Friedman Test Statistic Research Articles

SOSYAL BİLGİLER DERSİNDE ALTERNATİF BİR MODEL KULLANMAK: HAREZMİ EĞİTİM MODELİ

The Harezmi education model is a teaching model that was designed to equip students with various types of skills about various subjects or problem situations in an interdisciplinary manner. The research examined the students’ views and the effects of using the Harezmi Education Model for teaching the social studies course on the students in terms of academic achievement, permanent learning, meta-cognitive awareness. The research was carried out using the diversification of (parallel-convergent design) mixed methods. The quantitative dimension of the research was conducted using a quasi-experimental pre-test/post-test control group design. Qualitative research was carried out with case study using a holistic single case design. The study group consists of a total of 54 students studying in the seventh grade of secondary school. Quantitative research data were collected with an Academic Achievement Test and the Junior Meta cognitive Awareness Inventory (Jr.MAI). Qualitative data were collected with student interview forms, self-evaluation forms and Harezmi student activity diaries. Mann Whitney U test, Wilcoxon signed-rank test and Friedman test statistics were used for the analysis of quantitative data. Qualitative data were analyzed using descriptive and content analysis techniques. As a result of the analysis, tables were prepared, and statistical information and some student opinions were presented. It was concluded that using the Harezmi Education Model for the purpose of teaching the social studies course had a significant positive effect on the academic achievement and meta cognitive awareness of the students. However no statistically significant effect of the Harezmi Education Model could be determined on permanent learning. The students described the social studies lessons taught using the Harezmi Education Model as catchy, entertaining, surprising, and useful. In line with the results, suggestions were presented about the dissemination of the Harezmi Education Model and the implementation of the model on different courses.

An Analysis of Knowledge and Adoption of Critical Crop Interventions in Rice Cultivation by Tenant Farmers in A.P.

Agriculture is dependent on nature but appropriate interventions at critical stages of crop can yield good harvest. The study was conducted in East Godavari district of Andhra Pradesh state. Three mandals viz., Kirlampudi, Peddapuram, Kajuluru were selected using simple random sampling procedure. A total sample of 135 were selected for the study. Knowledge and adoption of critical interventions in rice cultivation by the tenant farmers, owners cum tenant farmers and owner farmers was studied. Majority of the tenant farmers had low (80.00%) knowledge on critical interventions in rice cultivation, followed by medium (15.56%) and high (4.44%) knowledge. More than two-third of the owner cum tenant farmers had medium (66.67%) knowledge on critical interventions in cultivation, followed by high (17.78%) and low (15.56%) knowledge. More than three-fourth of the owner farmers had high (75.56%) knowledge on critical interventions in cultivation, followed by medium (15.56%) and low (8.89%) knowledge. Friedman test statistic and chi-square value for the knowledge levels of the respondents inferred that there is a signifi cant diff erence in knowledge levels between diff erent groups. Adoption is based on the knowledge level. Friedman test statistic and chi-square value inferred that there is a signifi cant diff erence in adoption levels between diff erent groups.

Clinically Screening Hospital Patients for Social Risk Factors Across Multiple Hospitals: Results and Implications for Intervention Development.

Hospitals are increasingly screening patients for social risk factors to help improve patient and population health. Intelligence gained from such screening can be used to inform social need interventions, the development of hospital-community collaborations, and community investment decisions. We evaluated the frequency of admitted patients' social risk factors and examined whether these factors differed between hospitals within a health system. A central goal was to determine if community-level social need interventions can be similar across hospitals. We described the development, implementation, and results from Northwell Health's social risk factor screening module. The statistical sample included patients admitted to 12 New York City/Long Island hospitals (except for maternity/pediatrics) who were clinically screened for social risk factors at admission from June 25, 2019, to January 24, 2020. We calculated frequencies of patients' social needs across all hospitals and for each hospital. We used chi-square and Friedman tests to evaluate whether the hospital-level frequency and rank order of social risk factors differed across hospitals. Patients who screened positive for any social need (n = 5196; 6.6% of unique patients) had, on average, 2.3 of 13 evaluated social risk factors. Among these patients, the most documented social risk factor was challenges paying bills (29.4%). The frequency of 12 of the 13 social risk factors statistically differed across hospitals. Furthermore, a statistically significant variance in rank orders between the hospitals was identified (Friedman test statistic 30.8 > 19.6: χ2 critical, p = 0.05). However, the hospitals' social need rank orders within their respective New York City/Long Island regions were similar in two of the three regions. Hospital patients' social needs differed between hospitals within a metropolitan area. Patients at different hospitals have different needs. Local considerations are essential in formulating social need interventions and in developing hospital-community partnerships to address these needs.

Preliminary studies of Volten VR4® Kaempferia parviflora herb extracts on blood glucose levels in human type-2 diabetes mellitus and its mineral element analysis

Summary Introduction Volten VR4® capsules containing herb extract of Kaempferia parviflora has been claimed to reduce blood glucose in patients with diabetes. Objectives This preliminary study is conducted to evaluate the efficacy of Volten VR4® on healthy individuals and type-2 diabetes mellitus volunteers. The extracts of 400 mg capsules of Kaempferia parviflora (KP) were used to measure the blood glucose level of 2-hour postprandial. Methods The healthy group consists of 15 young adults aged 20-30 with no history of serious diseases, while the diabetic group includes 12 individuals aged 35-75 diagnosed with type-2 diabetes mellitus. Data were validated through the Willcoxon and Friedman test statistics and error distribution. The investigation was continued to trace the capsules contents of elements using inductively coupled plasma optical emission spectrometry (ICP-OES) techniques. Results It has been shown that KP reducing blood sugar levels has been associated with flavonoids and methoxyflavones components. The result specifically showed that consuming VR4® capsules can significantly reduce blood glucose, either at the state of fasting or postprandially. In the study the content of mineral and heavy metal elements in VR4® capsules has been evaluated. Conclusion Volten VR4® Kaempferia parviflora extract is safe to be consumed at a single dose of 400 mg. The study also has shown that the participants are free from adverse reactions and hypoglycaemia.

Evaluating the Effect of Volten VR4® Kaempferia parviflora Extracts on Blood Glucose Levels in Human Type-2 Diabetes Mellitus and Healthy Individual: A Case-Control Study

Background: Volten VR4® capsules contain extract of Kaempferia parviflora (KP), which has been claimed to reduce blood glucose in patients with diabetes. Objective: To evaluate the efficacy of Volten VR4® on healthy individuals and Type-2 Diabetes Mellitus volunteers. Materials and Methods: The extracts of 400 mg capsules of KP were consumed for five days. The fasting and blood glucose levels of 2-hour postprandial were measured at baseline and day 5. A group of 15 healthy young adults between the age of 20- and 30-years old were the control group of the present study, while 12 volunteers aged 35 to 75 years old diagnosed with Type-2 Diabetes Mellitus constituted the experimental group. Data were validated through the Willcoxon and Friedman test statistics and error distribution. Results: It had been shown that the specificity of KP reduced blood glucose levels and has associated with the flavonoids and polymethoxyflavones components. The results showed that consuming VR4® capsules significantly reduced blood glucose, either at the state of fasting or postprandially in diabetic individual. Conclusion: Volten VR4® Kaempferia parviflora extract is safe to be consumed at 400 mg at one time. The study also has shown that the participants are free from adverse reactions and hypoglycaemia. Keywords: Kaempferia parviflora; Blood glucose; Type-2 Diabetes Mellitus; Flavonoids; Polymethoxyflavones; Hypoglycemia and heavy metal elements

EDUKASI KESEHATAN REPRODUKSI MENGGUNAKAN MEDIA FILM PADA REMAJA PUTUS SEKOLAH DI PUSKESMAS SITOPENG KOTA CIREBON TAHUN 2019EDUKASI KESEHATAN REPRODUKSI MENGGUNAKAN MEDIA FILM PADA REMAJA PUTUS SEKOLAH DI PUSKESMAS SITOPENG KOTA CIREBON TAHUN 2019

PROVISION OF REPRODUCTIVE HEALTH EDUCATION USING MOVIES AMONG SCHOOL DROP OUT ADOLESCENTS IN SITOPENG HEALTH CENTER OF CIREBON CITY IN 2019 ABSTRACT Background: Adolescent reproductive health is a health promotion program that involves the adolescents’ reproductive systems, functions and processes. Adolescents are a potential group that needs serious attention. In addition, the proportion of the population of adolescents shows a fairly large number. Objective: To determine the effect of adolescent knowledge about reproductive health using movies among school drop outs in Sitopeng Health Center of Cirebon City in 2019. Methods: This quasi experimental study used a quantitative approach. Data were collected by conducting pre-tests and post-tests for 7 consecutive days regarding adolescent knowledge about reproductive health. Results: The mean pretest result score of the subjects’ knowledge about reproductive health was 4.03 with a standard deviation of 1.47 and a score range of 1-6. The mean knowledge from posttest to the 7 th day increased. Friedman test statistic results revealed that there was an increase in the score of knowledge until the 7 th day with a pvalue of <0.001. From the results of Wilcoxon Signed Rank Test analysis, it can be concluded that after intervention, the most significant increase in the knowledge scores between pretest and posttest was in day 4, 5, 6 and 7. Recommendation: Health center is advised to form adolescent classes to increase knowledge about reproductive health and use short movies in providing reproductive health education. Keywords: movies, reproductive health.

ANALISIS PENGARUH AKREDITASI PROGRAM STUDI TERHADAP INTENSITAS BELAJAR DAN HARAPAN MASA DEPAN (Studi Kasus di Fakultas Sains dan Teknologi UIN Walisongo Semarang)

The quality of a study program is assessed from the results of accreditation. Accreditation is also one of the requirements in applying for a job in a public or private institution. The hope is that the results of university accreditation will be satisfactory when students graduate from the college. With the Friedman test statistic, it can be seen the effect of the study program accreditation in the Faculty of Science and Technology on the learning intensity and future expectations in this study. It turned out that descriptively, the A study program's accreditation motivated students to study diligently and students really hoped to get a job or reputable college for further studies. In contrast, the students from study programs are accredited B, and C have medium and low learning intensity. Their hopes of getting a good job or place of further study are almost ordinary or almost nonexistent.

PENGARUH PENAMBAHAN TEPUNG SUKUN (Artocarpus communis), PISANG HIJAU (Musa paradisiaca L.), COKLAT (Theobroma cacao L.) DAN KURMA (Phoenix dactylifera) TERHADAP DAYA TERIMA DAN NILAI KARBOHIDRAT EGG ROLL

Carbohydrates have an important role for endurance athletes to replenish glycogen in muscle and liver that had been used during muscle contraction. This research aims to analyze the effect of adding breadfruit flour (Artocarpus communis), green banana (Musa paradisiaca L.), dates (Phoenix dactylifera) and chocolate (Theobroma cacao L.) toward the acceptance and carbohydrate content of egg roll as an alternative snack for endurance athletes. This research use True Experimental Research, completely randomized design with four formula and repeated four times for each formula. Panelist in this study consist of 30 athletes of Local Training Center, Indonesian National Sport Committee in East Java Region. Based on the test of acceptance on the modification of egg roll formula, the most preferred formula was F1 (breadfruit flour 150 g, chocolate 500 g, dates 150 g) with the highest mean rank values were on color (2.65) and flavor (2.70), while the aroma and texture aspect had the lower mean rank (2.50) each compared to F0 (2.87 and 2.58). The result of Friedman Test statistic on all characteristics of the acceptability include color, aroma, texture and flavor found there was not significant diffrence on the acceptance of egg roll (p>0.05). The highest carbohydrate content was F1 (59.4/100 g). Based on the best acceptance value and the highest carbohydrate content, it was conclude that the optimal formula was F1. Total egg roll that should be consumed by the athletes before sport was 125 grams (12 sticks egg roll) and 60-95 grams (6-8 sticks egg roll) for after sport

Statistically tested comparisons of the accuracy of forecasting methods for age-specific and sex-specific mortality and life expectancy

Although there are continuing developments in the methods for forecasting mortality, there are few comparisons of the accuracy of the forecasts. The subject of the statistical validity of these comparisons, which is essential to demographic forecasting, has all but been ignored. We introduce Friedman's test statistics to examine whether the differences in point and interval forecast accuracies are statistically significant between methods. We introduce the Nemenyi test statistic to identify which methods give results that are statistically significantly different from others. Using sex-specific and age-specific data from 20 countries, we apply these two test statistics to examine the forecast accuracy obtained from several principal component methods, which can be categorized into coherent and non-coherent forecasting methods.

Effects of Religious Tourists on Rural Development of Rural Settlements from the Perspective (Case Study: Nodeh-e-Enghelab Village in Khushab County)

Purpose: Religious beliefs of the distant past, had a major role in the establishment and development of human settlements. In order to earn religious tourism and the preservation of cultural heritage is taken into consideration. This paper attempts to influence of presence of religious tourists on the development of rural settlements must be examined from the perspective of the villagers. Methodology: Research methods in this study, the target application and the method is analytical. The research community, including the f households of the Novdeh-e-Enghelab Village, shoots the census of 2011, with 1050 households and 3469 people are, Cochran formula required sample size was 165 households. Finding: Presence of religious tourists in rural areas in the field of social and cultural were most affected by the development of rural settlement has left out 3.4. In addition, Friedman test statistic shows that this index is 3.24 for the villager's highest priority. Research limitation: One of the main challenges in this study is to access the information of religious tourists. Practical implications: Based on the findings, suggestions and advertising tourist attractions include Shrine of Ibrahim (AS), the provision of space for parking and accommodations, in compliance with the Privacy religious monument wall of green space, coordination of services in the field of tourism organizations, etc. have been proposed. Original/value: This study is important in the sense that possible to detect traces of religious tourism, rural development fields provided.

Improving the efficiency of the cardiac catheterization laboratories through understanding the stochastic behavior of the scheduled procedures

In this study, we sought to analyze the stochastic behavior of Catherization Laboratories (Cath Labs) procedures in our institution. Statistical models may help to improve estimated case durations to support management in the cost-effective use of expensive surgical resources. We retrospectively analyzed all the procedures performed in the Cath Labs in 2012. The duration of procedures is strictly positive (larger than zero) and has mostly a large minimum duration. Because of the strictly positive character of the Cath Lab procedures, a fit of a lognormal model may be desirable. Having a minimum duration requires an estimate of the threshold (shift) parameter of the lognormal model. Therefore, the 3-parameter lognormal model is interesting. To avoid heterogeneous groups of observations, we tested every group-cardiologist-procedure combination for the normal, 2- and 3-parameter lognormal distribution. The total number of elective and emergency procedures performed was 6,393 (8,186 h). The final analysis included 6,135 procedures (7,779 h). Electrophysiology (intervention) procedures fit the 3-parameter lognormal model 86.1% (80.1%). Using Friedman test statistics, we conclude that the 3-parameter lognormal model is superior to the 2-parameter lognormal model. Furthermore, the 2-parameter lognormal is superior to the normal model. Cath Lab procedures are well-modelled by lognormal models. This information helps to improve and to refine Cath Lab schedules and hence their efficient use.

Model Selection by Friedman Statistics

This study investigates an application of Friedman test statistic as a model selection methodology on post estimation data. Although there are various model selection criteria, their main focus is to fit the model tothe estimation data. Some of these criteria are appropriate for nested model selection while the rest is suitable for non -nested model selection. The suggested model selection methodology is indifferent to the distinction between nested or non -nested modelselections. In suggested methodology, the dataset are sub divided into two parts: First part is used to estimate all the competing models while the rest are used for performance comparison of competing models. In this respect, all competing models are ran ked according to their forecast performance based on proximity between observed and estimated values of the dependent variable in post estimation data. Then, we showed that the suitability of Friedman test statistic in order to evaluate the prediction perf ormance of competing models.

Nonparametric statistics for non-statisticians: a step-by-step approach

Preface. 1 Nonparametric Statistics: An Introduction. 1.1 Objectives. 1.2 Introduction. 1.3 The Nonparametric Statistical Procedures Presented in this Book. 1.4 Ranking Data. 1.5 Ranking Data with Tied Values. 1.6 Counts of Observations. 1.7 Summary. 1.8 Practice Questions. 1.9 Solutions to Practice Questions. 2 Testing Data for Normality. 2.1 Objectives. 2.2 Introduction. 2.3 Describing Data and the Normal Distribution. 2.4 Computing and Testing Kurtosis and Skewness for Sample Normality. 2.5 The Kolmogorov-Smirnov One-Sample Test. 2.6 Summary. 2.7 Practice Questions. 2.8 Solutions to Practice Questions. 3 Comparing Two Related Samples: The Wilcoxon Signed Ranks Test. 3.1 Objectives. 3.2 Introduction. 3.3 Computing the Wilcoxon Signed Ranks Test Statistic. 3.4 Examples from the Literature. 3.5 Summary. 3.6 Practice Questions. 3.7 Solutions to Practice Questions. 4 Comparing Two Unrelated Samples: The Mann-Whitney U -Test. 4.1 Objectives. 4.2 Introduction. 4.3 Computing the Mann-Whitney U -Test Statistic. 4.4 Examples from the Literature. 4.5 Summary. 4.6 Practice Questions. 4.7 Solutions to Practice Questions. 5 Comparing More Than Two Related Samples: The Friedman Test. 5.1 Objectives. 5.2 Introduction. 5.3 Computing the Friedman Test Statistic. 5.4 Examples from the Literature. 5.5 Summary. 5.6 Practice Questions. 5.7 Solutions to Practice Questions. 6 Comparing More than Two Unrelated Samples: The Kruskal-Wallis H -Test. 6.1 Objectives. 6.2 Introduction. 6.3 Computing the Kruskal-Wallis H -Test Statistic. 6.4 Examples from the Literature. 6.5 Summary. 6.6 Practice Questions. 6.7 Solutions to Practice Questions. 7 Comparing Variables of Ordinal or Dichotomous Scales: Spearman Rank-Order, Point-Biserial, and Biserial Correlations. 7.1 Objectives. 7.2 Introduction. 7.3 The Correlation Coefficient. 7.4 Computing the Spearman Rank-Order Correlation Coefficient. 7.5 Computing the Point-Biserial and Biserial Correlation Coefficients. 7.6 Examples from the Literature. 7.7 Summary. 7.8 Practice Questions. 7.9 Solutions to Practice Questions. 8 Tests for Nominal Scale Data: Chi-Square and Fisher Exact Test. 8.1 Objectives. 8.2 Introduction. 8.3 The Chi-Square Goodness-of-Fit Test. 8.4 The Chi-Square Test for Independence. 8.5 The Fisher Exact Test. 8.6 Examples from the Literature. 8.7 Summary. 8.8 Practice Questions. 8.9 Solutions to Practice Questions. 9 Test For Randomness: The Runs Test. 9.1 Objectives. 9.2 Introduction. 9.3 The Runs Test for Randomness. 9.4 Examples from the Literature. 9.5 Summary. 9.6 Practice Questions. 9.7 Solutions to Practice Questions. Appendix A: SPSS at a Glance. A.1 Introduction. A.2 Opening SPSS. A.3 Inputting Data. A.4 Analyzing Data. A.5 The SPSS Output. Appendix B: Tables of Critical Values. Table B.1: The Normal Distribution. Table B.2: The Chi-Square Distribution. Table B.3: Critical Values for the Wilcoxon Signed Ranks Test Statistics, T . Table B.4: Critical Values for the Mann-Whitney U -Test Statistic. Table B.5: Critical Values for the Friedman Test Statistic, F r . Table B.6: The Critical Values for the Kruskal-Wallis H -Test Statistic. Table B.7: Critical Values for the Spearman Rank-Order Correlation Coefficient, r s . Table B.8: Critical Values for the Pearson Product-Moment Correlation Coefficient, r. Table B.9: Factorials. Table B.10: Critical Values for the Runs Test for Randomness. Bibliography. Index.

Uterine Activity in Women Receiving 17 α-Hydroxyprogesterone Caproate for the Prevention of Preterm Birth: An Observational Study

We evaluated uterine contraction frequency in women receiving 17 alpha-hydroxyprogesterone caproate (17-OHP-C) for the prevention of preterm delivery. Women with singleton pregnancies and receiving weekly 17-OHP-C and outpatient tococardiography were identified from a database. The mean and maximum contraction frequencies per hour were compared from 3 days before to 3 days after 17-OHP-C dosing. McNemar chi(2), Mann-Whitney U, and Friedman test statistics were used for analysis. Data were obtained from 388 women. Median contraction frequency was greater for women with subsequent preterm birth versus those delivering at term (1.5 [range 0, 14.5] versus 1.2 [range 0, 21.0] contractions per hour, P < 0.001). No reduction in contraction frequency was observed after 17-OHP-C administration, and in fact, the converse was observed for the average contractions 3 days prior compared with 3 days posttreatment ( P < 0.001). In the subgroup of women with a subsequent spontaneous preterm, the proportion who had an average contraction frequency of more than five per hour 1 day preinjection versus 1 day postinjection was not significantly different (2.6% versus 3.0%, P = 1.0). Administration of 17-OHP-C was not associated with a reduction in contraction frequency. To be effective, this drug likely has effects by mechanisms other than tocolysis. Although a statistically significant increase in contractions was identified posttherapy versus pretherapy, the clinical importance of this observation is unknown.

A Modification on the Friedman Test Statistic

A modification on the well-known, nonparametric Friedman test statistic is suggested in this article. Probability distributions of the suggested test statistic under the null hypothesis are tabulated for some small sample cases. In addition to an example, simulation results for various sample sizes are presented. The simulation indicates that the modified test statistic performs better than the Friedman test in detecting treatment effects of small differences especially when the sample size is small.

Application Of Principal Component Estimators To A Simultaneous Equation Model Of Nigerian Economy

Six instrumental variable estimators are used to obtain consistent estimates of the structural parameters of a model developed for Nigeria economy called MAC III model. The performances of the estimators were ranked using Friedman test statistics based on four criteria namely: Root Mean Square Error (RMSE), Theils inequality coefficients, Bias and variance proportions. The result of this ranking show that the six (6) estimators rank differently or vary in performances. Based on this study, the preference ordering of the estimators is: 2SP1C4, 2SP2C4, 2SP1C5, 2SP2C5, 2SP2C6 and 2SP1C6. KEY WORDS: Principal Component, Simultaneous, Model, Economy. Global Journal of Pure and Applied Sciences Vol.11(1) 2005: 113-119

The analysis of ranked data in blocked factorial experiments

A non-parametric method for the analysis of blocked factorial experiments, based on ranking within blocks, is proposed and shown to be equivalent to partitioning Friedman's test statistic into a set of contrasts reflecting polynomial components of the main effects and interaction. A slightly modified version of the procedure is suggested to partially overcome the problem of loss of power to detect one component when the model includes other components. This alternative procedure is shown to be equivalent to applying a standard normal theory analysis of variance to the ranks. The null distributions and power comparisons are investigated using simulation methods, and it is shown that the non-parametric methods are almost as powerful as the analysis of variance.

Using common statistical program packages for the friedman test when there are ties among treatments and a multiple comparison procedure is needed

It is investigated which form of the Friedman test statistic is implemented in the statistical program packages BMDP, SAS, SPSS, and STATGRAPHICS. Special attention is focused on the handling of ties and whether a multiple comparison procedure (MCP) is available. As none of the considered software systems offer both, namely adjustment for ties and an MCP, two SAS/IML modules are proposed, which use the formula given by CONOVER (1980) for computing the Friedman test statistic with adjustment for ties and the sequentially rejective test procedure of HOLM (1979) for performing smultiple comparisons.

Prediction of environmental availability of cadmium from ash morphology

Morphologies of ash from six different sources were examined and characterized by secondary electron imaging using the JOEL Model JSM 6100 scanning electron microscope. Ash sources included an aluminum smelter, conventional lignite electrical generating plant, fluidized bed lignite electrical generating plant, municipal refuse incineration, sewage sludge incineration, and household wood stove. These characterized morphologies were ranked by their estimated volume to surface area ratio, and their rankings were tested nonparametrically against rankings derived from reported pozzolana‐induced reductions (prior to steady‐state and at steady‐state conditions) in the environmental availability of cadmium. The null hypothesis tested was that there was no predictability in the rankings by these three criteria. The Friedman test statistic value was 9.333 and the probability of a type I error was equal to 0.096. The null hypothesis was rejected, with the logical conclusion that the rankings vary predictably. This p...

A Multiple Comparisons Procedure for Use in Conjunction with the Benard-van Elteren Test

SUMMARY The Benard-van Elteren test statistic is a generalization of the Friedman test statistic that permits multiple and unequal replicates per treatment per block. A multiple comparisons procedure for pairwise comparisons of treatments is developed for use in conjunction with the Benard-van Elteren test. This procedure is applied to an example arising from a clinical trial. Sufficient conditions for use of this multiple comparisons procedure are given, with examples of designs for which these conditions are met. This multiple comparisons procedure is shown to be identical to a procedure developed by Nemenyi (unpublished doctoral thesis, Princeton University, 1963; presented by Hollander and Wolfe, 1973, Nonparametric Statistical Methods, New York, Wiley) for the randomized complete block design with one replicate per treatment per block, and to a procedure given by Campbell (1980, in Proceedings of the American Statistical Association: Section on Statistical Education, 24-27) for the balanced incomplete block design.