An Empirical Study of Students’ Performance at Assessing Normality of Data Through Graphical Methods

When applying statistical methods for analyzing data, with normality as an assumption there are different procedures of determining if a sample is drawn from a normally distributed population. Because normality is such a central assumption, the reliability of the procedures is of most importance. Much research focus on how good formal tests of normality are, while the performance of statisticians when using graphical methods are far less examined. Therefore, the aim of the study was to empirically examine how good students in statistics are at assessing if samples are drawn from normally distributed populations through graphical methods, done by a web survey. The results of the study indicate that the students distinctly get better at accurately determining normality in data drawn from a normally distributed population when the sample size increases. Further, the students are very good at accurately rejecting normality of data when the sample is drawn from a symmetrical non-normal population and fairly good when the sample is drawn from an asymmetrical distribution. In comparison to some common formal tests of normality, the students' performance is superior at accurately rejecting normality for small sample sizes and inferior for large, when drawn from a non-normal population.