Split-plot ANOVA tests for interactions between a fixed factor (e.g. player type) and repeated measures variable (e.g. before and after season). It analyzes a main effect for each factor and their interaction. A significant interaction indicates groups changed differently over time. For example, a treatment group may improve more from pre-test to post-test than a control group, revealing an effective intervention.

1. Split Plot ANOVA

2. • Another application of ANOVA is mixed design or
“split plot” ANOVA.

3. • Another application of ANOVA is mixed design or
“split plot” ANOVA.
• Split plot ANOVA is a special instance of factorial
ANOVA. Recall that in factorial ANOVA, 2 or more
independent variables are tested for possible
interaction effects on a single dependent variable.

4. • For example, if we compare the number of pizza
slices consumed in one sitting between football,
basketball, and soccer players we would run a One-
Way ANOVA.

5. • For example, if we compare the number of pizza
slices consumed in one sitting between football,
basketball, and soccer players we would run a One-
Way ANOVA.
• Here is how we would input the data:

6. • For example, if we compare the number of pizza
slices consumed in one sitting between football,
basketball, and soccer players we would run a One-
Way ANOVA.
• Here is how we would input the data:
Player Type Pizza Slices Consumed
1 = Football Player 8
1 = Football Player 9
1 = Football Player 11
1 = Football Player 12
2 = Basketball Player 4
2 = Basketball Player 5
2 = Basketball Player 7
2 = Basketball Player 8
3 = Soccer Player 1
3 = Soccer Player 2
3 = Soccer Player 4
3 = Soccer Player 5

7. • For example, if we compare the number of pizza
slices consumed in one sitting between football,
basketball, and soccer players we would run a One-
Way ANOVA.
• Here is how we would input the data:
Player Type Pizza Slices Consumed
1 = Football Player 8
1 = Football Player 9
1 = Football Player 11
1 = Football Player 12
2 = Basketball Player 4
2 = Basketball Player 5
2 = Basketball Player 7
2 = Basketball Player 8
3 = Soccer Player 1
3 = Soccer Player 2
3 = Soccer Player 4
3 = Soccer Player 5

8. • A Factorial ANOVA tests at least two independent
variables or main effects (1. Player Type / 2. Team
Type) along with the interaction between them
(Player Type & Team Type).

9. • A Factorial ANOVA tests at least two independent
variables or main effects (1. Player Type / 2. Team
Type) along with the interaction between them
(Player Type & Team Type).
• Here is how we would input the data for a simple
factorial ANOVA:

10. • A Factorial ANOVA tests at least two independent
variables or main effects (1. Player Type / 2. Team
Type) along with the interaction between them
(Player Type & Team Type).
• Here is how we would input the data for a simple
factorial ANOVA:
Player Type Team Type Pizza Slices Consumed
1 = Football Player 1 = Junior Varsity 8
1 = Football Player 1 = Junior Varsity 9
1 = Football Player 2 = Varsity 11
1 = Football Player 2 = Varsity 12
2 = Basketball Player 1 = Junior Varsity 4
2 = Basketball Player 1 = Junior Varsity 5
2 = Basketball Player 2 = Varsity 7
2 = Basketball Player 2 = Varsity 8
3 = Soccer Player 1 = Junior Varsity 1
3 = Soccer Player 1 = Junior Varsity 2
3 = Soccer Player 2 = Varsity 4
3 = Soccer Player 2 = Varsity 5

11. • A Factorial ANOVA tests at least two independent
variables or main effects (1. Player Type / 2. Team
Type) along with the interaction between them
(Player Type & Team Type).
• Here is how we would input the data for a simple
factorial ANOVA:
Player Type Team Type Pizza Slices Consumed
1 = Football Player 1 = Junior Varsity 8
1 = Football Player 1 = Junior Varsity 9
1 = Football Player 2 = Varsity 11
1 = Football Player 2 = Varsity 12
2 = Basketball Player 1 = Junior Varsity 4
2 = Basketball Player 1 = Junior Varsity 5
2 = Basketball Player 2 = Varsity 7
2 = Basketball Player 2 = Varsity 8
3 = Soccer Player 1 = Junior Varsity 1
3 = Soccer Player 1 = Junior Varsity 2
3 = Soccer Player 2 = Varsity 4
3 = Soccer Player 2 = Varsity 5

12. • A Factorial ANOVA tests at least two independent
variables or main effects (1. Player Type / 2. Team
Type) along with the interaction between them
(Player Type & Team Type).
• Here is how we would input the data for a simple
factorial ANOVA:
Player Type Team Type Pizza Slices Consumed
1 = Football Player 1 = Junior Varsity 8
1 = Football Player 1 = Junior Varsity 9
1 = Football Player 2 = Varsity 11
1 = Football Player 2 = Varsity 12
2 = Basketball Player 1 = Junior Varsity 4
2 = Basketball Player 1 = Junior Varsity 5
2 = Basketball Player 2 = Varsity 7
2 = Basketball Player 2 = Varsity 8
3 = Soccer Player 1 = Junior Varsity 1
3 = Soccer Player 1 = Junior Varsity 2
3 = Soccer Player 2 = Varsity 4
3 = Soccer Player 2 = Varsity 5
Independent
Samples
Another set of
Independent Samples

13. • Split plot ANOVA tests for interactions in the same
way. However, in split plot ANOVA one of the
independent variables is a fixed factor such as group
membership (e.g., player type) and the other
independent variable is a repeated measures
variable (e.g., before and after the season).

14. • Split plot ANOVA tests for interactions in the same
way. However, in split plot ANOVA one of the
independent variables is a fixed factor such as group
membership (e.g., player type) and the other
independent variable is a repeated measures
variable (e.g., before and after the season).
Player Type Before or After the Season Pizza Slices Consumed
1 = Football Player 1 = Before 8
1 = Football Player 1 = Before 9
1 = Football Player 2 = After 11
1 = Football Player 2 = After 12
2 = Basketball Player 1 = Before 4
2 = Basketball Player 1 = Before 5
2 = Basketball Player 2 = After 7
2 = Basketball Player 2 = After 8
3 = Soccer Player 1 = Before 2
3 = Soccer Player 1 = Before 3
3 = Soccer Player 2 = After 4
3 = Soccer Player 2 = After 5

15. • Split plot ANOVA tests for interactions in the same
way. However, in split plot ANOVA one of the
independent variables is a fixed factor such as group
membership (e.g., player type) and the other
independent variable is a repeated measures
variable (e.g., before and after the season).
Player Type Before or After the Season Pizza Slices Consumed
1 = Football Player 1 = Before 8
1 = Football Player 1 = Before 9
1 = Football Player 2 = After 11
1 = Football Player 2 = After 12
2 = Basketball Player 1 = Before 4
2 = Basketball Player 1 = Before 5
2 = Basketball Player 2 = After 7
2 = Basketball Player 2 = After 8
3 = Soccer Player 1 = Before 2
3 = Soccer Player 1 = Before 3
3 = Soccer Player 2 = After 4
3 = Soccer Player 2 = After 5

16. • Split plot ANOVA tests for interactions in the same
way. However, in split plot ANOVA one of the
independent variables is a fixed factor such as group
membership (e.g., player type) and the other
independent variable is a repeated measures
variable (e.g., before and after the season).
Player Type Before or After the Season Pizza Slices Consumed
1 = Football Player 1 = Before 8
1 = Football Player 1 = Before 9
1 = Football Player 2 = After 11
1 = Football Player 2 = After 12
2 = Basketball Player 1 = Before 4
2 = Basketball Player 1 = Before 5
2 = Basketball Player 2 = After 7
2 = Basketball Player 2 = After 8
3 = Soccer Player 1 = Before 2
3 = Soccer Player 1 = Before 3
3 = Soccer Player 2 = After 4
3 = Soccer Player 2 = After 5

17. • Split plot ANOVA tests for interactions in the same
way. However, in split plot ANOVA one of the
independent variables is a fixed factor such as group
membership (e.g., player type) and the other
independent variable is a repeated measures
variable (e.g., before and after the season).
Player Type Before or After the Season Pizza Slices Consumed
1 = Football Player 1 = Before 8
1 = Football Player 1 = Before 9
1 = Football Player 2 = After 11
1 = Football Player 2 = After 12
2 = Basketball Player 1 = Before 4
2 = Basketball Player 1 = Before 5
2 = Basketball Player 2 = After 7
2 = Basketball Player 2 = After 8
3 = Soccer Player 1 = Before 2
3 = Soccer Player 1 = Before 3
3 = Soccer Player 2 = After 4
3 = Soccer Player 2 = After 5
Independent
samples
Repeated
samples

18. • Split-plot ANOVA very effectively tests whether
groups change differently over time.

19. • Split-plot ANOVA very effectively tests whether
groups change differently over time.
Pizza Slices Before the
Season
After the
Season
12
11
10
9
8
7
6
5
4
3
2
1

20. • Split-plot ANOVA very effectively tests whether
groups change differently over time.
Pizza Slices Before the
Season
After the
Season
12
11
10
9
8
7
6
5
4
3
2
1

21. • Split-plot ANOVA very effectively tests whether
groups change differently over time.
Pizza Slices Before the
Season
After the
Season
12
11
10
9
8
7
6
5
4
3
2
1
Football Players
Basketball Players
Soccer Players
2.5 average
slices
4.5 average
slices
4.5 average
slices
6.5 average
slices
8.5 average
slices
10.5 average
slices

22. • Split-plot ANOVA very effectively tests whether
groups change differently over time.
• For example, a treatment group may change more
rapidly (or in a different direction) from pre-test to
post-test than a non-treatment control group

23. • Think of the example of a class that receives
innovative instruction (treatment group) and a class
that does not (non-treatment control group). The
pre-test scores and post-test scores are seen below:

24. • Think of the example of a class that receives
innovative instruction (treatment group) and a class
that does not (non-treatment control group). The
pre-test scores and post-test scores are seen below:
Treatment – Non Treatment Pre-test scores Post-test scores
1 = Treatment Group 5 12
1 = Treatment Group 6 13
1 = Treatment Group 5 14
1 = Treatment Group 6 12
1 = Treatment Group 4 14
2 = Nontreatment Control Group 6 8
2 = Nontreatment Control Group 5 7
2 = Nontreatment Control Group 4 8
2 = Nontreatment Control Group 5 7
2 = Nontreatment Control Group 6 7

25. • Think of the example of a class that receives
innovative instruction (treatment group) and a class
that does not (non-treatment control group). The
pre-test scores and post-test scores are seen below:
Treatment – Non Treatment Pre-test scores Post-test scores
1 = Treatment Group 5 12
1 = Treatment Group 6 13
1 = Treatment Group 5 14
1 = Treatment Group 6 12
1 = Treatment Group 4 14
2 = Nontreatment Control Group 6 8
2 = Nontreatment Control Group 5 7
2 = Nontreatment Control Group 4 8
2 = Nontreatment Control Group 5 7
2 = Nontreatment Control Group 6 7

26. • In a split-plot ANOVA there will be a main effect for
groups, a main effect for time, and an interaction
between group and time.

27. • In a split-plot ANOVA there will be a main effect for
groups, a main effect for time, and an interaction
between group and time.
• In our previous example the main effect for groups
would be the average scores between the treatment
and the non-treatment control group:

28. • In a split-plot ANOVA there will be a main effect for
groups, a main effect for time, and an interaction
between group and time.
• In our previous example the main effect for groups
would be the average scores between the treatment
and the non-treatment control group:
– Average scores for the treatment group – 9.1
– Average scores for the non-treatment group – 6.3

29. • In a split-plot ANOVA there will be a main effect for
groups, a main effect for time, and an interaction
between group and time.
• In our previous example the main effect for groups
would be the average scores between the treatment
and the non-treatment control group:
– Average scores for the treatment group – 9.1
– Average scores for the non-treatment group – 6.3
• This difference is impressive and tells the story
that the treatment scored higher on average
than the non-treatment group.

30. • In a split-plot ANOVA there will be a main effect for
groups, a main effect for time, and an interaction
between group and time.
• The second main effect is between pre and post-tests.

31. • In a split-plot ANOVA there will be a main effect for
groups, a main effect for time, and an interaction
between group and time.
• The second main effect is between pre and post-tests.
– Average pre-test score – 5.2
– Average post-test score – 10.2

32. • In a split-plot ANOVA there will be a main effect for
groups, a main effect for time, and an interaction
between group and time.
• The second main effect is between pre and post-tests.
– Average pre-test score – 5.2
– Average post-test score – 10.2
• This difference is also impressive.

33. • In a split-plot ANOVA there will be a main effect for
groups, a main effect for time, and an interaction
between group and time.
• The second main effect is between pre and post-tests.
– Average pre-test score – 5.2
– Average post-test score – 10.2
• This difference is also impressive.
• But what we don’t know is how different their
growth trajectory is across time.

34. • The interaction term will reveal whether there is
differential change over time according to group
membership. If it is significant, then plotting the
interaction will reveal the nature of the differential
change.

35. • The interaction term will reveal whether there is
differential change over time according to group
membership. If it is significant, then plotting the
interaction will reveal the nature of the differential
change.
• Here is a graph that shows the interaction effect or
compares the growth or decay trajectory over time:

36. Scores Pre-test Post-test
14
13
12
11
10
9
8
7
6
5
4
3
2
1

37. Scores Pre-test Post-test
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Treatment Group
Non-Treatment
Control Group
7.4 points
5.2 points
5.2 points
13.0 points

38. Scores Pre-test Post-test
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Treatment Group
Non-Treatment
Control Group
7.4 points
5.2 points
5.2 points
13.0 points
• In this case the
interaction effect is
very impressive.

39. Scores Pre-test Post-test
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Treatment Group
Non-Treatment
Control Group
7.4 points
5.2 points
5.2 points
13.0 points
• In this case the
interaction effect is
very impressive.
⁻ Pre-post
differential for
treatment group
(5.2 – 13 = 7.8
absolute value)

40. Scores Pre-test Post-test
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Treatment Group
Non-Treatment
Control Group
7.4 points
5.2 points
5.2 points
13.0 points
• In this case the
interaction effect is
very impressive.
⁻ Pre-post
differential for
treatment group
(5.2 – 13 = 7.8
absolute value)
⁻ Pre-post
differential for
non-treatment
control group (5.2
– 7.4 = 2.2
absolute value)

41. • Now we see that the growth differential between the
two groups is vastly different. The non-treatment
control group increased by only 2.2 points between
pre and post-tests. The treatment group increased
by 7.8 points. This adds a more informative piece to
the puzzle we are trying to put together.

42. • Now we see that the growth differential between the
two groups is vastly different. The non-treatment
control group increased by only 2.2 points between
pre and post-tests. The treatment group increased
by 7.8 points. This adds a more informative piece to
the puzzle we are trying to put together.
• If the interaction term is not significant, then an
interpretation of the main effects may be
informative.

43. Scores Pre-test Post-test
14
13
12
11
10
9
8
7
6
5
4
3
2
1

44. Scores Pre-test Post-test
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Treatment Group
Non-Treatment
Control Group
7.4 points
5.2 points
10.8 points
13.0 points
• For example, in the
table the groups have
the same measured
difference at the
beginning as they do
at the end, but their
growth is identical.

45. Scores Pre-test Post-test
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Treatment Group
Non-Treatment
Control Group
7.4 points
5.2 points
10.8 points
13.0 points
• For example, in the
table the groups have
the same measured
difference at the
beginning as they do
at the end, but their
growth is identical.
• In this case there is no
interaction effect
because their growth
rates are similar.

46. Scores Pre-test Post-test
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Treatment Group
Non-Treatment
Control Group
7.4 points
5.2 points
10.8 points
13.0 points
• For example, in the
table the groups have
the same measured
difference at the
beginning as they do
at the end, but their
growth is identical.
• In this case there is no
interaction effect
because their growth
rates are similar.
• Therefore, the main
effect (pre-post
difference) is the only
difference we are
interested in.