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

 NNS.ANOVA R Documentation

## NNS ANOVA

### 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

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

### 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. `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.

### 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 `"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" 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

``` ## 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)

### 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)

## End(Not run)
```

NNS documentation built on Nov. 4, 2022, 1:06 a.m.