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 evaluate differences between control and treatment groups. Returns a certainty metric (0-1) indicating separation likelihood rather than traditional p-values. Includes bootstrapped effect size bounds.

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.

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: Separation certainty (0-1)

• 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. 5, 2025, 7:27 p.m.