Two Way ANOVA (Analysis of Variance) With Replication

Jay Arthur
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When to Use Two Way Anova

Two Way Anova (Analysis of variance) , also known as two factor 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. The alternate hypothesis is that the means are not equal.

• H₀: Mean1 = Mean2
• 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%).

Excel and the QI Macros can perform:

• Anova One Way analysis
• Anova Two Way analysis without replication
• Anova Two Way analysis with replication

Two-Way ANOVA Analysis With Replication

What if you have two populations of patients (male/female) and three different kinds of medications, and you want to evaluate their effectiveness? You might run a study with two or more "replications", three men and three women.

Using Excel and the QI Macros, run a two-way Anova analysis with replication (alpha=0.05 for a 95% confidence).

Interpreting the Anova Two Way Results

Here, the P-value for Male/Female is greater than alpha (.17894 > .05), so we accept the null hypothesis that the means are the same. The P-Value for Drugs is greater than alpha (.10634 > .05), so the null hypothesis holds as well (means are the same).

The P-value for the interaction of the drugs and patients is less than alpha (.00581 < .05), so we reject the null hypotheis and can say that the effectiveness of the drugs is not the same for the two categories of patients.

Tips on Setting Up Your Data in Excel

To analyze data, Excel requires you to set the data up in a way that can be analyzed.

The example below shows how to set up the data for two categories of patients treated with three different drugs.

Then, if you're just interested in the single factor DRUGS, select and run a Anova single factor on the three drug columns.

If you're interested in a Anova two-factor analysis (patients vs drugs), select and run a two-factor analysis with repetition (more than one patient in the category receives the same drug).

Other Statistical tests in the QI Macros

• data normality test
• test of proportion
• t test in Excel
• f test in Excel

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

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