NNS.ANOVA: NNS ANOVA: Nonparametric Analysis of Variance

In NNS: Nonlinear Nonparametric Statistics

NNS ANOVA: Nonparametric Analysis of Variance

Description

Performs a distribution-free ANOVA using partial-moment statistics to assess differences between control and treatment groups. Depending on the setting of means.only, the procedure tests either differences in central tendency (means or medians) or differences across the full empirical distributions.

Usage

NNS.ANOVA(
  control,
  treatment,
  means.only = FALSE,
  medians = FALSE,
  confidence.interval = 0.95,
  tails = "Both",
  pairwise = FALSE,
  plot = TRUE,
  robust = FALSE
)

Arguments

control	Numeric vector of control group observations
treatment	Numeric vector of treatment group observations
means.only	Logical; FALSE (default) uses full distribution analysis. Set TRUE for mean-only comparison
medians	Logical; FALSE (default) uses means. Set TRUE for median-based analysis
confidence.interval	Numeric [0,1]; confidence level for effect size bounds (e.g., 0.95)
tails	Character; specifies CI tail(s): "both", "left", or "right"
pairwise	logical; FALSE (default) Returns pairwise certainty tests when set to pairwise = TRUE.
plot	Logical; TRUE (default) generates distribution plot
robust	logical; FALSE (default) Generates 100 independent random permutations to test results, and returns / plots 95 percent confidence intervals along with robust central tendency of all results for pairwise analysis only.

Details

The key output is the Certainty metric, a calibrated probability in [0, 1] representing the likelihood that the groups being compared are the *same* with respect to the chosen comparison mode:

• If means.only = TRUE: Certainty is the probability that the group means (or medians, if medians = TRUE) are the same.

• If means.only = FALSE: Certainty is the probability that the two entire distributions are the same.

This makes Certainty the conceptual inverse of a classical p-value. A *low* Certainty (e.g., < 0.10) indicates strong evidence of difference, while a *high* Certainty (e.g., > 0.90) indicates strong evidence of similarity.

Value

Returns a list containing:

• Control_Statistic: Mean/median of control group

• Treatment_Statistic: Mean/median of treatment group

• Grand_Statistic: Grand mean/median

• Control_CDF: CDF value at grand statistic (control)

• Treatment_CDF: CDF value at grand statistic (treatment)

• Certainty: Probability that the groups are the same (means-only or full distribution depending on means.only).

• Effect_Size_LB: Lower bound of treatment effect (if CI requested)

• Effect_Size_UB: Upper bound of treatment effect (if CI requested)

• Confidence_Level: Confidence level used (if CI requested)

Author(s)

Fred Viole, OVVO Financial Systems

References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)

Viole, F. (2017) "Continuous CDFs and ANOVA with NNS" \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2139/ssrn.3007373")}

Examples

 ## Not run: 
### Binary analysis and effect size
set.seed(123)
x <- rnorm(100) ; y <- rnorm(100)
NNS.ANOVA(control = x, treatment = y)

### Two variable analysis with no control variable
A <- cbind(x, y)
NNS.ANOVA(A)

### Medians test
NNS.ANOVA(A, means.only = TRUE, medians = TRUE)

### Multiple variable analysis with no control variable
set.seed(123)
x <- rnorm(100) ; y <- rnorm(100) ; z <- rnorm(100)
A <- cbind(x, y, z)
NNS.ANOVA(A)

### Different length vectors used in a list
x <- rnorm(30) ; y <- rnorm(40) ; z <- rnorm(50)
A <- list(x, y, z)
NNS.ANOVA(A)

## End(Not run)

NNS documentation built on Nov. 28, 2025, 5:09 p.m.