NNS.ANOVA: NNS ANOVA

In NNS: Nonlinear Nonparametric Statistics

NNS ANOVA

Description

Analysis of variance (ANOVA) based on lower partial moment CDFs for multiple variables, evaluated at multiple quantiles (or means only). Returns a degree of certainty to whether the population distributions (or sample means) are identical, not a p-value.

Usage

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

Arguments

control	a numeric vector, matrix or data frame, or list if unequal vector lengths.
treatment	NULL (default) a numeric vector, matrix or data frame.
means.only	logical; FALSE (default) test whether difference in sample means only is zero.
medians	logical; FALSE (default) test whether difference in sample medians only is zero. Requires means.only = TRUE.
confidence.interval	numeric [0, 1]; The confidence interval surrounding the control mean, defaults to (confidence.interval = 0.95).
tails	options: ("Left", "Right", "Both"). tails = "Both"(Default) Selects the tail of the distribution to determine effect size.
pairwise	logical; FALSE (default) Returns pairwise certainty tests when set to pairwise = TRUE.
plot	logical; TRUE (default) Returns the boxplot of all variables along with grand mean identification and confidence interval thereof.
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 the following:

• "Control Mean" control mean.

• "Treatment Mean" treatment mean.

• "Grand Mean" mean of means.

• "Control CDF" CDF of the control from the grand mean.

• "Treatment CDF" CDF of the treatment from the grand mean.

• "Certainty" the certainty of the same population statistic.

• "Lower Bound Effect" and "Upper Bound Effect" the effect size of the treatment for the specified confidence interval.

• "Robust Certainty Estimate" and "Lower 95 CI", "Upper 95 CI" are the robust certainty estimate and its 95 percent confidence interval after permutations if robust = TRUE.

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 Oct. 14, 2024, 5:09 p.m.