chi2.stat | R Documentation |
Calculates the chi-squared test statistic for a two-way contingency table.
chi2.stat(tab)
tab |
A |
Suppose that tab
consists of counts from K
populations (rows) in C
categories. The chi-squared test statistic is computed as
\sum_{i=1}^K \sum_{j=1}^C (E_{ij} - O_{ij})^2/E_{ij},
where O_{ij}
is the observed number of counts in the i
th row and j
th column of tab
, and E_{ij}
is the expected number of counts under H_0
that the populations have indentical proportions in each category:
E_{ij} = \frac 1 N \sum_{i=1}^K O_{ij} \times \sum_{j=1}^C O_{ij}.
where N
is the total number of counts in tab
.
The calculated value of the chi-squared statistic.
# simple contingency table
ctab <- rbind(pop1 = c(5, 3, 0, 3),
pop2 = c(4, 10, 2, 5))
colnames(ctab) <- LETTERS[1:4]
ctab
chi2.stat(ctab) # chi^2 test statistic
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