NNS.ANOVA {NNS}

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,
  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.

means.only

logical; FALSE (default) test whether difference in sample means only is zero.

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 "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" 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)