ANOVA (Chapter - 04/D) Dr. C. Ertuna

One-Way Analysis of Variance ANOVA exemines differences among the means of 3 or more independent groups at once. ANOVA exemines, how nominal independent variables (groups) influence an interval dependnet variable. Y interval; X nominal Dr. C. Ertuna

One-Way Analysis of Variance A factor refers to a quantity under examination in an experiment as a possible cause of variation in the response variable. A factor (X) is an explanatory (or predictor) variable with several categories. Note: factor has levels, or categories (not values). Dr. C. Ertuna

One-Way ANOVA For example: In a study comparing the appeal of four different destination types, the factor under investigation is the destination which has four levels (types). Destination Type-1 Type-2 Type-3 Type-4 Appeal : Dr. C. Ertuna

One-Way ANOVA Levels (factor levels) refer to the categories, measurements, or strata of a factor of interest (Type-1, Type-2, etc.). For example in the appeal study, each destination type is a factor level. Dr. C. Ertuna

One-Way ANOVA One-way ANOVA is a design in which independent samples are obtained from k levels of a single factor for the purpose of testing whether the k levels have equal means. Use of ANOVA: to investigate the effect of categorical predictor variables on interval response variable. Dr. C. Ertuna

One-Way ANOVA Assumptions: Normality: All Groups have normal distribution ANOVA is relatively robust if data is symetrical. Homogeneity of Variance: All Groups (or factor levels) have equal variances Independence: Groups are independent Random Selection: Observations are randomly obtained Dr. C. Ertuna

One-Way ANOVA Null hypothesis in an ANOVA experiment: Alternative hypothesis in an ANOVA experiment: Dr. C. Ertuna

One-Way ANOVA SPSS Application: Stack data in Excel & Copy it to SPSS Analyze / General Linear Model / Univariate Groups (categorical variable) → Fixed Factor(s): Observations (interval variable) → Dependent Variable: Post Hoc (Tukey & Games-Howell) Options – (OVERALL) into right pane (Descriptive & Homogeneity of Var.) Dr. C. Ertuna

One-Way ANOVA Reading the Output of SPSS Check - Tests of Between-Subjects Effects If “Corrected Model” is not significant there are no differences between the group means. If “Corrected Model” is significant Check - Descriptive Statistics and Levene's Test of Equality of Error Variances If N’s are equal and Levene’s test is not significant Check – Post Hoc Tests / Tukey HDS If “ii” doesn’t hold then check – Post Hoc Tests / Games-Howell Dr. C. Ertuna

Dr. C. Ertuna Group means are equal No Yes Post Hoc Tests / Tukey HDS Is Corrected Model Significant? Are N’s of Groups equal? Is Levene’s test Significant? Post Hoc Tests / Games-Howell Yes   No Post Hoc Tests / Tukey HDS Group means are equal Dr. C. Ertuna

ANOVA - Example Page 449 Example Are the mean strength of tensiles provided by five suppliers different? Dr. C. Ertuna

Simple Linear Regression Next Lesson (Chapter - 06/A) Simple Linear Regression Dr. C. Ertuna

One-Way ANOVA Excel application: Tools/ Data Analysis / Single Factor ANOVA Input Range (w/out Labels Alpha level Output Range Dr. C. Ertuna