of biological diversity. It is therefore essential to understand the distribution pattern and the factors influencing such patterns. The present study is aimed at observin...Epiphytic plant species are an important part of biological diversity. It is therefore essential to understand the distribution pattern and the factors influencing such patterns. The present study is aimed at observing the patterns of species richness, abundances and species composition of epiphytic orchids and ferns in two subtropical forests in Nepal. We also studied the relationship of host plants(Schima wallichii and Quercus lanata) and epiphyte species. Data were collected in Naudhara community forest(CF) and the national forest(NF) in Shivapuri Nagarjun National Park. The data were analyzed using univariate and multivariate tests. In total, we recorded 41 species of epiphytes(33 orchid and 8 fern species). Orchid species abundance is significantlyhigher in CF compared to NF. Orchid species richness and abundance increased with increasing southern aspect whereas it decreased with increasing canopy cover, and fern species richness increased with host bark roughness. Orchid abundance was positively correlated with increasing bark p H, stem size, tree age and tree height and negatively correlated with increasing steepness of the area. Likewise, fern abundances were high in places with high canopy cover, trees that were tall and big, but decreased with increasing altitude and southern aspect. The composition of the orchid and fern species was affected by altitude, aspect, canopy cover, DBH, number of forks and forest management types. We showed that the diversity of orchid and fern epiphytes is influenced by host characteristics as well as host types. The most important pre-requisite for a high epiphyte biodiversity is the presence of oldrespectively tall trees, independent of the recent protection status. This means:(i) for protection, e.g.in the frame of the national park declaration, such areas should be used which host such old tall trees;and(ii) also in managed forests and even in intensively used landscapes epiphytes can be protected by letting a certain number of trees be and by giving them space to grow old and tall.展开更多
Breast cancer is one of the leading diseases that affect women’s lives. It affects their lives in so many ways by denying them the required standard of health needed to carry out all of their daily activities for som...Breast cancer is one of the leading diseases that affect women’s lives. It affects their lives in so many ways by denying them the required standard of health needed to carry out all of their daily activities for some days, weeks, months or years before eventually causing death. This research estimates the survival rate of breast cancer patients and investigates the effects of stage of tumor, gender, age, ethnic group, occupation, marital status and type of cancer upon the survival of patients. Data used for the study were extracted from the case file of patients in the Radiation Oncology Department, University College Hospital, Ibadan using a well-structured pro forma in which 74 observations were censored and 30 events occurred. The Kaplan-Meier estimator was used to estimate the overall survival probability of breast cancer patients following their recruitment into the study and determine the mean and median survival times of breast cancer patients following their time of recruitment into the study. Since there are different groups with respect to the stages of tumor at the time of diagnosis, the log-rank test was used to compare the survival curve of the stages of tumor with considering p-values below 0.05 as statistically significant. Multivariate Cox regression was used to investigate the effects of some variables on the survival of patients. The overall cumulative survival probability obtained is 0.175 (17.5%). The overall estimated mean time until death is 28.751 weeks while the median time between admission and death is 23 weeks. As the p-value (0.000032) of the log-rank test for comparing stages of tumor is less than 0.05, it is concluded that there is significant evidence of a difference in survival times for the stages of tumor. The survival function plot for the stages of tumor shows that patients with stage III tumor are less likely to survive. From the estimated mean time until death for the stages of tumor, it was deduced that stage I tumor patients have an increased chance of survival. Types of cancer, gender, marital status, ethnic group, occupation and patient’s age at entry into the study are not important predictors of chances of survival.展开更多
We introduce the so-called naive tests and give a brief review of the new developments. Naive testing methods are easy to understand and perform robustly, especially when the dimension is large. We focus mainly on rev...We introduce the so-called naive tests and give a brief review of the new developments. Naive testing methods are easy to understand and perform robustly, especially when the dimension is large. We focus mainly on reviewing some naive testing methods for the mean vectors and covariance matrices of high-dimensional populations, and we believe that this naive testing approach can be used widely in many other testing problems.展开更多
文摘In this study, to power comparison test, different univariate normality testing procedures are compared by using new algorithm. Different univariate and multivariate test are also analyzed here. And also review efficient algorithm for calculating the size corrected power of the test which can be used to compare the efficiency of the test. Also to test the randomness of generated random numbers. For this purpose, 1000 data sets with combinations of sample size n = 10, 20, 25, 30, 40, 50, 100, 200, 300 were generated from uniform distribution and tested by using different tests for randomness. The assessment of normality using statistical tests is sensitive to the sample size. Observed that with the increase of n, overall powers are increased but Shapiro Wilk (SW) test, Shapiro Francia (SF) test and Andeson Darling (AD) test are the most powerful test among other tests. Cramer-Von-Mises (CVM) test performs better than Pearson chi-square, Lilliefors test has better power than Jarque Bera (JB) Test. Jarque Bera (JB) Test is less powerful test among other tests.
文摘In 2023,a multivariate normality test based on a chi-square approximation was developed.This method assumes independence among Gaussian random variables,and defines the test statistic,denoted by Q,as the sum of squared values.This study aims to develop R scripts that implement the Q-test for mul-tivariate normality using either the Shapiro-Wilk W statistic(QSWa)or the Shapiro-Francia W’statistic(QSFa).A bootstrap version of the Q-test(QSWb and QSFb),which does not assume independence,is also included.Addition-ally,it incorporates Royston’s H-test.The use of the scripts is illustrated with a sample of 50 participants assessed on a variable across four yearly admin-istrations.The sampling distribution generated by the bootstrap method dif-fers from the chi-square distribution and corresponds to a generalized chisquare distribution-namely,the distribution of a sum of squares of correlated variables.This distribution is less peaked and has a heavier right tail than the chi-square distribution.It is concluded that the bootstrap approach is con-servative under the null hypothesis of multivariate normality;however,it is theoretically more appropriate than the chi-square approximation.To ap-proximate the distributions of the two versions of the Q-test,it is recom-mended that the z or z’values set to zero in the calculation of the Q statistic not be subtracted when determining the degrees of freedom in the chi-square approximation.Moreover,a significance level of 10%is suggested for the bootstrap approach,rather than the conventional 5%.
基金“Bauer-Stiftung und Glaser-Stiftung im Stifterverband für die Deutsche Wissenschaft” Project No. T237/24905/2013/Kg for the research grantgrant number 14-36098G of the Czech Science Foundation and the institutional support RVO 67985939
文摘Epiphytic plant species are an important part of biological diversity. It is therefore essential to understand the distribution pattern and the factors influencing such patterns. The present study is aimed at observing the patterns of species richness, abundances and species composition of epiphytic orchids and ferns in two subtropical forests in Nepal. We also studied the relationship of host plants(Schima wallichii and Quercus lanata) and epiphyte species. Data were collected in Naudhara community forest(CF) and the national forest(NF) in Shivapuri Nagarjun National Park. The data were analyzed using univariate and multivariate tests. In total, we recorded 41 species of epiphytes(33 orchid and 8 fern species). Orchid species abundance is significantlyhigher in CF compared to NF. Orchid species richness and abundance increased with increasing southern aspect whereas it decreased with increasing canopy cover, and fern species richness increased with host bark roughness. Orchid abundance was positively correlated with increasing bark p H, stem size, tree age and tree height and negatively correlated with increasing steepness of the area. Likewise, fern abundances were high in places with high canopy cover, trees that were tall and big, but decreased with increasing altitude and southern aspect. The composition of the orchid and fern species was affected by altitude, aspect, canopy cover, DBH, number of forks and forest management types. We showed that the diversity of orchid and fern epiphytes is influenced by host characteristics as well as host types. The most important pre-requisite for a high epiphyte biodiversity is the presence of oldrespectively tall trees, independent of the recent protection status. This means:(i) for protection, e.g.in the frame of the national park declaration, such areas should be used which host such old tall trees;and(ii) also in managed forests and even in intensively used landscapes epiphytes can be protected by letting a certain number of trees be and by giving them space to grow old and tall.
文摘Breast cancer is one of the leading diseases that affect women’s lives. It affects their lives in so many ways by denying them the required standard of health needed to carry out all of their daily activities for some days, weeks, months or years before eventually causing death. This research estimates the survival rate of breast cancer patients and investigates the effects of stage of tumor, gender, age, ethnic group, occupation, marital status and type of cancer upon the survival of patients. Data used for the study were extracted from the case file of patients in the Radiation Oncology Department, University College Hospital, Ibadan using a well-structured pro forma in which 74 observations were censored and 30 events occurred. The Kaplan-Meier estimator was used to estimate the overall survival probability of breast cancer patients following their recruitment into the study and determine the mean and median survival times of breast cancer patients following their time of recruitment into the study. Since there are different groups with respect to the stages of tumor at the time of diagnosis, the log-rank test was used to compare the survival curve of the stages of tumor with considering p-values below 0.05 as statistically significant. Multivariate Cox regression was used to investigate the effects of some variables on the survival of patients. The overall cumulative survival probability obtained is 0.175 (17.5%). The overall estimated mean time until death is 28.751 weeks while the median time between admission and death is 23 weeks. As the p-value (0.000032) of the log-rank test for comparing stages of tumor is less than 0.05, it is concluded that there is significant evidence of a difference in survival times for the stages of tumor. The survival function plot for the stages of tumor shows that patients with stage III tumor are less likely to survive. From the estimated mean time until death for the stages of tumor, it was deduced that stage I tumor patients have an increased chance of survival. Types of cancer, gender, marital status, ethnic group, occupation and patient’s age at entry into the study are not important predictors of chances of survival.
基金supported by National Natural Science Foundation of China (Grant Nos. 11301063 and 11571067)Science and Technology Development Foundation of Jilin (Grant No. 20160520174JH)Science and Technology Foundation of Jilin during the "13th Five-Year Plan"
文摘We introduce the so-called naive tests and give a brief review of the new developments. Naive testing methods are easy to understand and perform robustly, especially when the dimension is large. We focus mainly on reviewing some naive testing methods for the mean vectors and covariance matrices of high-dimensional populations, and we believe that this naive testing approach can be used widely in many other testing problems.
