Description Usage Arguments Details Value Author(s) References See Also Examples
This function allows for computing the weighted mean and weighted variance of a vector of continuous values.
1 2  fuzzy.ttest(x, w1, w2, alternative=c("two.sided", "less", "greater"),
check.w = TRUE, na.rm = FALSE)

x 
an object containing the observed values. 
w1 
a numerical vector of weights of the same length as 
w2 
a numerical vector of weights of the same length as 
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 

na.rm 

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.
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 pvalue.
Benjamin HaibeKains
http://en.wikipedia.org/wiki/T_test
weighted.mean
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21  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)

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diff t.value n1 n2 df p.value
0.46562992 2.10753749 50.00000000 50.00000000 97.37120588 0.03763985
t.value
0.001
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