Sweating the Small Stuff: Does data cleaning and testing ... - Frontiers

Hoekstra et al.Why assumptions are seldom checkedRESULTSOf the six datasets that the 30 participants were required to analyze,in all but three instances the expected technique was chosen. In theremaining three instances, ANOVA was used to analyze data setsthat were meant to be analyzed by means of a t-test. Since ANOVAis in this case completely equivalent to an independent-samples t-test, it can be concluded that an appropriate technique was chosenfor all data sets. In none of these cases, an unconditional techniquewas chosen.Violations of,or conformance with,the assumptions of normalityand homogeneity of variance were correctly checked in 12%(95%CI = [8%, 18%]) and 23% (95%CI = [18%, 30%]), respectively,of the analyzed data sets. Figure 2 shows for each of the threetechniques how frequently possible violations of the assumptionsof normality and homogeneity of variance occurred, and whetherthe checking was done correctly, or whether a preliminary test wasused. Note that the assumption of normality was rarely checked forregression, and never correctly. In the few occasions that normalitywas checked the normality of the scores instead of the residualswas examined. Although this approach might be useful for studyingthe distribution of the scores, it is insufficient for determiningwhether the assumption of normality has been violated.The percentages of participants giving each of the four reasonsfor not checking assumptions as measured by the questionnaireare given in Figure 3. A majority of the participants were unfamiliarwith the assumptions. For each assumption, only a minority ofparticipants mentioned at least one of the correct ways to checkfor a violation of the assumption. The majority of the participantsfailed to indicate that the alleged robustness of a technique againstviolations of the relevant assumption was a reason not to checkthese assumptions in the first place. Many participants did notknow whether a violation of an assumption was important or not.Only in a minority of instances was an acceptable remedy for aviolation of an assumption mentioned. No unacceptable remedieswere mentioned. In general, participants indicated little knowledgeof how to overcome a violation of one of the assumptions,and most participants reported never having looked for a remedyagainst a violation of statistical assumptions.Participants had been told what the relevant assumptions werebefore they had to answer these questions. Therefore, the resultsfor the last three explanations per assumption in Figure 3 arereported for all participants,despite the fact that many participantsreported being unfamiliar with the assumption. This implies that,especially for the assumption of normality and to a lesser extentfor the assumption of equal variances, the results regarding the lastthree explanations should be interpreted with caution.DISCUSSIONIn order to examine people’s understanding of the assumptionsof statistical tests and their behavior with regard to checkingthese assumptions, 30 researchers were asked to analyze six datasets using the t-test, ANOVA, regression or a non-parametricFIGURE 2 | The frequency of whether two assumptions were checked atall, whether they were checked correctly, and whether a preliminary testwas used for three often used techniques in percentages of the totalnumber of cases. Between brackets are 95% CIs for the percentages.www.frontiersin.org May 2012 | Volume 3 | Article 137 | 12