Correct application of the classical factorial F-test depends on normality and homogeneity of variance assumptions. If these assumptions are violated the type I error rate will be inflated and power of the test will be decreased. Therefore nonparametric statistical tests have been proposed to analyze the interaction effects in factorial designs. | The comparison of nonparametric statistical tests for interaction effects in factorial design Decision Science Letters 8 2019 309 316 Contents lists available at GrowingScience Decision Science Letters homepage dsl The comparison of nonparametric statistical tests for interaction effects in factorial design Ampai Thongteeraparp Department of Statistics Faculty of Science Kasetsart University Bangkok Thailand 10900 CHRONICLE ABSTRACT Article history Correct application of the classical factorial F-test depends on normality and homogeneity of Received October 9 2018 variance assumptions. If these assumptions are violated the type I error rate will be inflated and Received in revised format power of the test will be decreased. Therefore nonparametric statistical tests have been proposed October 18 2018 to analyze the interaction effects in factorial designs. A simulation was conducted to investigate Accepted November 16 2018 Available online the effect of non-normality on type I error rate and power of the test of the classical factorial F- November 16 2018 test and five nonparametric tests namely rank transformation FR Winsorized mean FW Keywords modifies mean FM adjusted rank transform ART and adjusted median transform AMT Factorial design using program SAS with 1 000 replications. The study used 2 2 factorial design with Rank transformation replications of 3 4 and 6 making sample sizes of 12 16 and 24 respectively and 3 3 factorial Modified mean designs with replication of 3 making a sample size of 27 studied at level of significance. As Adjusted rank transform test a results when the normality of assumption is satisfied all six statistical tests have the ability to Winsorized mean control type I error in all situations. The ART test cannot control type I error rate for 3 3 factorial Adjusted median transform design when sample size is 27 when normality assumption is violated. For power of the test the F-test provided the highest .
