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Two Way ANOVA

In the One Way ANOVA example the five replications within each row were all taken under the same test conditions. Consider the example where three treatments are evaluated on four different patients:

 Therapy Andrew Belinda Chris Dave Relaxed 110 140 100 130 Normal 115 150 105 135 High Intensity 117 155 100 135

The hypothesis is:

H0 The therapies all give the same result
H1 At least one of the therapies gives a different response

Use a level of significance of 0.05.

The patients are all different, and a 'One Way ANOVA' would not cause the null hypothesis to be rejected. However a two way ANOVA separates the variation due to the therapy from that due to different patient characteristics:

 Source of Variation Sum of Squares Degrees of Freedom Mean Square F0 p-value Therapy 113.17 2 56.58 5.40 0.046 Patient 3832.67 3 1277.56 121.99 0 Error 62.83 6 10.47 Total 4008.67 11

The null hypothesis is rejected, the therapies give different results at the 0.05 level of significance.

 Analysis of Variance (ANOVA) is covered in the MiC Quality online course Advanced Statistics. The use of ANOVA in experimental design is covered in the MiC Quality Design of Experiments course. Try out our courses by taking the first module of the Primer in Statistics free of charge.
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