I need to do a cell chi square test, but googling availeth me not (I suspect because of all the pages about the cells in chi square discussions generally). How does one calculate this? Any good sources on it, or on it in R specifically?
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3$\begingroup$ What is the "cell" chi-squared test? $\endgroup$– gung - Reinstate MonicaCommented Jun 3, 2013 at 15:59
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$\begingroup$ It tests whether each cell is significantly different from its expected value in the overall table; I know SPSS does it, but I don't currently have access to SPSS, and I'm having trouble finding enough information that would let me recreate it. $\endgroup$– KrystaCommented Jun 3, 2013 at 16:01
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2$\begingroup$ To get an idea what the OP means, see here. $\endgroup$– COOLSerdashCommented Jun 3, 2013 at 16:24
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5$\begingroup$ @gung It collapses a larger table to a bunch of 2x2 chi-square tests (the cells [i,j]; [(i),j]; [i,(j)] and [(i),(j)]) - nothing more. (If you already have a 2x2 table, it's simply the ordinary 2x2 chisquare test repeated four times - about as pointless as things get) $\endgroup$– Glen_bCommented Jun 3, 2013 at 16:45
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5$\begingroup$ Regarding google, you might want to look for “partitioning chi-squared” for a similar idea and other material that might be relevant to your purpose. “Cell chi-square test” appears to be SPSS-specific terminology. Also relevant would be standardized residuals (cf. Agresti). $\endgroup$– GalaCommented Jun 3, 2013 at 19:18
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1 Answer
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As @Glen noted in the comments, the cell $\chi^{2}$-test simply calculates a bunch of $\chi^{2}$-tests on the collapsed 2x2 tables. It is fairly easy to implement in R:
# Example table
M <- as.table(rbind(c(762, 327, 468), c(484, 239, 477)))
dimnames(M) <- list(gender = c("M","F"),
party = c("Democrat","Independent", "Republican"))
M
party
gender Democrat Independent Republican
M 762 327 468
F 484 239 477
res.table <- matrix(NA, nrow=dim(M)[1], ncol=dim(M)[2])
dimnames(res.table) <- dimnames(M)
# Loop over all cells of the table
for ( i in 1:dim(M)[1] ) {
for ( j in 1:dim(M)[2] ) {
temp.table <- matrix(NA, 2, 2) # the collapsed 2x2 table
temp.table[1,1] <- M[i,j]
temp.table[1,2] <- sum(M[-i, j], na.rm=TRUE)
temp.table[2,1] <- sum(M[i, -j], na.rm=TRUE)
temp.table[2,2] <- sum(M[-i, -j], na.rm=TRUE)
chi2 <- chisq.test(temp.table, correct=TRUE) # chi2-test with continuity correction
# Automatically choose significance level (see SPSS documentation)
sig.level <- ifelse(M[i,j] <= 300, 0.1,
ifelse(M[i,j] > 300 & M[i,j] <= 1000, 0.05,
ifelse(M[i,j] > 1000 & M[i,j] <= 4000, 0.025,
ifelse(M[i,j] > 4000 & M[i,j] <= 20000,0.005,0.001)
)
)
)
if ( chi2$p.value < sig.level ) {
res.table[i, j] <- paste(
chi2$observed[1],
ifelse(chi2$observed[1] < chi2$expected[1], "<", ">"),
round(chi2$expected[1], 2))
} else {
res.table[i, j] <- "n.s."
}
}
}
res.table
party
gender Democrat Independent Republican
M "762 > 703.67" "n.s." "468 < 533.68"
F "484 < 542.33" "n.s." "477 > 411.32"
answered Jun 3, 2013 at 17:19