ANOVA

1
ANOVA

• (Chapter - 04/D)

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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 is an explanatory (or predictor)
  variable (as oppose to a response variable).

3
One-Way ANOVA

• For example
• In a study comparing the appeal of four different
  destination types, the factor under investigation
  is the destination type.

4
One-Way ANOVA

• Levels (factor levels) refer to the categories,
  measurements, or strata of a factor of interest
  in the current experiment.
• Level is a particular form of a factor.
• For example in the appeal study, each destination
  type is a factor level.

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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.

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One-Way ANOVA
Assumptions

• Factor levels (or groups) are independent,
• Observations are randomly obtained,
• Observations are normally distributed,
• Groups have equal variances.

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One-Way ANOVA
Null hypothesis in an ANOVA experiment
Alternative hypothesis in an ANOVA experiment
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One-Way ANOVA

• Excel application
• Tools/ Data Analysis / Single Factor ANOVA
• Input Range (w/out Labels
• Alpha level
• Output Range

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ANOVA - Example

• Using Transmission cost data, please determine
  whether alternative Processes A or B is less
  costly than current process in production of
  transmission.

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ANOVA - Example
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Contingency Table

• A Contingency Table is a matrix of r rows and
  c columns that shows the value of two
  categorical variables together.
• Use of Contingency Tables is to determine whether
  two categorical variables are independent.
• Decision is based on Chi-Square test

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Contingency Table - Example

• Are there more females accountants holding CPA
  designation than their male counter parts?
• Data

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Contingency Table - Example

• Excel Application
• 1. Create Expected Frequency Table

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Contingency Table - Example

• Excel Application
• Create Expected Frequency Table
• Compute p CHITEST(Obsr_range, Exp_range)
• Compare with alpha

NOTE Rage should include numbers excluding
totals and labels
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Next Lesson

• (Chapter - 06/A)
• Simple Linear Regression