Analysis of Variance (ANOVA)

Jay Arthur
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When to use ANOVA? When you want to determine if the means (i.e., averages) are the same or different.

Analysis of variance (ANOVA) can help you determine if two or more samples have the same "mean" or average. This is a form of "hypothesis testing."

The null hypothesis is that the means are equal:

• H₀: Mean1 = Mean2

The alternate hypothesis is that the means are not equal:

• H_a: Mean1 <> Mean2

The goal is to accept or reject the null hypothesis (i.e., the samples have different means) at a certain confidence level (95% or 99%).

What's cool about QI Macros ANOVA? When you run ANOVA, you don't have to think. QI Macros automatically compare the p-value to the signficance and tell you if you should accept or reject the hypothesis and if the means are the same or different.

Excel and the QI Macros can perform:

• One-Way, Single Factor ANOVA
  - Example (click here)
  
• Two-Factor ANOVA - without replication
  - Example (click here)
  
• Two-Factor ANOVA Example - with replication
  - Example (click here)

ANOVA Assumptions

ANOVA assumes three things:

• The data is randomly selected.
• The data is normally distributed.
• The populations have equal variances.

Hypothesis Testing with the QI Macros

• Hypothesis testing in Excel with QI Macros
  - Click Here
• See Also: t Test - Two Sample for means

Analysis of Variance is just one of the tools included in the QI Macros for Excel SPC Software for Excel.

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