Details
| Original language | English |
|---|---|
| Pages (from-to) | 738-759 |
| Number of pages | 22 |
| Journal | Electronic journal of statistics |
| Volume | 6 |
| Publication status | Published - 2012 |
Abstract
We study simultaneous rank procedures for unbalanced designs with independent observations. The hypotheses are formulated in terms of purely nonparametric treatment effects. In this context, we derive rank-based multiple contrast test procedures and simultaneous confidence intervals which take the correlation between the test statistics into account. Hereby, the individual test decisions and the simultaneous confidence intervals are compatible. This means, whenever an individual hypothesis has been rejected by the multiple contrast test, the corresponding simultaneous confidence interval does not include the null, i.e. the hypothetical value of no treatment effect. The procedures allow for testing arbitrary purely nonparametric multiple linear hypotheses (e.g. many-to-one, all-pairs, changepoint, or even average comparisons). We do not assume homogeneous variances of the data; in particular, the distributions can have different shapes even under the null hypothesis. Thus, a solution to the multiple nonparametric Behrens-Fisher problem is presented in this unified framework.
Keywords
- Multiple comparisons, Nonparametric Behrens-Fisher problem, Rank statistics
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Electronic journal of statistics, Vol. 6, 2012, p. 738-759.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Rank-based multiple test procedures and simultaneous confidence intervals
AU - Konietschke, Frank
AU - Hothorn, Ludwig A.
AU - Brunner, Edgar
PY - 2012
Y1 - 2012
N2 - We study simultaneous rank procedures for unbalanced designs with independent observations. The hypotheses are formulated in terms of purely nonparametric treatment effects. In this context, we derive rank-based multiple contrast test procedures and simultaneous confidence intervals which take the correlation between the test statistics into account. Hereby, the individual test decisions and the simultaneous confidence intervals are compatible. This means, whenever an individual hypothesis has been rejected by the multiple contrast test, the corresponding simultaneous confidence interval does not include the null, i.e. the hypothetical value of no treatment effect. The procedures allow for testing arbitrary purely nonparametric multiple linear hypotheses (e.g. many-to-one, all-pairs, changepoint, or even average comparisons). We do not assume homogeneous variances of the data; in particular, the distributions can have different shapes even under the null hypothesis. Thus, a solution to the multiple nonparametric Behrens-Fisher problem is presented in this unified framework.
AB - We study simultaneous rank procedures for unbalanced designs with independent observations. The hypotheses are formulated in terms of purely nonparametric treatment effects. In this context, we derive rank-based multiple contrast test procedures and simultaneous confidence intervals which take the correlation between the test statistics into account. Hereby, the individual test decisions and the simultaneous confidence intervals are compatible. This means, whenever an individual hypothesis has been rejected by the multiple contrast test, the corresponding simultaneous confidence interval does not include the null, i.e. the hypothetical value of no treatment effect. The procedures allow for testing arbitrary purely nonparametric multiple linear hypotheses (e.g. many-to-one, all-pairs, changepoint, or even average comparisons). We do not assume homogeneous variances of the data; in particular, the distributions can have different shapes even under the null hypothesis. Thus, a solution to the multiple nonparametric Behrens-Fisher problem is presented in this unified framework.
KW - Multiple comparisons
KW - Nonparametric Behrens-Fisher problem
KW - Rank statistics
UR - http://www.scopus.com/inward/record.url?scp=84875391826&partnerID=8YFLogxK
U2 - 10.1214/12-EJS691
DO - 10.1214/12-EJS691
M3 - Article
AN - SCOPUS:84875391826
VL - 6
SP - 738
EP - 759
JO - Electronic journal of statistics
JF - Electronic journal of statistics
SN - 1935-7524
ER -