mcnemar_test_pv {DiscreteTests}

McNemar's Test for Count Data

Description

Performs McNemar's chi-square test or an exact variant to assess the symmetry of rows and columns in a 2-by-2 contingency table. In contrast to stats::mcnemar.test(), it is vectorised, only calculates p-values and offers their exact computation. Furthermore, it is capable of returning the discrete p-value supports, i.e. all observable p-values under a null hypothesis. Multiple tables can be analysed simultaneously. In two-sided tests, several procedures of obtaining the respective p-values are implemented. It is a special case of the binomial test.

Note: Please use mcnemar_test_pv()! The older mcnemar.test.pv() is deprecated in order to migrate to snake case. It will be removed in a future version.

Usage

mcnemar_test_pv(
  x,
  alternative = "two.sided",
  exact = TRUE,
  correct = TRUE,
  simple_output = FALSE
)

mcnemar.test.pv(
  x,
  alternative = "two.sided",
  exact = TRUE,
  correct = TRUE,
  simple.output = FALSE
)

Arguments

x

integer vector with four elements, a 2-by-2 matrix or an integer matrix (or data frame) with four columns where each line represents a 2-by-2 table to be tested.

alternative

character vector that indicates the alternative hypotheses; each value must be one of "two.sided" (the default), "less" or "greater".

exact

logical value that indicates whether p-values are to be calculated by exact computation (exact = TRUE; the default) or by a continuous approximation.

correct

logical value that indicates if a continuity correction is to be applied (correct = TRUE; the default) or not. Ignored, if exact = TRUE.

simple_output, simple.output

logical value that indicates whether an R6 class object, including the tests' parameters and support sets, i.e. all observable p-values under each null hypothesis, is to be returned (see below).

Details

The parameters x and alternative are vectorised. They are replicated automatically, such that the number of x's rows is the same as the length of alternative. This allows multiple null hypotheses to be tested simultaneously. Since 'x is (if necessary) coerced to a matrix with four columns, it is replicated row-wise.

It can be shown that McNemar's test is a special case of the binomial test. Therefore, its computations are handled by binom_test_pv(). In contrast to that function, mcnemar_test_pv() does not allow specifying exact two-sided p-value calculation procedures. The reason is that McNemar's exact test always tests for a probability of 0.5, in which case all these exact two-sided p-value computation methods yield exactly the same results.

Value

If simple.output = TRUE, a vector of computed p-values is returned. Otherwise, the output is a DiscreteTestResults R6 class object, which also includes the p-value supports and testing parameters. These have to be accessed by public methods, e.g. ⁠$get_pvalues()⁠.

References

Agresti, A. (2002). Categorical data analysis (2nd ed.). New York: John Wiley & Sons. pp. 411–413. doi:10.1002/0471249688

See Also

stats::mcnemar.test(), binom_test_pv()

Examples

# Constructing
S1 <- c(4, 2, 2, 14, 6, 9, 4, 0, 1)
S2 <- c(0, 0, 1, 3, 2, 1, 2, 2, 2)
N1 <- rep(148, 9)
N2 <- rep(132, 9)
F1 <- N1 - S1
F2 <- N2 - S2
df <- data.frame(S1, F1, S2, F2)

# Computation of exact p-values and their supports
results_ex  <- mcnemar_test_pv(df)
raw_pvalues <- results_ex$get_pvalues()
pCDFlist    <- results_ex$get_pvalue_supports()

# Computation of chisquare p-values and their supports
results_cs  <- mcnemar_test_pv(df, exact = FALSE)
raw_pvalues <- results_cs$get_pvalues()
pCDFlist    <- results_cs$get_pvalue_supports()