ANOVA is a statistical technique used to compare two or more groups on one or more dependent variables. It seeks to identify sources of variation in a numerical dependent variable (the response variable). ANOVA compares means and each possible value of a factor or combination of factors is a treatment. Sample observations within each treatment are viewed as coming from populations with possibly different means.
ANOVA test can be One-Factor ANOVA or Two or more-factor ANOVA. However, One-factor ANOVA is the most common and suffices for many business situations. The null and alternate hypothesis of ANOVA test is written as
(The means are the same)
(At least one mean is different)
Example 1: ABC Company manufactures a product in four manufacturing unit and wants to test whether weight of the product is same across all four manufacturing unit (treatment variable). Product weight is a numerical response variable and measured in kilograms. For this scenario, the One-factor model is
One factor: Product weight = (Manufacturing unit)
Example 2: Alpha Retail Sales wants to test sales over a week period at four outlets (treatment variable) in New York. Sales is a numerical response variable and measured in $ million. For this scenario, the One-factor model is
One factor: Sales = (Outlet)
Example 3: XYZ Hospital management want to test, whether a patient’s length of stay in hospital depends on the diagnostic-related group (DRG) code (treatment variable) and the patient’s age group (blocking variable). Considering the case of a bone fracture. Length of stay is a numerical response variable and is measured in hours. The five types of fracture organized by hospital are facial, radius or ulna, hip or femur, other lower extremity and all other. In addition, patients are also divided in 3 age categories as under 18 years, 18 to 64 years, and 65 and over (Doane & Seward, 2007). For this scenario, the two possible ANOVA models are
One factor: Length of stay = (Type of fracture)
One factor: Length of stay = (Type of fracture, Age Group)
One-Factor ANOVA and Two-Factor ANOVA as shown in figure 1 can summarize the above scenario in example 3.
Figure 1: ANOVA models for hospital length of stay (Source: Doane & Seward, 2007)
Doane D.P. & Seward L.E. (2007). Applied Statistics in Business and Economics. McGraw-Hill/Irwin: New York
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