T2EQ {T2EQ}

Function for applying the T^2-test for equivalence

Description

The function T2EQ() implements the T^2-test for equivalence (see Wellek,2010 or Hoffelder et al., 2015). The T^2-test for equivalence is a multivariate two-sample equivalence test. Distance measure of the test is the Mahalanobis distance.

Usage

T2EQ(X, Y, eq_margin, alpha = 0.05, print.results = TRUE)

Arguments

X

numeric data matrix of the first sample. The rows of X contain the individual observations of the sample, the columns contain the variables/components of the multivariate sample.

Y

numeric data matrix of the second sample. The rows of X contain the individual observations of the sample, the columns contain the variables/components of the multivariate sample.

eq_margin

numeric (>0). The equivalence margin of the test.

alpha

numeric (0<alpha<1). The significance level of the T^2-test for equivalence. Usually set to 0.05 which is the default.

print.results

logical; if TRUE (default) summary statistics and test results are printed in the output. If NO no output is created

Details

For multivariate normally distributed data the T^2-test for equivalence is exact and UMPI.

Value

a data frame; three columns containing the results of the test

p.value

numeric; the p-value of the T^2-test for equivalence

testresult.num

numeric; 0 (null hypothesis of nonequivalence not rejected) or 1 (null hypothesis of nonequivalence rejected, decision in favor of equivalence)

testresult.text

character; test result of the T^2-test for equivalence in text mode

Author(s)

Thomas Hoffelder <thomas.hoffelder at boehringer-ingelheim.com>

References

Wellek, S. (2010), Testing Statistical Hypotheses of Equivalence and Noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC.

Hoffelder, T., Goessl, R., Wellek, S. (2015). Multivariate Equivalence Tests for Use in Pharmaceutical Development. Journal of Biopharmaceutical Statistics, 25:3, 417-437. URL: http://dx.doi.org/10.1080/10543406.2014.920344

Examples

## Not run: A recalculation of the example evaluation in Hoffelder et al. (2015) 
can be done with the following code:
## End(Not run)

data(ex_data_JoBS)
REF_JoBS <- cbind(ex_data_JoBS[ which(ex_data_JoBS$Group=='REF'), ]
            [c("Diss_15_min","Diss_20_min","Diss_25_min")])
TEST_JoBS <- cbind(ex_data_JoBS[ which(ex_data_JoBS$Group=='TEST'), ]
            [c("Diss_15_min","Diss_20_min","Diss_25_min")])
equivalence_margin_JoBS <- 0.74^2
test_T2EQ_JoBS <- T2EQ(X=REF_JoBS,Y=TEST_JoBS,eq_margin = equivalence_margin_JoBS)