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- Published: October 30, 2021
- Updated: October 30, 2021
- University / College: University of Illinois at Urbana-Champaign
- Level: Bachelor's Degree
- Language: English
- Downloads: 27

Analysis of Variance (ANOVA) Phase-3(DB2) MGM600-0803B-02: Applied Managerial Decision-Making Analysis of Variance (ANOVA) Phase-3(DB2) An ANOVAtest is a technique for analyzing the variances in multiple populations to check they have similar distribution and hence an equivalent mean. In simple words, an ANOVA test is a comparison of means in multiple datasets (populations). 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. The test uses the F distribution and can handle any number of factors, but the researcher often is interested only in a few (Doane, & Seward, 2007).

ANOVA test have in common a set of two assumptions (QMSS e-Lessons: ANOVA):

1. The standard deviations (SD) of the populations for all groups are equal (also referred as an assumption of the homogeneity of variance). For groups 1 through n

2. The samples are randomly selected from the population.

According to Doane, & Seward (2007), the five steps required to perform the F-Ratio test for ANOVA are

Step 1: Formulate the Hypotheses

Step 2: Select significance level (α)

Step 3: State the Decision Rule

Step 4: Calculate the Test Statistic

Step 5: Make the Decision

According to Freund & Wilson (1998), a few important characteristics of the F distribution are

The F distribution is defined only for nonnegative values.

The F distribution is not symmetric.

A different table is needed for each combination of degrees of freedom.

The F distribution always gives the right tail value.

ANOVA test is of two types, One-Factor ANOVA and Two-Factor ANOVA (with and without replication). In One-Factor ANOVA, Dependent Variable (numerical) may be affected by one independent variable (categorical). In Two-Factor ANOVA, Dependent Variable (numerical) may be affected by two independent variables (categorical).

An ANOVA test is useful, when different data sets (more than two) need to be compared for similar distribution population (treatment. A t-test can also be used for comparison; however, it is limited to two samples. For more than two data sets, many t-test needs to be carried out sequentially that will increase statistical error due to accumulation. An ANOVA test lessons the statistical error due to analysis of entire data set at once and makes it more likely that a determination can be made in valid manner (Skrzypczak, 2006; Pieniazekon, A. 2007).

Example 1: Manufacturing Defect Rates

Suppose 10 day’s daily defect rates for automotive computer chips manufactured production data for four different plant locations were available. Now for this data ANOVA can be useful for determining whether the observed differences in the plants’ sample mean defect rates merely due to random variation or the observed differences between the plants’ defect rates too great to be attributed to chance. Here ANOVA hypothesis will be ‘mean defects rates are same for at all four plants (H0)’ and ‘at least one mean differs from the others (H1)’. The One-Factor ANOVA dependent variable will be defect rate and independent variable will be plant locations (Doane, & Seward, 2007).

Example 2: Hospital Length of Stay

Suppose a hospital management needs to test whether a patient’s length of a stay (LOS) depends on the diagnostic-related group (DRG) code and the patient’s age group, so that resources and fixed costs are correctly allocated. Considering case of bone fracture, LOS is a dependent variable measured in hours and type of fracture (facial, radius or ulna, hip or femur, other lower extremity, all other) and three age groups (under 18, 18 to 64, 65 and over) are dependent variables. For One-Factor ANOVA test, Length of Stay will be taken as dependent variable and Type of Fracture will be taken as independent variable. For Two-Factor ANOVA test, Length of Stay will be taken as dependent variable and Type of Fracture and Age Group will be taken as independent variables (Doane, & Seward, 2007).

Example 3: Automobile Painting

Quality of paint is a major concern for car markets. One of the main characteristics of paint is its viscosity. Suppose viscosity is to be tested for dependence on application temperature (low, medium, high) and/or the supplier of the paint. For One-Factor ANOVA test, Viscosity will be taken as dependent variable and Temperature will be taken as independent variable. For Two-Factor ANOVA test, Viscosity will be taken as dependent variable and Temperature and Supplier will be taken as independent variables (Doane, & Seward, 2007).

ANOVA can help determining sales of snack foods in different location for Company W so that its marketing objectives fulfilled.

References:

Doane, D.P. & Seward, L.E. (2007). Applied Statistics in Business and Economics. New York: McGraw-Hill/Irwin.

Freund, R.J. & Wilson, W.J. (1998). Regression Analysis: Statistical Modeling of a Response Variable. Academic Press.

Pieniazekon, A. (2007, April 28). One Way Analysis of Variance (ANOVA). Retrieved September 16, 2008, from http://www.adampieniazek.com/statistics/one-way-analysis-of-variance-anova/

QMSS e-Lessons: ANOVA. Retrieved September 16, 2008, from http://www.columbia.edu/ccnmtl/projects/qmss/anova_about.html

Skrzypczak, P. (2006, April 27). ANOVA Testing, Treatments and Blocking Variables. Retrieved September 16, 2008, from http://www.jaculis.org/reference_articles/ANOVA2.html

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