# NNS.ANOVA: NNS ANOVA In NNS: Nonlinear Nonparametric Statistics

## Description

Analysis of variance (ANOVA) based on lower partial moment CDFs for multiple variables. Returns a degree of certainty the difference in sample means is zero, not a p-value.

## Usage

 ```1 2 3 4 5 6 7 8``` ```NNS.ANOVA( control, treatment, confidence.interval = 0.95, tails = "Both", pairwise = FALSE, plot = TRUE ) ```

## Arguments

 `control` a numeric vector, matrix or data frame. `treatment` `NULL` (default) a numeric vector, matrix or data frame. `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.

## 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.

## Author(s)

Fred Viole, OVVO Financial Systems

## References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp

Viole, F. (2017) "Continuous CDFs and ANOVA with NNS" https://www.ssrn.com/abstract=3007373

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```### 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) ### 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) ```

NNS documentation built on June 26, 2021, 1:07 a.m.