Examination of Statistical Methods Used in Group Comparisons in Visual Analogue Scale (VAS) Data in Terms of Type I Error Rate and Power of Test: Monte Carlo simulation study for VAS data

In this study, how the application changes with the size of the scale, type I error rate and power of test values were examined in different sample sizes. The material of this study is the random numbers generated according to different sample sizes and different group means of standard deviation out of populations that hold multinomial distribution. In the study, permutation test, F-test and Kruskal-Wallis (KW) test were examined using combinations with different sample sizes (n = 5, 10, 20, 30, 50) and different p values (probability of occurrence of events which are 0.25, 0.50, 0.75) first interms of Type I error rate and then power of the test using different group averages (Δ =1.0, 1.5, 2.0). As a result of the simulations, it is seen that with small sample sizes, Kruskal-Wallis test was unable to maintain Type I error rate at 0.05 level. In the evaluation of such Likert-type data, it can be stated that, permutation test, one of the distribution free tests, is more practical than other tests in terms of maintaining the Type I error rate at 0.05 level and high power of test values. The permutation test is satisfactory in terms of both the type I error rate and the power of the test. Also, permutation test is a distribution-free test. Therefore, can be used without prerequisites. In almost every combination (π, Δ, k, n), permutation test had similar or superior type 1 error and power values than the F and KW tests. It was observed that compared to the 5 visual analogue scale, when the data is measured in 10 and 20 visual analogue scale, the power of test values decreased. In other words, if more than 5 visual analogue scale are made on the visual analogue scale data, the results would negatively be affected.