Cohen's g and odds ratio for paired contingency tables

Calculates Cohen's g and odds ratio for paired contingency tables, such as those that might be analyzed with McNemar or McNemar-Bowker tests.

Usage

cohenG(
  x,
  ci = FALSE,
  conf = 0.95,
  type = "perc",
  R = 1000,
  histogram = FALSE,
  digits = 3,
  reportIncomplete = FALSE,
  ...
)

Arguments

x: A two-way contingency table. It must be square. It can have two or more levels for each dimension.
ci: If TRUE, returns confidence intervals by bootstrap. May be slow.
conf: The level for the confidence interval.
type: The type of confidence interval to use. Can be any of "norm", "basic", "perc", or "bca". Passed to boot.ci.
R: The number of replications to use for bootstrap.
histogram: If TRUE, produces a histogram of bootstrapped values.
digits: The number of significant digits in the output.
reportIncomplete: If FALSE (the default), NA will be reported in cases where there are instances of the calculation of the statistic failing during the bootstrap procedure.
...: Additional arguments (ignored).

Value

A list containing: a data frame of results of the global statistics; and a data frame of results of the pairwise statistics.

Details

For a 2 x 2 table, where a and d are the concordant cells and b and c are discordant cells: Odds ratio is b/c; P is b/(b+c); and Cohen's g is P - 0.5.

In the 2 x 2 case, the statistics are directional. That is, when cell [1, 2] in the table is greater than cell [2, 1], OR is greater than 1, P is greater than 0.5, and g is positive.

In the opposite case, OR is less than 1, P is less than 0.5, and g is negative.

In the 2 x 2 case, when the effect is small, the confidence interval for OR can pass through 1, for g can pass through 0, and for P can pass through 0.5.

For tables larger than 2 x 2, the statistics are not directional. That is, OR is always >= 1, P is always >= 0.5, and g is always positive. Because of this, if type="perc", the confidence interval will never cross the values for no effect (OR = 1, P = 0.5, or g = 0). Because of this, the confidence interval range in this case should not be used for statistical inference. However, if type="norm", the confidence interval may cross the values for no effect.

When the reported statistics are close to their extremes, or with small counts, the confidence intervals determined by this method may not be reliable, or the procedure may fail.

References

https://rcompanion.org/handbook/H_05.html

Author

Salvatore Mangiafico, mangiafico@njaes.rutgers.edu

Examples

### 2 x 2 repeated matrix example
data(AndersonRainBarrel)
cohenG(AndersonRainBarrel)
#> $Global.statistics
#>   Dimensions    OR     P      g
#> 1      2 x 2 0.294 0.227 -0.273
#> 
                    
### 3 x 3 repeated matrix
data(AndersonRainGarden)
cohenG(AndersonRainGarden)
#> $Global.statistics
#>   Dimensions   OR    P    g
#> 1      3 x 3 11.5 0.92 0.42
#> 
#> $Pairwise.statistics
#>                                        Comparison  OR     P     g
#> 1       Yes.before/Yes.after : No.before/No.after Inf     1   0.5
#> 2 Yes.before/Yes.after : Maybe.before/Maybe.after  11 0.917 0.417
#> 3   No.before/No.after : Maybe.before/Maybe.after   7 0.875 0.375
#>