# Analyzing a repeated measures design

You can use Fit General Linear Model to analyze a repeated measures design in Minitab. To use Fit General Linear Model, choose Stat > ANOVA > General Linear Model > Fit General Linear Model.

In all cases, you must arrange the data in the Minitab worksheet so the response values are in one column, subject IDs are in a different column, and each factor has its own separate column.

The following examples show analyses of several different repeated measures designs. You can find the data and more information on these examples in J. Neter, M.H. Kutner, C.J. Nachtsheim, and W. Wasserman (1996). Applied Linear Statistical Models, 4th edition. WCB/McGraw-Hill.

## Example of a single-factor experiment with repeated measures on all treatments

In this designed experiment each subject receives each treatment in succession. Create three columns in the Minitab worksheet: one column for the measurements, one column identifying which subject corresponds to that measurement, and one column identifying the treatment applied to that subject. Each row represents a single measurement.

For more information, see page 1166, model 29.1 in Neter, Kutner, Nachtsheim, and Wasserman (1996).

C1 C2 C3
Subject Dosage Measurement
A low 1.33
A medium 0.27
B medium 0.49
B low 0.99
C medium 0.41
C low 1.12
1. Choose Stat > ANOVA > General Linear Model > Fit General Linear Model.
2. In Responses, enter Measurement.
3. In Factors, enter Subject Dosage.
4. Click Random/Nest.
5. Under Factor type, choose Random in the field beside Subject.
6. Click OK in each dialog box.

## Example of a two-factor experiment with repeated measures on both factors

In this designed experiment each subject is measured after receiving, successively, every combination of the levels of the two factors A and B. For example, suppose there are three subjects, and factors A and B each have two levels. For more information, see page 1177, model 29.10 in Neter, Kutner, Nachtsheim, and Wasserman (1996). The designed experiment continues as follows:
1 2 3 4
Subject 1 A1B2 A2B2 A1B1 A2B1
Subject 2 A2B1 A1B2 A2B2 A1B1
Subject 3 A1B1 A2B1 A1B2 A2B2
1. Create four columns in the Minitab worksheet: one column for the measurements, one column identifying which subject corresponds to that measurement, one column for Factor A, and one column for Factor B.
C1 C2 C3 C4
Subject Temperature Fabric Measurement
A High Old 10.4
A High New 9.5
A Low New 7.6
A Low Old 6.9
B High New 9.1
B High Old 7.9
B Low New 10.0
B Low Old 8.1
2. Choose Stat > ANOVA > General Linear Model > Fit General Linear Model.
3. In Responses, enter Measurement.
4. In Factors, enter Subject Temperature Fabric.
5. Click Random/Nest.
6. Under Factor type, choose Random in the field beside Subject.
7. Click OK.
8. Click Model.
9. Use the dialog box to add interactions to the model. For example, to add the interaction between Temperature and Fabric:
1. In the field under Factors and covariates, select both Temperature and Fabric.
2. Verify that 2 is selected beside Interactions through order.
3. Click Add beside the field that has 2 selected.
4. Click OK in each dialog box.

## Example of a two-factor experiment with repeated measures on one factor

In this designed experiment each subject is measured after receiving, successively, all levels of Factor B in combination with only one level of Factor A. For more information, see page 1186, model 29.16 in Neter, Kutner, Nachtsheim, and Wasserman (1996). This designed experiment continues as follows:
Factor A Factor B Treatment Order 1 Treatment Order 2
A1

1

...

n

A1B1

...

A1B2

A1B2

...

A1B1

A2

n+1

...

2n

A2B2

...

A2B1

A2B1

...

A2B2

1. Create four columns in the Minitab worksheet: one column for the measurement, one column identifying which subject corresponds to that measurement, one column for Factor A, and one column for Factor B.
C1 C2 C3 C4
Subject Temperature Fabric Measurement
A High Old 1.1
A High New 2.2
B High New 1.9
B High Old 1.2
C Low Old 0.8
C Low New 1.1
D Low Old 0.9
D Low New 1.3
2. Choose Stat > ANOVA > General Linear Model > Fit General Linear Model.
3. In Responses, enter Measurement.
4. In Factors, enter Subject Temperature Fabric.
5. Click Random/Nest.
6. Under Nested in specified factors, enter Temperature beside Subject.
7. Under Factor type, choose Random in the field beside Subject.
###### Note

If any factors besides Subject are random, choose Random for them too.

8. Click OK.
9. Click Model.
10. Use the dialog box to add interactions to the model. For example, to add the interaction between Temperature and Fabric:
1. In the field under Factors and covariates, select both Temperature and Fabric.
2. Verify that 2 is selected beside Interactions through order.
3. Click Add beside the field that has 2 selected.
4. Click OK in each dialog box.
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