Nothing

```
NNS.ANOVA.bin<- function(control, treatment, confidence.interval = NULL, tails = NULL, plot = TRUE){
mean.of.means <- mean(c(mean(control), mean(treatment)))
#Continuous CDF for each variable from Mean of Means
LPM_ratio.1 <- LPM.ratio(1, mean.of.means, control)
LPM_ratio.2 <- LPM.ratio(1, mean.of.means, treatment)
#Continuous CDF Deviation from 0.5
MAD.CDF <- mean(c(abs(LPM_ratio.1 - 0.5), abs(LPM_ratio.2 - 0.5)))
#Certainty associated with samples
NNS.ANOVA.rho <- (0.5 - MAD.CDF) ^ 2 / 0.25
#Graphs
if(plot){
boxplot(list(control, treatment), las = 2, names = c("Control", "Treatment"),
xlab = "Means", horizontal = TRUE, main = "NNS ANOVA and Effect Size",
col = c("grey", "white"),
cex.axis = 0.75)
#For ANOVA Visualization
abline(v = mean.of.means, col = "red", lwd = 4)
mtext("Grand Mean", side = 3, col = "red", at = mean.of.means)}
if(is.null(confidence.interval)){
return(list("Control Mean" = mean(control),
"Treatment Mean" = mean(treatment),
"Grand Mean" = mean.of.means,
"Control CDF" = LPM_ratio.1,
"Treatment CDF" = LPM_ratio.2,
"Certainty" = NNS.ANOVA.rho))}
if(!is.null(confidence.interval)){
#Upper end of CDF confidence interval for control mean
if(tails == "Both"){
CI = confidence.interval+(1-confidence.interval)/2
}
if(tails == "Left" | tails == "Right") {
CI = confidence.interval
}
a = UPM.VaR(CI, 1, control)
b = mean(control)
if(plot){
if(tails == "Both" | tails == "Right"){
abline(v = max(a, b), col = "green", lwd = 4, lty = 3)
text(max(a, b), pos = 2, 0.75, "mu+", col = "green")
text(max(a, b), pos = 4, 0.75, paste0((1 - CI) * 100, "% --->"), col = "green")}
}
#Lower end of CDF confidence interval for control mean
c = LPM.VaR(CI, 1, control)
d = mean(control)
if(plot){
if(tails == "Both" | tails == "Left"){
abline(v = min(c, d), col = "blue", lwd = 4, lty = 3)
text(min(c, d), pos = 4, 0.75, "mu-", col = "blue")
text(min(c, d), pos=2, 0.75, paste0( "<--- ", (1 - CI) * 100, "%"), col = 'blue')}
}
#Effect Size Lower Bound
if(tails == "Both"){
Lower.Bound.Effect = min(mean(treatment) - max(a, b), 0)
}
if(tails == "Left"){
Lower.Bound.Effect = min(mean(treatment) - max(c, d), 0)
}
if(tails == "Right"){
Lower.Bound.Effect = min(mean(treatment) - max(a, b), 0)
}
#Effect Size Upper Bound
if(tails == "Both"){
Upper.Bound.Effect = max(mean(treatment) - min(c, d), 0)
}
if(tails == "Left"){
Upper.Bound.Effect = max(mean(treatment) - min(c, d), 0)
}
if(tails == "Right"){
Upper.Bound.Effect = max(mean(treatment) - min(a, b), 0)
}
#Certainty Statistic and Effect Size Given Confidence Interval
return(list("Control Mean" = mean(control),
"Treatment Mean" = mean(treatment),
"Grand Mean" = mean.of.means,
"Control CDF" = LPM_ratio.1,
"Treatment CDF" = LPM_ratio.2,
"Certainty" = NNS.ANOVA.rho,
"Lower Bound Effect" = Lower.Bound.Effect,
"Upper Bound Effect" = Upper.Bound.Effect))
}
}
```

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