Nonparametric One-Way ANOVA Task

About the Nonparametric One-Way ANOVA Task

The Nonparametric One-Way ANOVA task consists of nonparametric tests for location and scale differences across a one-way classification. The task also provides a standard analysis of variance on the raw data and statistics based on the empirical distribution function.

Example: Wilcoxon Scores for MPG_Highway Classified by Origin

To create this example:
  1. In the Tasks section, expand the Statistics folder and double-click Nonparametric One-Way ANOVA. The user interface for the Nonparametric One-Way ANOVA task opens.
  2. On the Data tab, select the SASHELP.CARS data set.
  3. Assign columns to these roles:
    Role
    Column Name
    Dependent variable
    MPG_Highway
    Classification variable
    Origin
  4. To run the task, click Submit SAS code.
Distribution of Wilcoxon Scores for MPG_Highway

Assigning Data to Roles

To run the Nonparametric One-Way ANOVA task, you must assign columns to the Dependent variable and Classification variable roles.
Role Name
Description
Roles
Dependent variable
specifies the column to use as the dependent variable.
Classification variable
defines the subgroups. Separate analyses are performed for each subgroup. You can specify whether to treat missing values as a valid level.
Additional Roles
Frequency count
specifies that each row in the table is assumed to represent n observations. In this example, n is the value of the frequency count for that observation.
Group analysis by
sorts the table by these columns. The task performs analyses on each group.

Setting Options

Option Name
Description
Plots
By default, plots are included in the results. These plots are determined by the options that you select. Here are some of the plots that you can create:
  • By selecting the options in the Location Differences section, you can create a box plot of Wilcoxon scores, a stacked bar chart showing frequencies above or below the overall median, a box plot of Van der Waerden scores, and a box plot of Savage scores.
  • By selecting the options in the Scale Differences section, you can create a box plot of Ansari-Bradley scores, a box plot of Klotz scores, a box plot of Mood scores, and a box plot of Siegel-Tukey scores.
  • By selecting the options in the Location and Scale Differences section, you can create a box plot of Conover scores.
  • By selecting the Empirical distribution function tests, including Kolmogorov-Smirnov and Cramer-von Mises tests option, you can create a plot of the empirical distribution test.
You can specify whether to display the p-values in the plot.
To suppress the plots from the results, select the Suppress plots check box.
Tests
Tests
specifies whether to calculate only the asymptotic tests or both the asymptotic tests and exact tests for the various analyses.
Location Differences
Wilcoxon scores
ranks of the observations.
Median scores
equals 1 for observations greater than the median and 0 otherwise.
Van der Waerden scores
the quantiles of a standard normal distribution. These scores are also known as quantile normal scores.
Savage scores
the expected values of order statistics from the exponential distribution with 1 subtracted to center the scores around 0.
Scale Differences
Ansari-Bradley scores
similar to the Siegel-Tukey scores, but assigns the same scores to corresponding extreme ranks.
Klotz scores
the squares of the Van der Waerden (or quantile normal) scores.
Mood scores
the square of the difference between each rank and the average rank.
Siegel-Tukey scores
scores are computed as eh open 1 close equals 1 comma eh open n close equals 2 comma eh open n minus 1 close equals 3 comma eh open 2 close equals 4 comma eh open 3 close equals 5 comma eh open n minus 2 close equals 6 comma ... .
The score values continue to increase in this pattern toward the middle ranks until all observations are assigned a score.
Location and Scale Differences
Conover scores
based on the squared ranks of the absolution deviations from the sample means.
Empirical distribution function tests, including Kolmogorov-Smirnov and Cramer-von Mises tests
the empirical distribution function (EDF) statistics.
Pairwise multiple comparison analysis (asymptotic only)
computes the Dwass, Steel, Critchlow-Fligner (DSCF) multiple comparison analyses.
Methods
Continuity Correction
Continuity correction for two sample Wilcoxon and Siegel-Tukey tests
uses a continuity correction for the asymptotic two-sample Wilcoxon and Siegel-Tukey tests by default. The task incorporates this correction when computing the standardized test statistic z by subtracting 0.5 from the numerator open s minus , e sub 0 , open s close close if it is greater than zero. If the numerator is less than zero, the task adds 0.5.
Exact Statistics Computation
Use Monte Carlo estimation
requests the Monte Carlo estimation of the exact p-values instead of using the direct exact p-value computation. You can also specify the level of the confidence limits for the Monte Carlo p-value estimates.
Limit computation time
specifies the time limit for calculating each exact p-value. Calculating exact p-values can consume a large amount of time and memory.
Output Data Set
You can specify whether to save the statistics to a data set. By default, the data set is saved to the Work library.
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