ANALYSIS O F VARIANCE Q U R R O T I N AY U N I N A A R T YA L AT H I FA H M A N A J E M E N R E K AYA S A U N I V E R S I TA S I N T E R N A S I O N A L S E M E N I N D O N E S I A 2 0 1 6
LEARNING OBJECTIVES 1.Describe Analysis of Variance (ANOVA)2.Explain the Rationale of ANOVA experiment3.Compare Experimental Designs (Test the Equality of 2 or More Means)Completely Randomized DesignFactorial DesignRandomized Complete Block ANOVA4. Conduct and interpret post-analysis of variance pair wise comparisons procedures
EXPERIMENT 1. Investigator Controls One or More Independent Variables Called Treatment Variables or Factors Contain Two or More Levels ( Subcategories ) 2. Observes Effect on Dependent Variable Response to Levels of Independent Variable 3. Experimental Design: Plan Used to Test Hypotheses
EXPERIMENTAL DESIGNS Experiment al Designs Completely Randomized Factorial Two-Way ANOVA with replication One-Way ANOVA - F Test - Tukey Kramer Test Randomized Complete Block ANOVA - F Test - Fisher’s Least Significant Difference test
C O M P L E T E LY R A N D O M I Z E D D E S I G N
EXPERIMENTAL DESIGNS Experiment al Designs Completely Randomized Factorial Two-Way ANOVA with replication One-Way ANOVA Randomized Complete Block ANOVA
COMPLETELY RANDOMIZED DESIGN 1. Experimental Units (Subjects) Are Assigned Randomly to Treatments • Subjects are Assumed Homogeneous 2. One Factor or Independent Variable • 2 or More Treatment Levels or Classifications 3. Analyzed by One-Way ANOVA
RANDOMIZED DESIGN EXAMPLE Are the mean training times the same for 3 different methods? 9 subjects 3 methods (factor levels) Factor (Training Method ) Factor levels (Treatments) Level 1 Level 2 Level 3 Experimental units Dependent 21 hrs. 17 hrs. 31 hrs. variable 27 hrs. 25 hrs. 28 hrs. (Response) 29 hrs. 20 hrs. 22 hrs.
ONE-WAY ANOVA F- TEST Experiment al Designs Factorial Two-Way ANOVA with replication One-Way ANOVA Randomized Complete Block ANOVA Completely Randomized
ONE-WAY ANOVA F-TEST 1. Tests the Equality of 2 or More ( p ) Population Means 2. Variables • One Nominal Scaled Independent Variable (factor) • 2 or More ( p ) Treatment Levels or Classifications • One Interval or Ratio Scaled Dependent Variable 3. Used to Analyze Completely Randomized Experimental Designs if it has more than one dependent variable called MANOVA
JUST REFRESH FOR A BIT: DATA MEASUREMENT LEVELS Ratio/Interval Data Ordinal Data Nominal Data Highest Level Complete Analysis Higher Level Mid-level Analysis Lowest Level Basic Analysis Categorical Codes ID Numbers Category Names Rankings Ordered Categories Measurements
ONE-WAY ANOVA F-TEST ASSUMPTIONS 1. Randomness & Independence of Errors • Independent Random Samples are Drawn 2. Normality • Populations are Normally Distributed 3. Homogeneity of Variance • Populations have Equal Variances
ONE-WAY ANOVA F-TEST HYPOTHESES • H 0 : 1 = 2 = 3 = ... = p – All Population Means are Equal – No Treatment Effect • H a : Not All j Are Equal – At Least 1 Pop. Mean is Different – Treatment Effect – 1 2 ... p Is Wrong
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- Spring '17