Lecture 3_ANOVA

Lecture 3_ANOVA - Treatment or classification variables...

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1 1 ECON1320 - Lecture 3 Analysis of Variance (ANOVA) Chapter 11.1 – 11.5 2 Topics 1. Introduction to the concept of experimental 2. Completely randomised design & one-way ANOVA 3. Multiple comparison tests 4. Randomised block design & two-way ANOVA without replication 3 Topic 1: Experimental design • is a plan or a structure to test hypotheses in which the researcher controls one or more variables • It is made up of independent and dependent variables dependent variable (or response variable) is the response to different levels of the independent variable • An independent variable (or factor ) may be either a treatment variable or a classification variable. 4 Treatment or classification variables? • The treatment variable is under the control of the analyst. – Examples: amount of light, temperature • The classification variable is an existing characteristic of the experimental subjects which is outside the control of the analyst. Classification variables are present prior to experiment, – Examples: work shift, gender, type of machine 5 Treatment or classification variables? • Each variable has two or more levels or classifications/subcategories used by researcher • Levels can be categorical or numerical 6 Example 1: Experimental design • ABC Airlines flies three different versions of the Boeing 737: the 737-838, the 737-476 and the 737- 376. ABC Airlines wants to conduct a study to determine if there is a significant difference in the average annual maintenance costs for the three Boeing types used. What are – A dependent variable? – Possible independent variables? – Levels of independent variables?
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2 7 Example 1: Solutions • A dependent variable: average annual maintenance cost – Levels of Type of 737 : Type I (737–838), Type II (737– 476), Type III (737–376) – Levels of Age of plane : 0–2 years, 3–5 years, 6–10 years, over 10 years – Levels of Number of flights per week: 0–5, 6–10, over 10 – Levels of City : Sydney, Melbourne, Brisbane, Perth 8 ANOVA • ANOVA is a statistical analysis technique • In the experiment, individual items/people being studied are not all the same. • There is existence of variation and ANOVA explores possible reasons for variation. • ANOVA breaks down total variation into possible causes. 9 ANOVA methodology • k samples are analysed and ANOVA is used to test the following hypotheses – H 0 : all population means are equal – H 1 : At least one of the means is different from the others • In this case, there are k treatment levels (groups) 10 ANOVA methodology • ANOVA partitions the total variance of the data into two variances – among (between)-group variation attributable to treatment effects – within-group variation = experimental error which is unexplained by the treatment • Given that the variances of populations are equal, a
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Lecture 3_ANOVA - Treatment or classification variables...

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