Comments on the paper ‘Type I error and test power of different tests for testing interaction effects in factorial experiments’ by M. Mendes and S. Yigit (Statistica Neerlandica, 2013, pp. 1–26)

We give some comments on the paper by Mendes and Yigit where some misleading statements on rank tests have been given. Also, we give some additional important references on the same topic, which are not cited in this paper. By extending the simulations presented in the Mendes and Yigit paper to larger and unequal sample sizes, we demonstrate that the main conclusions are misleading.     

Comment on ‘Type I error and test power of different tests for testing interaction effects in factorial experiments’

We discuss the rank transform method and particularly the hypotheses being tested. Some counter examples show that the rank transformation method is invalid in factorial designs.     

A comment on Mendeş and Yiğit (2013), ‘Type I error and test power of different tests for testing interaction effects in factorial experiments’, Statistica Neerlandica, 67:1–26

In their advocacy of the rank‐transformation (RT) technique for analysis of data from factorial designs, Mende? and Yi?it (Statistica Neerlandica, 67, 2013, 1–26) missed important analytical studies identifying the statistical shortcomings of the RT technique, the recommendation that the RT technique not be used, and important advances that have been made for properly analyzing data in a non‐parametric setting. Applied data analysts are at risk of being misled by Mende? and Yi?it, when statistically sound techniques are available for the proper non‐parametric analysis of data from factorial designs. The appropriate methods express hypotheses in terms of normalized distribution functions, and the test statistics account for variance heterogeneity.     

The analysis of ranked data in blocked factorial experiments

A non-parametric method for the analysis of blocked factorial experiments, based on ranking within blocks, is proposed and shown to be equivalent to partitioning Friedman's test statistic into a set of contrasts reflecting polynomial components of the main effects and interaction. A slightly modified version of the procedure is suggested to partially overcome the problem of loss of power to detect one component when the model includes other components. This alternative procedure is shown to be equivalent to applying a standard normal theory analysis of variance to the ranks. The null distributions and power comparisons are investigated using simulation methods, and it is shown that the non-parametric methods are almost as powerful as the analysis of variance. Received: February 1999     

On Tests for a Normal Mean with Known Coefficient of Variation

Hinkley (1977) derived two tests for testing the mean of a normal distribution with known coefficient of variation (c.v.) for right alternatives. They are the locally most powerful (LMP) and the conditional tests based on the ancillary statistic for μ. In this paper, the likelihood ratio (LR) and Wald tests are derived for the one‐ and two‐sided alternatives, as well as the two‐sided version of the LMP test. The performances of these tests are compared with those of the classical t, sign and Wilcoxon signed rank tests. The latter three tests do not use the information on c.v. Normal approximation is used to approximate the null distribution of the test statistics except for the t test. Simulation results indicate that all the tests maintain the type‐I error rates, that is, the attained level is close to the nominal level of significance of the tests. The power functions of the tests are estimated through simulation. The power comparison indicates that for one‐sided alternatives the LMP test is the best test whereas for the two‐sided alternatives the LR or the Wald test is the best test. The t, sign and Wilcoxon signed rank tests have lower power than the LMP, LR and Wald tests at various alternative values of μ. The power difference is quite large in several simulation configurations. Further, it is observed that the t, sign and Wilcoxon signed rank tests have considerably lower power even for the alternatives which are far away from the null hypothesis when the c.v. is large. To study the sensitivity of the tests for the violation of the normality assumption, the type I error rates are estimated on the observations of lognormal, gamma and uniform distributions. The newly derived tests maintain the type I error rates for moderate values of c.v.     

Asymptotically optimal nonparametric one- and two-way analysis of variance tests for the log linear model under censoring

We considerr ×c populations with failure ratesλ _ij(t) satisfying the condition