yuen function

Independent samples t-tests on robust location measures including effect sizes.

The function yuen performs Yuen's test for trimmed means, yuenbt is a bootstrap version of it. akp.effect and yuen.effect.ci can be used for effect size computation. The pb2gen function performs a t-test based on various robust estimators, medpb2 compares two independent groups using medians, and qcomhd compares arbitrary quantiles.

yuen(formula, data, tr = 0.2, ...)
yuenbt(formula, data, tr = 0.2, nboot = 599, side = TRUE, ...)
akp.effect(formula, data, EQVAR = TRUE, tr = 0.2, nboot = 200, alpha = 0.05, ...)
yuen.effect.ci(formula, data, tr = 0.2, nboot = 400, alpha = 0.05, ...)
pb2gen(formula, data, est = "mom", nboot = 599, ...)
medpb2(formula, data, nboot = 2000, ...)
qcomhd(formula, data, q = c(0.1, 0.25, 0.5, 0.75, 0.9),
       nboot = 2000, alpha = 0.05, ADJ.CI = TRUE, ...)

Arguments

• formula: an object of class formula.
• data: an optional data frame for the input data.
• tr: trim level for the mean.
• nboot: number of bootstrap samples.
• side: side = TRUE indicates two-sided method using absolute value of the test statistics within the bootstrap; otherwise the equal-tailed method is used.
• est: estimate to be used for the group comparisons: either "onestep" for one-step M-estimator of location using Huber's Psi, "mom" for the modified one-step (MOM) estimator of location based on Huber's Psi, or "median", "mean".
• q: quantiles to be used for comparison.
• alpha: alpha level.
• ADJ.CI: whether CIs should be adjusted.
• EQVAR: whether variances are assumed to be equal across groups.
• ...: currently ignored.

Details

If yuenbt is used, p-value computed only when side = TRUE. medpb2 is just a wrapper function for pb2gen with the median as M-estimator. It is the only known method to work well in simulations when tied values are likely to occur.qcomhd returns p-values and critical p-values based on Hochberg's method.

Returns

Returns objects of classes "yuen" or "pb2" containing:

• test: value of the test statistic (t-statistic)

• p.value: p-value

• conf.int: confidence interval

• df: degress of freedom

• diff: trimmed mean difference

• effsize: explanatory measure of effect size

• call: function call

qcomhd returns an object of class "robtab" containing:

• partable: parameter table

References

Algina, J., Keselman, H.J., & Penfield, R.D. (2005). An alternative to Cohen's standardized mean difference effect size: A robust parameter and confidence interval in the two independent groups case. Psychological Methods, 10, 317-328.

Wilcox, R. (2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Elsevier.

Wilcox, R., & Tian, T. (2011). Measuring effect size: A robust heteroscedastic approach for two or more groups. Journal of Applied Statistics, 38, 1359-1368.

Yuen, K. K. (1974). The two sample trimmed t for unequal population variances. Biometrika, 61, 165-170.

See Also

t1way,t1waybt

Examples

set.seed(123)
## Yuen's test
yuen(Anxiety ~ Group, data = spider)

## Bootstrap version of Yuen's test (symmetric CIs)
yuenbt(Anxiety ~ Group, data = spider)

## Robust Cohen's delta
akp.effect(Anxiety ~ Group, data = spider)

## Using an M-estimator
pb2gen(Anxiety ~ Group, data = spider, est = "mom")
pb2gen(Anxiety ~ Group, data = spider, est = "mean")
pb2gen(Anxiety ~ Group, data = spider, est = "median")

## Using the median
medpb2(Anxiety ~ Group, data = spider)

## Quantiles
set.seed(123)
qcomhd(Anxiety ~ Group, data = spider, q = c(0.8, 0.85, 0.9), nboot = 500)