NNS (version 0.5.6)

NNS.ANOVA: 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,
  binary = 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 when (binary = TRUE). 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 (defualt) Returns pairwise certainty tests when set to pairwise = TRUE.

plot

logical; TRUE (default) Returns the boxplot of all variables along with grand mean identification. When (binary = TRUE), returns the boxplot of both variables along with grand mean identification and confidence interval thereof.

binary

logical; TRUE (default) Selects binary analysis between a control and treatment variable.

Value

For (binary = FALSE) returns the degree certainty the difference in sample means is zero [0, 1].

For (binary = TRUE) returns:

• "Control Mean"

• "Treatment Mean"

• "Grand Mean"

• "Control CDF"

• "Treatment CDF"

• "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

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)
# }