Analyzing data from a randomized block design

This tutorial covers the steps for doing a randomized block design analysis using repeated measures ANOVA in StatCrunch. To begin, load the Granola comparison data set, which will be used throughout this tutorial. Ten subjects in this fictional study were each asked to sample three kinds of granola cereal, labelled simply "A", "B", and "C", and to rate the granola's taste on a scale of 1 to 10. Each subject was given the three granola samples in random order. The goal is to determine whether the mean ratings for the three granola types differ significantly.

Analysis using two way ANOVA

This is a randomized block design, where each of the ten subjects is a "block".
Choose Stat > ANOVA > Two Way.
Select the Rating column for Responses in.
Select the Subject column for Row factor in.
Select the Granola column for Column factor in.
Check the boxes for Display means table
and for Fit additive model,
then click Compute!
The resulting ANOVA table shows the following mean ratings: mean A=6.1, mean B=6.2, and mean C=7.3. The P-value for Granola is shown as 0.0007, meaning that there is about a 7 in 10,000 chance that differences this large would occur by random chance.

Analysis using repeated measures ANOVA

To analyze the data using repeated measures ANOVA,
choose Stat > ANOVA > Repeated Measures.
Select the Rating column for Responses in.
Select the Granola column for Treatments in.
Select the Subject column for Blocks in
and click Compute!
The resulting ANOVA table shows exactly the same means and P-value for Granola as does two way ANOVA. In fact, two way ANOVA with Fit additive model specified will always give the same results as repeated measures ANOVA. Fit additive model indicates that there is no interaction between the two factors, and is required when there is only one observation for each combination of factor levels. (Repeated measures ANOVA always assumes an additive model, so it is not specified in that procedure.)

If a one way ANOVA had been performed instead, without the benefit of blocking, the mean for each Granola type would have been the same as with two way or repeated measures ANOVA, but the P-value would instead be 0.113, meaning that there is about a 1 in 9 chance of differences this large occurring by random chance. The two way ANOVA gives a far more sensitive test (that is, a much smaller P-value) in this case because it removes the variation due to subjects. Looking at the means table for two way ANOVA (above), it is clear that there is not much variation for the ratings of an individual subject across the three granola types. There is more variation in ratings across subjects.

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