QT2week06_ANOVA_1701.pdf - Week 6 Analysis of...

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Week 6-1 Week 6 Analysis of Variance (ANOVA)
Week 6-2 Week 6 - Learning Objectives Recognize situations in which to use analysis of variance Understand different Analysis of Variance (ANOVA) designs Perform a single-factor hypothesis test and interpret results Conduct and interpret post-hoc multiple comparisons procedures
Week 6-3 Parametric Hypothesis Testing Single sample Two independent samples Two dependent samples or paired samples More than two independent samples ***
Week 6-4 Chapter Overview Analysis of Variance (ANOVA) F-test Tukey- Kramer test One-Way ANOVA
Week 6-5 ANOVA AN alysis O f VA riance One-Way ANOVA/ Completely Randomized Design Two-Way ANOVA/ ANOVA for Randomized Block Design Not discussed in this chapter
Week 6-6 General ANOVA Setting Investigator controls one or more independent variables Called factors (or treatment variables) Each factor contains two or more levels. Observe effects on the dependent variable Response to levels of independent variable Experimental design: the plan used to collect the data
Week 6-7 Completely Randomized Design Experimental units (subjects) are assigned randomly to treatments Subjects are assumed homogeneous Only one factor or independent variable With two or more treatment levels Analyzed by one-factor analysis of variance (one-way ANOVA)
Week 6-8 The Assumptions of One-Way ANOVA Hypothesis Testing the populations are normally distributed. samples are randomly or independently selected. sample sizes must be large enough. Populations have the same variances (each group has equal population variance). Before we test, we must assume that
Week 6-9 The Steps in One-Way ANOVA Hypothesis Testing Step 1: State the null and alternative hypothesis Step 2: State the significance level. Step 3: State the statement of decision rule to determine the rejection region(s). Step 4: Find the critical value of the test from the statistical table. Step 5: Determine the appropriate statistical technique and the test statistic to use. Step 6: Make the comparison between test statistics value and critical value to make statistical decision. Step 7: Making conclusion.
Week 6-10 The Steps in One-Way ANOVA Hypothesis Testing (continue) Additional steps (more information): Find the p-value from statistical table based on test statistic value. Conduct the Tukey-Kramer test.
Week 6-11 Step 1: State the null and alternative hypothesis H 0 : m 1 = m 2 = m 3 = … = m k All population means are equal There is no treatment effect (no variation in means among groups) H 1 : At least one of m i is not equal; i = 1, 2, 3,…, k Not all population means are equal There is a treatment effect Does not mean that all population means are different (some pairs may still be the same statistically)
Week 6-12 Step 1 (Continue) All Means are the same: The Null Hypothesis is True (No Treatment Effect) 3 2 1 μ μ μ H 0 : m 1 = m 2 = m 3 = … = m k
Week 6-13 Step 1 (Continue) i m At least one mean is different: The Null Hypothesis is NOT true (Treatment Effect is present) 3 2 1 μ μ μ 3 2 1 μ μ μ or H 1 : At least one of m i is not equal; i = 1, 2, 3,…, k
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