Two Way ANOVA (Analysis of Variance) - Without Replication

Jay Arthur
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What's cool about QI Macros Two-Way ANOVA?
Unlike other statistical software, the QI Macros is the only SPC software that compares the p-values to the significance level and tells you when to "Accept or Reject the Null Hypothesis" and what that tells you: "Means are Same or Different ".

Two Way Anova (Analysis of variance) , also known as two factor Anova, can help you determine if two factors have the same "mean" or average. This is a form of "hypothesis testing."

The null hypothesis is that the means are equal:

• H₀: Factor 1's Means = Factor 2's Means

The alternate hypothesis is:

• H_a: The means are different.

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%).

Two-Way ANOVA Analysis Without Replication

What if you want to know if there is a difference in driving distance between three brands of golf balls for different golfers? (From Advanced Statistics Demystified by Dr. Larry J. Stephens.)

Using Excel and the QI Macros, run a two-way analysis without replication (alpha=0.05 for a 95% confidence). Click on QI Macros menu and select: ANOVA Two Factor without replication.

Here are the results:

Interpreting the Anova Two Way Without Replication Results

In case you want to know how to do this manually, use these instructions.

Here, the P-value for Rows (i.e., golfers) is less than alpha (0.05), so we can reject the hypothesis that all of the golfers are the same. The P-Value for Columns (i.e., golf balls) is also less than alpha, so we can reject the hypothesis that all of the golf balls are the same.

It does look like Brand B and C are similar. We could run a paired two sample t test on Brands B and C to determine if they deliver the same average distance.

Since the p values are greater than alpha (0.05), we can accept the null hypothesis that there is no difference between the two brands of golf balls, except perhaps price.

The QI Macros can perform the following types of tests and interpret the results for you by indicating whether you should accept or reject the null hypothesis:

• One Way ANOVA analysis
• Two-Way ANOVA analysis without replication - see below
• Two-Way ANOVA analysis with replication

Other Statistical tests in the QI Macros

• data normality test
• test of proportion
• t test two sample in Excel
• F test in Excel

Two Way Analysis of Variance is just one of the tools included in the QI Macros Statistical Process Control Software for Excel.

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