fuzzy.ttest {genefu} | R Documentation

## 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 <= w <= 1 and (w1[i] + w2[i]) < 1 for 1 <= i <= length(x), `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.

### 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.

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.

### 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.

### Author(s)

Benjamin Haibe-Kains

### 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)
    ## Not run:
    ## 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)

    ## End(Not run)

[Package genefu version 2.16.0 Index]