Two Factor Multivariate Repeated Measures


MANOVA can be used instead of a Two Factor Repeated Measures ANOVA, especially when the sphericity assumption doesn’t hold. We illustrate the approach by repeating Example 1 of Two Factor Repeated Measures ANOVA.

Example 1 A new drug is tested on a random sample of insomniacs: 7 young people (20-40 yrs), 7 middle aged people (40-60 yrs) and 7 older people (60+ yrs). The number of minutes each person sleeps per night is recorded for 5 successive nights in Figure 1. Determine whether the drug is effective.

Two factors repeated measures

Figure 1 – Data for Repeated Measures Analysis

As described in Multivate One Factor Repeated Measures, we first calculate the differences between the data in the adjacent columns, as shown on the left side of Figure 2.

Manova repeated measures

Figure 2 – Repeated Measures Analysis using MANOVA

Next we use the Real Statistics MANOVA data analysis tool by pressing Ctrl-m, double clicking on Analysis of Variance (or Multivariate Analyses) and selecting MANOVA from the list of options on the dialog box that appears. Finally we fill in the dialog box that now appears as shown in Figure 3 and press the OK button.

MANOVA dialog box

Figure 3 – MANOVA dialog box

The result is shown on the right side of Figure 2. All the tests show there is no significant difference between the mean hours of sleep for the three age groups. Interestingly enough this is the opposite conclusion from the univariate test.

Observation: It is important that none of the labels in range A6:A26 (and then H6:H26) be blank. This is acceptable for the univariate test since we had to inform the data analysis tool that there are 7 rows per group. For MANOVA the rows can appear in any order and the labels are mandatory.

Using Repeated Measures Option to MANOVA

We can also use the Repeated Measures option to the Real Statistics MANOVA data analysis tool to carry out this test directly. To perform the analysis for Example 1, as before, we press Ctrl-m, double click on Analysis of Variance and select MANOVA from the list of options on the dialog box that appears. This time when the dialog box shown in Figure 3 appears, we insert A5:F26 in the Input Range field and select Repeated Measures as the Analysis Type.

The output is similar to that shown in Figure 2.

Observation: Note that we can also select any of the various options shown in Figure 3, although in the current release of the software any Contrasts which rely on the fact that the columns are a repeated measures factor have to be performed using the Repeated Measures ANOVA data analysis tools using the input data in range H5:L26.

Observation: The approach described above using the Repeated Measures option to the MANOVA data analysis tool works provided that the input range has at least three columns of data. With only two columns of data, we use the approach described in Example 2.

Example 2: Perform the analysis from Example 1 using the data shown on the left side of Figure 4 (i.e. range A5:C26).

Repeated measures two variables

Figure 4 – Data for Repeated Measures Analysis with Two Dependent Variables

We begin as before by creating a table of differences, as shown on the right side of Figure 4 (i.e. range E5:F26). This can be done manually (e.g. by inserting the formula =C6-B6 in cell F6, highlighting range F6:F26 and pressing Ctrl-D) or by using the MANOVA data analysis tool and selecting Repeated Measures as before. This time the MANOVA data analysis will contain error cells, and so we will only use the range of differences (E5:F26).

To conduct the analysis we use the Single Factor ANOVA data analysis tool inserting E6:F26 in the Input Range field and selecting Standard (stacked) format as the Input Format. The output is shown in Figure 5.

oneway anova repeated measures

Figure 5 – Analysis using Single Factor ANOVA

16 Responses to Two Factor Multivariate Repeated Measures

  1. manasi says:

    Can you also advise me how to arrange data in excel. My data is in this format:
    Subject day time alertness concentration
    1. 1. 1. 6. 5
    1. 1. 2 5 4
    How can I rearrange this data. I know the standard format for manova but can you explain how I can easily rearrange this data instead of manual entries.

    • Charles says:

      How many days/times values do you have?

      • manasi says:

        I have 15 subjects. Two days. Four times and 10 constructs like alertness etc.

        • Charles says:

          Sorry, but the version of MANOVA that is available on the Real Statistics Resource Pack doesn’t support this level of complexity.

          • Manasi says:

            Day 1: Experimental condition with social networking break
            Day 2: Experimental condition with physically active break
            Fatigue questionnaire is administered four times (T1, T2, T3, T4) on both days.
            All 15 participants complete fatigue questionnaire on both days.
            Fatigue questionnaire has 10 different constructs.

  2. juan says:

    Dear Sir,

    I want to know if MANOVA with repeated measures is the right test in this case:
    – 15 subjects
    – 1 Independent Variable: audio system (3 levels)
    – 7 Dependent Variables: (different constructs)

    The same 15 subjects had to asses the 3 audio systems (simultaneous listening task) using the 7 rating scales (for each system).

    Can I use the option “repeated measures” of the Real Statistics MANOVA data analysis tool (mac user) to analyze the data ?
    How should I arrange the data in Excel ?

    Thanks for your help,

  3. Aba says:

    I’m writing a research paper which requires made up data, and I chose to test the differences in Group A n=96 and Group B n=89 during 2 different time frames. at initial, then 1 year, than 3 year marks. I know that a MANOVA is the best tool to calculate statistical significance between the 2 groups, but how do I use the MANOVA to do this? I’ve tried i excel but a message pops up stating that I need a positive interger, or that I need more than 2 rows of data..Please help !

    Thank you

  4. Carlos Manacorda says:

    Dear Charles,

    First of all, thak you very much for your effort to develop such a useful tool!
    My question is:
    Is it possible (and how?) to study 22 dependent variables recorded 8 times in 40 subjects (23 controls and 17 treated) with some tool of the package? i. e.:

    2 Treatments
    8 times
    22 variables

    I´d like to know if there are treatments, days and interaction term significants.

    Thanks a lot and best wishes!

    • Charles says:

      I don’t completely understand your scenario.
      1. Are you saying that you have 2 treatments, one with 23 subjects and the other with 17 subjects?
      2. Are you saying that each subject is measured 8 times? Is each subject measured in day 1, day 2, …, day 8?
      3. Are you saying that 22 types of characteristics are being measured for each of the 40 subjects?

      • Carlos Manacorda says:

        The answers are yes, for all your questions.
        The characteristics that are being measured are shape coordinates (landmarks). As I have 11 points, there are 22 (X and Y) shape coordinates, which in principle I can assume they are independent.

        I think my problem is multivariate longitudinal data.

        • Charles says:

          Yes, this does seem like a fit for MANOVA.

          • Carlos Manacorda says:

            I thought so. But my problem is that the individuals that are being measured are the same across the experiment (it´s like a trial with a drug when patients are repeatedly examined for various reponse variables); and I cannot assume independence of the experimental units across days.
            Therefore, I thought that MANOVA is not an option… but is there a way to overcome this problem? Is it implemented in RealStatistics…?


          • Charles says:

            You can use repeated measures Manova in this case. Some versions of this are supported in Real Statistics.

  5. Te-hsin Liu says:

    Hi Charles,

    Can we rune a Three-way ANOVA here?

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