BESD: Binomial Effect Size Display (BESD) for correlations

In mottusrene/TESD: Estimate the pairwise proportions of low, medium and high values of two continously distributed variables, known as Trinomial Effect Size Display (TESD)

Description

Calculate and plot pairwise probabilities for low and high values for continuously distributed variables x and y. This is procedure is called Binomial Effect Size Display (BESD). BESD allows heuristically estimating the extents to which correlations apply to individual observations (e.g., the probability that a high value in one variable, x, is matched with a high value in another variable, y). For both variable, low values correspond to the lower half of the distribution and high values to the higher half of the distribution. You may also plot the expected BESD alongside BESD calculated from the supplied data. Missing values are not permitted!

For more precise and meaningful effect size display, it may be advisable to use the Trinomial Effect Size Display (TESD), however. TESD categorises observations into low, medium and high values and calculates their pairwie probabilities such as, for example, the propbability that high values in one variable are matched with high values in another. Use TESD() function for this.

Usage

BESD(x, y, plot = TRUE, Xlab = "X", Ylab = "Y", plot.expected.BESD = FALSE)

Arguments

x	First continuously distributed variable
y	Second continuously distributed variable
plot	Whether a scatterplot with a BESD overlay should be printed
Xlab	Label for the x variable
Ylab	Label for the y variable
plot.expected.BESD	Should expected BESD, given the correlation between x and y and assuming normal distribution for them, be printed (denoted with E)?

Details

When using this function, make sure that both variables can be meaningfully grouped into roughly equal low and high groups (the univariate and multivariate, cross-tabulated, proportions of high and low values for both variables will be printed, so you can see whether this assumption holds). Variables with limited values (e.g., Likert scale scores or those with only certain values possible) will lead to unequal group sizes. If the groups are not of equal size, the BESD calculated from the supplied data will not match the expected BESD (assuming normal distributions of continuously distributed variables). The function will warn you. In this case, it may be better to interpret the expected BESD (also printed), given the correlation between the supplied variables and assuming that they are normally distributed. This is always a safe option.

Value

univariate.x.proportions	Proportions for the two groups in variable x
univariate.y.proportions	Proportions for the two groups in variable y
cross.tabulations	Cross-tabulation of x and y groups
BESD.table	Cross-tabulation of the groups of variables x and y
multivariate.x.proportions	Sums of the proportions in the groups along variable x. If the sums are very different from 1, be careful! The variable may not be suitable for BESD, and you may want to interpret the expected BESD instead (always a safe option).

Author(s)

René Mõttus

See Also

BESD.expected(), BESD(), TESD(), TESD.expected()

Examples

Conscientiousness = rnorm(10000)
Performance = .3 * Conscientiousness + sqrt(1 - .3^2) + rnorm(length(Conscientiousness))
cor(Conscientiousness, Performance)
BESD(Conscientiousness, Performance)

mottusrene/TESD documentation built on Dec. 21, 2021, 9:05 p.m.