Engineering Probability and Statistics 8 -1 Analysis of Variances
8 Analysis of Variance
• Using Statistics
• The Hypothesis Test of Analysis of Variance
• The Theory and Computations of ANOVA
• The ANOVA Table and Examples
• Further Analysis
• Models, Factors, and Designs
• Two-Way Analysis of Variance
• Blocking Designs
• Using the Computer
• Summary and Review of Terms
nternational University – Dept. of ISE Assoc. Prof. Ho Thanh Phong
, Engineering Probability and Statistics 8 -2 Analysis of Variances
8-1 ANOVA: Introduction
• ANOVA (ANalysis Of VAriance) is a statistical
method for determining the existence of
differences among several population means.
– ANOVA is designed to detect differences among means
from populations subject to different treatments
– ANOVA is a joint test
• The equality of several population means is tested
simultaneously or jointly.
– ANOVA tests for the equality of several population
means by looking at two estimators of the population
variance (hence, analysis of variance).
nternational University – Dept. of ISE Assoc. Prof. Ho Thanh Phong
, Engineering Probability and Statistics 8 -3 Analysis of Variances
Analysis of Variance: Introduction
(continued)
• In an analysis of variance:
– We have k independent random samples, each one corresponding to
a population subject to a different treatment.
– We have:
• n = n1+ n2+ n3+ ...+nk total observations.
• k sample means: x1, x2 , x3 , ... , xk
– These k sample means can be used to calculate an
estimator of the population variance. If the population
means are equal, we expect the variance among the sample
means to be small.
• k sample variances: s12, s22, s32, ...,sr2
– These sample variances can be used to find a pooled
estimator of the population variance.
nternational University – Dept. of ISE Assoc. Prof. Ho Thanh Phong
8 Analysis of Variance
• Using Statistics
• The Hypothesis Test of Analysis of Variance
• The Theory and Computations of ANOVA
• The ANOVA Table and Examples
• Further Analysis
• Models, Factors, and Designs
• Two-Way Analysis of Variance
• Blocking Designs
• Using the Computer
• Summary and Review of Terms
nternational University – Dept. of ISE Assoc. Prof. Ho Thanh Phong
, Engineering Probability and Statistics 8 -2 Analysis of Variances
8-1 ANOVA: Introduction
• ANOVA (ANalysis Of VAriance) is a statistical
method for determining the existence of
differences among several population means.
– ANOVA is designed to detect differences among means
from populations subject to different treatments
– ANOVA is a joint test
• The equality of several population means is tested
simultaneously or jointly.
– ANOVA tests for the equality of several population
means by looking at two estimators of the population
variance (hence, analysis of variance).
nternational University – Dept. of ISE Assoc. Prof. Ho Thanh Phong
, Engineering Probability and Statistics 8 -3 Analysis of Variances
Analysis of Variance: Introduction
(continued)
• In an analysis of variance:
– We have k independent random samples, each one corresponding to
a population subject to a different treatment.
– We have:
• n = n1+ n2+ n3+ ...+nk total observations.
• k sample means: x1, x2 , x3 , ... , xk
– These k sample means can be used to calculate an
estimator of the population variance. If the population
means are equal, we expect the variance among the sample
means to be small.
• k sample variances: s12, s22, s32, ...,sr2
– These sample variances can be used to find a pooled
estimator of the population variance.
nternational University – Dept. of ISE Assoc. Prof. Ho Thanh Phong
