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Applied Statistics Midterm 1 Material 1. Two Sample Tests For the mean: (a) Welch’s test (using estimated degrees of freedom when the variances are not assumed to be the same. (b) Confidence intervals for the diﬀerence between two means 2. ANOVA (a) Assumptions and applications of the single factor ANOVA/ F test. (b) Definition of the F distribution in terms of χ2 random variables. (c) Definition of the χ2 in terms of normal random variables. (d) Explain why the ANOVA test works. (e) Check that the assumptions of the single factor ANOVA are valid for sample data. 3. Multiple Mean Comparisons (a) Apply Tukey’s method to determine which means, if any, are significantly diﬀerent. (b) Compute confidence intervals for linear functions of the means. R Code that would be useful to know 1. Application of the single factor analysis of variance 2. QQ plots/ Shapiro–Wilks Test. 3. Bartlett’s test 4. Tukey’s method 5. Imputing data from tables so that these procedures can be applied.