Hello dear R help group.

My question is statistical and not R specific, yet I hope some of you might
be willing to help.

*Experiment settings*:  We have a list of subjects. each of them went
through two tests with the answer to each can be either 0 or 1.
*Goal*: We want to know if the two experiments yielded different results in
the subjects answers.
*Statistical test (and why it won't work)*: Naturally we would turn to
performing a mcnemar test. But here is the twist: we have missing values in
our data.
For our purpose, let's assume the missingnes is completely at random, and we
also have no data to use for imputation. Also, we have much more missing
data for experiment number 2 then in experiment number 1.

So the question is, under these settings, how do we test for experiment
effect on the outcome?

So far I have thought of two options:
1) To perform the test only for subjects that has both values. But they are
too scarce and will yield low power.
2) To treat the data as independent and do a pearson's chi square test
(well, an exact fisher test that is) on all the non-missing data that we
have. The problem with this is that our data is not fully independent (which
is a prerequisite to chi test, if I understood it correctly). So I am not
sure if that is a valid procedure or not.

Any insights will be warmly welcomed.


p.s: here is an example code producing this scenario.

set.seed(102)

x1 <- rbinom(100, 1, .5)
x2 <- rbinom(100, 1, .3)

X <- data.frame(x1,x2)
tX <- table(X)
margin.table(tX,1)
margin.table(tX,2)
mcnemar.test(tX)

put.missings <- function(x.vector, na.percent)
{
turn.na <- rbinom(length(x.vector), 1, na.percent)
 x.vector[turn.na == 1] <- NA
return(x.vector)
}


x1.m <- put.missings(x1, .3)
x2.m <- put.missings(x2, .6)

tX.m <- rbind(table(na.omit(x1.m)), table(na.omit(x2.m)))
fisher.test(tX.m)




With regards,
Tal









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