NNS (version 11.1)

NNS.ANOVA: 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
)

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.

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.

Author

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" tools:::Rd_expr_doi("10.2139/ssrn.3007373")

Examples

 if (FALSE) {
### 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)
}