# Tukey Test steps.pdf - One-Way ANOVA Page 1 Post Hoc...

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One-Way ANOVA Page 1 Robert A. Powers University of Northern Colorado Post Hoc Analysis – Tukey’s Test Step 0: Verify Assumptions Tukey’s test has five assumptions. 1. The k samples are each obtained using simple random sampling. 2. The k samples data independent of each other within and among the samples. 3. The k populations are normally distributed. 4. The k populations have equal variances. 5. A decision to reject the null hypothesis that μ 1 = μ 2 = μ 3 = … = μ k was made during the one-way ANOVA. Step 1: State the Hypothesis A claim is made regarding pairs of population means. This claim is used to determine the following null and alternative hypotheses. H 0 : μ i = μ j H 1 : μ i μ j Step 2: Select a Level of Significance The level of significance α is determined by the one selected in the one-way ANOVA. Step 3: Calculate the Test Statistic The test statistic for Tukey’s test is given by: g1869= g1876 g1191 g3037 −g1876 g1191 g3036 g3496 g1871 g2870 2 g3436 1 g1866 g3036 + 1 g1866 g3037 g3440 where g1876 g1191 g3037 >g1876 g1191 g3036 , s 2 is the mean square error estimate of σ 2 (MSE) from ANOVA, n i is the sample size from population