When data is collected sample size and precision in measurements are often limited. In what sense this impacts the size, unadjusted and adjusted power of different normality tests is a relatively unexplored field. Therefore this paper is dedicated to perform a simulation study where these three properties of the normality tests Anderson-Darling, Jarque-Bera and Shapiro-Wilk are examined. The study is based on different combinations of sample sizes and roundings where repeated samples are drawn from both normally and asymmetrically distributed populations. The results from the study indicate that coarser roundings results in increased size and unadjusted power of Anderson-Darling and Shapiro-Wilk, while Jarque-Bera is seemingly unaffected by roundnings. The three tests have in common that a larger sample size leads to an increase in the size, unadjusted and adjusted power of the tests and that roundings have no substantial impact on adjusted power. / När data samlas in är ofta stickprovsstorlek och precision i mätningarna begränsad i olika grad. Vilken betydelse detta får för sannolikheten för typ I-fel, ojusterad samt justerad styrka hos olika normalitetstest är ett förhållandevis outforskat område. Därför dedikeras denna uppsats till att genomföra en simuleringsstudie där dessa tre egenskaper hos normalitetstesten Anderson-Darling, Jarque-Bera samt Shapiro-Wilk undersöks. Studien baseras på olika kombinationer av stickprovsstorlekar samt avrundningar där upprepade stickprov dras från både normalfördelade och asymmetriskt fördelade populationer. Resultaten från studien indikerar att grövre avrundningar leder till ökad sannolikhet för typ I-fel och ojusterad styrka hos Anderson-Darling och Shapiro-Wilk, medan Jarque-Bera inte påverkas nämnvärt av avrundningar. Gemensamt för samtliga test är att en större stickprovsstorlek leder till ökad sannolikhet för typ I-fel, ojusterad styrka och justerad styrka samt att avrundningar inte nämnvärt påverkar justerad styrka.

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.