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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

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

9. 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

10. 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

11. 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

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

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

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