Teaching Descriptive Statistics and Hypothesis Tests Measuring Water Density (Journal Article)

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Abstract: This laboratory experiment was divided into four parts. In the first part, students evaluate previously published data and check their normality using histograms, Q–Q plots, the Shapiro–Wilk test, and boxplots. In the second part, two different groups were compared. First, data normality and homoskedasticity were checked by using the Shapiro–Wilk test and Levene’s test, respectively. Then the group mean was compared using the Student, Welch, and Mann–Whitney tests. In the third part, the famous Iris flower data set was analyzed, where data normality and homoskedasticity were checked. Then, three independent groups were compared using ANOVA, without correction, and using the Welch and Brown-Forsythe corrections. The Iris flowers data set was also compared using the nonparametric version of ANOVA (Kruskal–Wallis test) and post hoc tests such as the Tukey test (parametric) and Dunn’s test (nonparametric). In the fourth part, students measured the density of water using four pieces of glassware (a beaker, a graduated cylinder, a volumetric pipet, and a graduated pipet). After the experiment, the data’ normality and homoskedasticity were checked. Then, the data was compared using ANOVA and post hoc tests. The results of these tests were visually interpreted using raincloud and discriminant plots. These data provide a starting point for teaching precision, accuracy, descriptive statistics, and hypothesis tests. Statistical analysis was carried out using Jeffreys’s Amazing Statistics Program (JASP), which is free and open-source software that provides several graphical interpretations of the hypothesis test.