Median test

About: Median test is a research topic. Over the lifetime, 357 publications have been published within this topic receiving 17453 citations.

Nonparametric Statistical Inference

Abstract: Introduction and Fundamentals Introduction Fundamental Statistical Concepts Order Statistics, Quantiles, and Coverages Introduction Quantile Function Empirical Distribution Function Statistical Properties of Order Statistics Probability-Integral Transformation Joint Distribution of Order Statistics Distributions of the Median and Range Exact Moments of Order Statistics Large-Sample Approximations to the Moments of Order Statistics Asymptotic Distribution of Order Statistics Tolerance Limits for Distributions and Coverages Tests of Randomness Introduction Tests Based on the Total Number of Runs Tests Based on the Length of the Longest Run Runs Up and Down A Test Based on Ranks Tests of Goodness of Fit Introduction The Chi-Square Goodness-of-Fit Test The Kolmogorov-Smirnov One-Sample Statistic Applications of the Kolmogorov-Smirnov One-Sample Statistics Lilliefors's Test for Normality Lilliefors's Test for the Exponential Distribution Anderson-Darling Test Visual Analysis of Goodness of Fit One-Sample and Paired-Sample Procedures Introduction Confidence Interval for a Population Quantile Hypothesis Testing for a Population Quantile The Sign Test and Confidence Interval for the Median Rank-Order Statistics Treatment of Ties in Rank Tests The Wilcoxon Signed-Rank Test and Confidence Interval The General Two-Sample Problem Introduction The Wald-Wolfowitz Runs Test The Kolmogorov-Smirnov Two-Sample Test The Median Test The Control Median Test The Mann-Whitney U Test and Confidence Interval Linear Rank Statistics and the General Two-Sample Problem Introduction Definition of Linear Rank Statistics Distribution Properties of Linear Rank Statistics Usefulness in Inference Linear Rank Tests for the Location Problem Introduction The Wilcoxon Rank-Sum Test and Confidence Interval Other Location Tests Linear Rank Tests for the Scale Problem Introduction The Mood Test The Freund-Ansari-Bradley-David-Barton Tests The Siegel-Tukey Test The Klotz Normal-Scores Test The Percentile Modified Rank Tests for Scale The Sukhatme Test Confidence-Interval Procedures Other Tests for the Scale Problem Applications Tests of the Equality of k Independent Samples Introduction Extension of the Median Test Extension of the Control Median Test The Kruskal-Wallis One-Way ANOVA Test and Multiple Comparisons Other Rank-Test Statistics Tests against Ordered Alternatives Comparisons with a Control Measures of Association for Bivariate Samples Introduction: Definition of Measures of Association in a Bivariate Population Kendall's Tau Coefficient Spearman's Coefficient of Rank Correlation The Relations between R and T E(R), tau, and rho Another Measure of Association Applications Measures of Association in Multiple Classifications Introduction Friedman's Two-Way Analysis of Variance by Ranks in a k x n Table and Multiple Comparisons Page's Test for Ordered Alternatives The Coefficient of Concordance for k Sets of Rankings of n Objects The Coefficient of Concordance for k Sets of Incomplete Rankings Kendall's Tau Coefficient for Partial Correlation Asymptotic Relative Efficiency Introduction Theoretical Bases for Calculating the ARE Examples of the Calculations of Efficacy and ARE Analysis of Count Data Introduction Contingency Tables Some Special Results for k x 2 Contingency Tables Fisher's Exact Test McNemar's Test Analysis of Multinomial Data Summary Appendix of Tables Answers to Problems References Index A Summary and Problems appear at the end of each chapter.

A wilcoxon-type test for trend

Abstract: An extension of the Wilcoxon rank-sum test is developed to handle the situation in which a variable is measured for individuals in three or more (ordered) groups and a non-parametric test for trend across these groups is desired. The uses of the test are illustrated by two examples from cancer research.

Statistics for Research

Abstract: Preface to the Third Edition. Preface to the Second Edition. Preface to the First Edition. 1. The Role of Statistics. 1.1 The Basic Statistical Procedure. 1.2 The Scientific Method. 1.3 Experimental Data and Survey Data. 1.4 Computer Usage. Review Exercises. Selected Readings. 2. Populations, Samples, and Probability Distributions. 2.1 Populations and Samples. 2.2 Random Sampling. 2.3 Levels of Measurement. 2.4 Random Variables and Probability Distributions. 2.5 Expected Value and Variance of a Probability Distribution. Review Exercises. Selected Readings. 3. Binomial Distributions. 3.1 The Nature of Binomial Distributions. 3.2 Testing Hypotheses. 3.3 Estimation. 3.4 Nonparametric Statistics: Median Test. Review Exercises. Selected Readings. 4. Poisson Distributions. 4.1 The Nature of Poisson Distributions. 4.2 Testing Hypotheses. 4.3 Estimation. 4.4 Poisson Distributions and Binomial Distributions. Review Exercises. Selected Readings. 5. Chi-Square Distributions. 5.1 The Nature of Chi-Square Distributions. 5.2 Goodness-of-Fit Tests. 5.3 Contingency Table Analysis. 5.4 Relative Risks and Odds Ratios. 5.5 Nonparametric Statistics: Median Test for Several Samples. Review Exercises. Selected Readings. 6. Sampling Distribution of Averages. 6.1 Population Mean and Sample Average. 6.2 Population Variance and Sample Variance. 6.3 The Mean and Variance of the Sampling Distribution of Averages. 6.4 Sampling Without Replacement. Review Exercises. 7. Normal Distributions. 7.1 The Standard Normal Distribution. 7.2 Inference From a Single Observation. 7.3 The Central Limit Theorem. 7.4 Inferences About a Population Mean and Variance. 7.5 Using a Normal Distribution to Approximate Other Distributions. 7.6 Nonparametric Statistics: A Test Based on Ranks. Review Exercises. Selected Readings. 8. Student's t Distribution. 8.1 The Nature of t Distributions. 8.2 Inference About a Single Mean. 8.3 Inference About Two Means. 8.4 Inference About Two Variances. 8.5 Nonparametric Statistics: Matched-Pair and Two-Sample Rank Tests. Review Exercises. Selected Readings. 9. Distributions of Two Variables. 9.1 Simple Linear Regression. 9.2 Model Testing. 9.3 Inferences Related to Regression. 9.4 Correlation. 9.5 Nonparametric Statistics: Rank Correlation. 9.6 Computer Usage. 9.7 Estimating Only One Linear Trend Parameter. Review Exercises. Selected Readings. 10. Techniques for One-way Analysis of Variance. 10.1 The Additive Model. 10.2 One-Way Analysis-of-Variance Procedure. 10.3 Multiple-Comparison Procedures. 10.4 One-Degree-of-Freedom Comparisons. 10.5 Estimation. 10.6 Bonferroni Procedures. 10.7 Nonparametric Statistics: Kruskal-Wallis ANOVA for Ranks. Review Exercises. Selected Readings. 11. The Analysis-of-Variance Model. 11.1 Random Effects and Fixed Effects. 11.2 Testing the Assumptions for ANOVA. 11.3 Transformations. Review Exercises. Selected Readings. 12. Other Analysis-of-Variance Designs. 12.1 Nested Design. 12.2 Randomized Complete Block Design. 12.3 Latin Square Design. 12.4 a xb Factorial Design. 12.5 a xb xc Factorial Design. 12.6 Split-Plot Design. 12.7 Split Plot with Repeated Measures. Review Exercises. Selected Readings. 13. Analysis of Covariance. 13.1 Combining Regression with ANOVA. 13.2 One-Way Analysis of Covariance. 13.3 Testing the Assumptions for Analysis of Covariance. 13.4 Multiple-Comparison Procedures. Review Exercises. Selected Readings. 14. Multiple Regression and Correlation. 14.1 Matrix Procedures. 14.2 ANOVA Procedures for Multiple Regression and Correlation. 14.3 Inferences About Effects of Independent Variables. 14.4 Computer Usage. 14.5 Model Fitting. 14.6 Logarithmic Transformations. 14.7 Polynomial Regression. 14.8 Logistic Regression. Review Exercises. Selected Readings. Appendix of Useful Tables. Answers to Most Odd-Numbered Exercises and All Review Exercises. Index.

Universal outlier detection for PIV data

Abstract: An adaptation of the original median test for the detection of spurious PIV data is proposed that normalizes the median residual with respect to a robust estimate of the local variation of the velocity. It is demonstrated that the normalized median test yields a more or less ‘universal’ probability density function for the residual and that a single threshold value can be applied to effectively detect spurious vectors. The generality of the proposed method is verified by the application to a large variety of documented flow cases with values of the Reynolds number ranging from 10−1 to 107.

Statistical methods in education and psychology

Abstract: 1 The Nature of Statistical Methods.- General Interest in Numbers.- The Purposes of Statistical Methods.- Preview of This Text.- Rounding, Significant Figures, and Decimals.- Supplement 1.- Rounding.- 2 Averages.- Raw Data.- The Mean Computed from Raw Data.- Grouping of Data.- The Mean Computed from Grouped Data.- The Median.- Choice of Mean or Median.- The Histogram and the Frequency Polygon.- Summary.- Supplement 2.- Other Averages.- Proof that Error Due to Grouping Is Small.- Cumulative Graphs.- Bar Diagrams.- 3 The Standard Deviation.- Need for a Measure of Variability.- Formula for the Standard Deviation.- Computing the Standard Deviation with Grouped Data.- Standard Deviation of a Finite Population.- Standard Scores.- Other Measures of Dispersion.- Summary.- Supplement 3.- How to Square Numbers.- Methods of Extracting Square Roots.- How to Check Square Roots.- How to Compute and Check the Standard Deviation.- Sheppard's Correction for Coarseness of Grouping.- Some Other Measures of Dispersion.- Types of Standard Scores.- 4 Normal Probability Curve.- The Nature of the Normal Probability Curve.- The Ordinates of the Normal Probability Curve.- Binomial Coefficients and the Normal Probability Curve.- Applications of the Binomial Coefficients.- The Area under the Normal Probability Curve.- Summary.- Supplement 4.- Simplifying the Equation for the Normal Curve.- Fitting a Normal Probability Curve to Any Frequency Distribution.- 5 Statistical Inference.- Dependability of Figures.- Speculation.- Samples and Populations.- Sampling Distributions and Standard Error of the Mean.- The t Test for Means.- Levels of Significance.- The z Test for Means.- Point and Interval Estimates.- Statistical Inference.- Sampling Distribution and Standard Error of the Median.- Sampling Distribution and Standard Error of the Standard Deviation.- Hypothesis Testing.- Summary.- Supplement 5.- Stability of the Median.- Standard Error of a Proportion.- 6 Percentiles and Percentile Ranks.- Percentiles.- Percentile Ranks.- Computation of Percentiles.- Percentiles and Percentile Ranks Compared.- Deciles.- Quartiles.- Standard Error of a Percentile.- Summary.- Supplement 6.- Method of Obtaining Percentile Ranks for Grouped Data.- Measures of Variability Based upon Percentiles.- The Range.- Relative Value of Measures of Variability.- 7 Skewness and Transformed Scores.- Skewness.- Kurtosis.- Transformed Scores.- The Description of Frequency Distributions.- Summary.- Supplement 7.- Additional Measures of Skewness and Kurtosis.- 8 Pearson Product Moment Coefficient of Correlation.- Definition of Pearson r.- Plotting a Scatter Diagram.- Illustrations of Pearson r's of Various Sizes.- Published Correlation Coefficients.- Some Characteristics of Pearson r.- Computing r Without Plotting the Data.- Plotting the Data and Computing r from the Scatter Diagram.- The z' Transformation and Its Standard Error.- Assumptions upon Which Pearson r Is Based.- Interpretation of Pearson r.- Summary.- Supplement 8.- Other Formulas for Pearson r.- Alternate Ways to Test the Significance of an Obtained Pearson r.- Reliability and Validity.- 9 Regression Equations.- The Purpose of a Regression Equation.- Formulas for Regression Equations.- The Use of Regression Equations.- The Graphic Representation of Prediction.- A Second Illustration of Regression Equations.- Further Interpretations of r.- Summary.- Supplement 9.- Making a Large Number of Predictions.- 10 More Measures of Correlation.- Why Other Correlations.- Biserial r.- Multiserial Correlation.- Point Biserial r.- Classification of Dichotomous Variables.- Tetrachoric r.- Phi.- Interrelations among rbis , rpb , rt, and ?.- Summary.- Supplement 10.- Cosine Pi Correlation Coefficient.- Rank Correlation Coefficient.- 11 Chi Square.- Nature of Chi Square.- Illustration of Correct Use of Chi Square.- Sources of Error in Chi Square.- Chi Square in the General Contingency Table.- The Exact Test of Significance in 2 x 2 Tables.- Use of Chi Square in Curve Fitting.- Advantages and Disadvantages of Chi Square.- Summary.- Supplement 11.- Unique Characteristics of Chi Square.- 12 Nonparametric Statistics Other than Chi Square.- The Purposes of Nonparametric Statistics.- The Sign Test.- The Runs Test.- The Median Test.- The Mann-Whitney U Test.- Which Nonparametric Statistic Should Be Used?.- Other Nonparametric Statistics.- Summary.- 13 Simple Analysis of Variance.- Why Not the t Test.- The Basis of Analysis of Variance.- A First Example.- Assumptions.- Checking.- Technicalities.- A Second Example.- Summary.- Supplement 13.- 14 Standard Errors of Differences.- Standard Error of Any Difference.- Standard Error of the Difference between Means.- Standard Error of the Difference between Standard Deviations.- The Standard Error of Other Differences.- Summary.- Supplement 14.- 15 Reorientation.- Moments.- Correlation.- Popular Concepts.- Future Courses.- Using Statistics.