genefu (version 2.4.2)

fuzzy.ttest: Function to compute the fuzzy Student t test based on weighted mean and weighted variance

Description

This function allows for computing the weighted mean and weighted variance of a vector of continuous values.

Usage

fuzzy.ttest(x, w1, w2, alternative=c("two.sided", "less", "greater"), 
check.w = TRUE, na.rm = FALSE)

Arguments

x

an object containing the observed values.

w1

a numerical vector of weights of the same length as x giving the weights to use for elements of x in the first class.

w2

a numerical vector of weights of the same length as x giving the weights to use for elements of x in the second class.

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.

check.w

TRUE if weights should be checked such that 0 <= 1="" w="" <="1" and="" (w1[i]="" +="" w2[i])="" for="" FALSE otherwise. Beware that weights greater than one may inflate over-optimistically resulting p-values, use with caution.

na.rm

TRUE if missing values should be removed, FALSE otherwise.

Value

• A numeric vector of six values that are the difference between the two weighted means, the value of the t statistic, the sample size of class 1, the sample size of class 2, the degree of freedom and the corresponding p-value.

Details

The weights w1 and w2 should represent the likelihood for each observation stored in x to belong to the first and second class, respectively. Therefore the values contained in w1 and w2 should lay in [0,1] and 0 <= (w1[i]="" +="" w2[i])="" <="1" for="" i="" in="" {0,1,...,n}="" where="" n="" is="" the="" length="" of="" x.<="" p="">

The Welch's version of the t test is implemented in this function, therefore assuming unequal sample size and unequal variance. The sample size of the first and second class are calculated as the sum(w1) and sum(w2), respectively.

References

http://en.wikipedia.org/wiki/T_test

See Also

weighted.mean

Examples

set.seed(54321)
## random generation of 50 normally distributed values for each of the two classes
xx <- c(rnorm(50), rnorm(50)+1)
## fuzzy membership to class 1
ww1 <- runif(50) + 0.3
ww1[ww1 > 1] <- 1
ww1 <- c(ww1, 1 - ww1)
## fuzzy membership to class 2
ww2 <- 1 - ww1
## Welch's t test weighted by fuzzy membership to class 1 and 2 
wt <- fuzzy.ttest(x=xx, w1=ww1, w2=ww2)
print(wt)
## permutation test to compute the null distribution of the weighted t statistic
wt <- wt[2]
rands <- t(sapply(1:1000, function(x,y) { return(sample(1:y)) }, y=length(xx)))
randst <- apply(rands, 1, function(x, xx, ww1, ww2) 
{ return(fuzzy.ttest(x=xx, w1=ww1[x], w2=ww2[x])[2]) }, xx=xx, ww1=ww1, ww2=ww2)
ifelse(wt < 0, sum(randst <= wt), sum(randst >= wt)) / length(randst)