# asymhd: Difference asymmetry function for two independent groups In GRousselet/rogme: Robust Graphical Methods For Group Comparisons

 asymhd R Documentation

## Difference asymmetry function for two independent groups

### Description

The difference asymmetry function provides perspective on the degree a distribution is symmetric about zero, by quantifying the sum of q and 1-q quantiles of the distribution of all pairwise differences between two independent groups x and y. If the distributions of x and y are identical, then the distribution of all pairwise differences is symmetric about zero. In particular, the sum of q and 1-q quantiles should be zero. If the distribution is symmetric the function should be approximately a horizontal line. If in addition the median of the difference scores is zero, the horizontal line will intersect the y-axis at zero. Confidence intervals and p values are returned for each quantile sum. The FWE is controlled via Hochberg's method, which is used to determine critical p values based on the argument alpha. To plot the results use `plot_diff_asym`.

### Usage

```asymhd(
data = df,
formula = obs ~ gr,
qseq = seq(5, 40, 5)/100,
alpha = 0.05,
nboot = 1000,
todo = NULL,
doall = FALSE
)
```

### Arguments

 `data` A data frame in long format. One column is a factor describing the groups; another column contains the values/observations for each group. A properly formatted data frame can be created using `mkt2`. Missing values are not allowed. `formula` A formula with format response variable ∼ predictor variable, where ~ (tilde) means "is modeled as a function of". `qseq` Quantiles to estimate - default = 0.05:0.05:.4 - must be <.5. `alpha` Expected long-run type I error rate - default = 0.05. `nboot` Number of bootstrap samples - default = 1000. `todo` A list of comparisons to perform - default = NULL. `doall` Set to TRUE to compute all comparisons - default = FALSE. Not executed if a `todo` list is provided.

### Value

A list of data frames, one data frame per comparison. Each data frame has one row per decile. The columns are:

• Column 1 = quantiles

• Column 2 = quantiles of differences

• Column 3 = 1 - quantiles of differences

• Column 4 = sum of quantiles

• Column 5 = lower bounds of the confidence intervals

• Column 6 = upper bounds of the confidence intervals

• Column 7 = critical p_values based on Hochberg's method

• Column 8 = p_values

### Note

This function combines Rand Wilcox's qwmwhd & cbmhd R functions, from Rallfun-v32.txt - see https://github.com/nicebread/WRS/, http://dornsife.usc.edu/labs/rwilcox/software/.

### References

Wilcox, R.R., Erceg-Hurn, D.M., Clark, F. & Carlson, M. (2014) Comparing two independent groups via the lower and upper quantiles. J Stat Comput Sim, 84, 1543-1551.

`hd` Harrell-Davis quantile estimator `allpdiff` to compute all pairwise differences `asymdhd` for dependent groups `plot_diff_asym` to plot results

### Examples

```set.seed(21) # generate data
n <- 100 # sample size
df <- tibble(gr = factor(c(rep("group1",n),rep("group2",n),rep("group3",n))),
obs= c(rnorm(n)+6, rnorm(n)+4, rnorm(n)*1.5+6)) # make tibble

out <- asymhd(df, obs ~ gr) # use the default parameters
out <- asymhd(df, obs ~ gr, alpha = .90) # specify alpha
out <- asymhd(df, obs ~ gr, nboot = 500) # specify the number of bootstrap samples
out <- asymhd(df, obs ~ gr, todo = list(c("group1","group2"),c("group3","group1"))) # specify list of comparisons
out <- asymhd(df, obs ~ gr, q = seq(.1,.4,.1)) # specify the quantiles
out <- asymhd(df, obs ~ gr, doall = TRUE) # compute all comparisons

```

GRousselet/rogme documentation built on Nov. 12, 2022, 4:38 a.m.