Cross-tabulation with tests and measures of association

Builds a two-way table from labels (counting rows, summing a count column of an aggregate table, or counting distinct ids per cell) and gives Pearson's chi-square test, the likelihood-ratio test, Cramer's V with an interval and its bias-corrected form, the contingency coefficient, phi for a 2 x 2 table, the share on the diagonal (the rows whose label is also the column's, as a region at placement against the region now), and on request Fisher's exact test with, for a 2 x 2 table, the conditional odds ratio and its exact interval.

Usage

ctabx(
  row,
  col = NULL,
  w = NULL,
  agg = NULL,
  correct = FALSE,
  exact = FALSE,
  level = 0.95
)

Arguments

row: The row label of each record (a factor by its levels, text or numbers by their sorted values); or a whole table: a numeric matrix or 2-d table of counts, with col NULL; or a clpre list from clprep().
col: The column label of each record.
w: NULL, or the value of each record that agg combines into its cell: a count ("sum"), a measure ("max", "min", "mean"), or an id ("dist", the distinct ids per cell).
agg: How the records of a cell combine: "n" (count them, the default without w), "sum" (the default with w), "max", "min", "mean" or "dist". An empty cell is 0.
correct: TRUE for the continuity correction of a 2 x 2 chi-square, as stats::chisq.test()'s default; FALSE (here the default) for Pearson's statistic.
exact: TRUE for Fisher's exact test.
level: The confidence level of the intervals: one number strictly between 0 and 1.

Value

An object of class ctabx, a list: tab, the table (all labels); expd and res, the expected counts and Pearson residuals of the table without empty rows and columns; stat, a one-row data frame: n, chisq, df, p, g2, g2p (the likelihood-ratio statistic and its p-value), v, vlo, vhi, vbc (bias-corrected V), cc (the contingency coefficient), phi, diag, fp (Fisher's p-value), or, orlo, orhi; and drop, agg, correct and level.

Details

Rows or columns with no counts are dropped before the statistics (their number is drop), as an unused factor level carries no information; the table tab keeps them. Cramer's V is sqrt(chisq / (n (k - 1))), k the smaller dimension, from the uncorrected statistic even when correct is TRUE; its interval inverts the noncentral chi-square distribution, sqrt(ncp / (n (k - 1))), as the default of DescTools::CramerV(); the bias-corrected V is Bergsma's. The exact test enumerates every table with the observed margins and refuses one that would take more than 1e7 tables. With agg other than "n", "sum" or "dist" the table holds values, not counts, and the statistics are NA.

References

Agresti, A. (2013). Categorical Data Analysis, 3rd ed. Wiley. ISBN 978-0-470-46363-5.

Bergsma, W. (2013). A bias-correction for Cramer's V and Tschuprow's T. Journal of the Korean Statistical Society, 42(3), 323-328. doi:10.1016/j.jkss.2012.10.002

Examples

# force type by weapon, one row per incident
wp <- c("none", "none", "knife", "gun", "none", "knife", "gun", "none")
fc <- c("hands", "hands", "CEW", "firearm", "CEW", "hands", "firearm",
        "hands")
ctabx(wp, fc)
#> ctabx: 3 x 3 table (n), n = 8
#>       CEW firearm hands
#> gun     0       2     0
#> knife   1       0     1
#> none    1       0     3
#> chi-square 8.5 on 4 df, p = 0.07488723
#> Cramer's V 0.728869 [0, 1], bias-corrected 0.586302
# region at placement against region now: the diagonal share
ctabx(c("N", "N", "E", "W", "E"), c("N", "E", "E", "W", "E"))
#> ctabx: 3 x 3 table (n), n = 5
#>   E N W
#> E 2 0 0
#> N 1 1 0
#> W 0 0 1
#> chi-square 6.666667 on 4 df, p = 0.1545873
#> Cramer's V 0.8164966 [0, 1], bias-corrected 0.5773503
#> diagonal share 0.8
# a published aggregate table: sum its count column
d <- data.frame(race = c("A", "A", "B", "B"), sex = c("F", "M", "F", "M"),
                n = c(12, 40, 9, 51))
ctabx(d$race, d$sex, w = d$n, exact = TRUE)
#> ctabx: 2 x 2 table (sum), n = 112
#>    F  M
#> A 12 40
#> B  9 51
#> chi-square 1.192899 on 1 df, p = 0.2747455
#> Cramer's V 0.1032031 [0, 0.2883748], bias-corrected 0.04070387
#> Fisher's exact p = 0.3348875