Class MannWhitneyU

java.lang.Object
  MannWhitneyU

public class MannWhitneyU
extends java.lang.Object

MannWhitneyU - a Java utility to perform a Mann-Whitney U test on a table of data

The Mann-Whitney U test is a non-parametric statistical test used to assess the difference between two independent samples, which is to say, between two conditions assigned between-subjects. The relationship with other non-parametric tests is illustrated below:

The test operates on ordinal data, such as rankings or questionnaire responses (where the responses are non-linear). Interval or ratio-scale data can be used, however the Mann-Whitney U test (and other non-parametric tests) pre-process the data into ranks. If the researcher believes the ANOVA assumptions of normality and homogeneity of variances are violated to the extent that the ANOVA is inappropriate as a test instrument, then a non-parametric test is a reasonable alternative. However, as Sheskin notes, "when a researcher elects to transform a set of interval/ratio data into ranks, information is sacrificed" (Sheskin, 1996, p. 423). A simple and obvious example is the transformation of student marks A = 49, B = 79, and C = 80, into ranks 1, 2, and 3. Yes, something is sacrificed. Others have noted that the parametric ANOVA is robust and relatively unperturbed by violations in its assumptions (e.g., Lowry, Subchapter 14a in "Concepts and Applications of Inferential Statistics"; http://vassarstats.net/textbook/index.html). So, the choice of a non-parametric test, such as the Mann-Whitney U, should not be taken lightly if the data are ratio scale or interval scale.

Invocation (usage message if invoked without arguments):

Example. Consider an experiment seeking to determine if there is a difference in the political leaning of MAC users vs. PC users. Are MAC or PC users more likely to have political views leaning to the "left" or "right"? The experimenter randomly selects 10 MAC users and 10 PC users. The participants are interviewed and asked a variety of questions about their political leaning. Each participant is assessed on a 10-point linear scale (1 = very left, 10 = very right) with the results stored in a text file as a matrix with two columns. The first column contains the assessments for the MAC users, the second column for the PC users (see mannwhitneyu-ex1.txt). The data are then processed by the MannWhitneyU utility. For example,

For convenience, the test statistic U is converted to a z-score. This facilitates computing p. Since the customary threshold for statistical significance (p < .05) was not exceeded, the null hypothesis remains tenable, inferring a likelihood that the two samples are from the same population. We conclude there is no difference between the political leaning of MAC users and PC users.

The test also provides z' which is corrected for ties. The difference is usually minor.

StatView provides the following output using the data above:

Missing data. Since the design is between-subjects, it is sometimes difficult to have equal-size groups. For example, if two of the MAC participants do not show up for the interview, then there will be 8 participants in the MAC group and 10 participants in the PC group. This is accommodated by using periods (".") for missing data (see mannwhitneyu-ex2.txt). For example,

The conclusion is the same. Note that "equal sample sizes" is one assumption of the parametric ANOVA that, if violated, justifies using a non-parametric test, such as the Mann-Whitney U (see Lowry reference, cited above).

Author:

Scott MacKenzie, 2012-2014

Constructor Summary

MannWhitneyU(double[][] dataArg, boolean vOption)

Method Summary

double	getP1()
double	getP2()
double[]	getRanks(double[] d)
double	getU()
double	getZ1()
double	getZ2()
static void	main(java.lang.String[] args)

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

MannWhitneyU

public MannWhitneyU(double[][] dataArg,
                    boolean vOption)

Method Detail

main

public static void main(java.lang.String[] args)
                 throws java.io.IOException

Throws:

java.io.IOException

getU

public double getU()

getZ1

public double getZ1()

getZ2

public double getZ2()

getP1

public double getP1()

getP2

public double getP2()

getRanks

public double[] getRanks(double[] d)