Lecture 5: Repeated Measures Analysis & Mixed Designs (ARMS, Utrecht University)

Repeated measures design

Designs with one or more within factors are called repeated measures designs. An example of a within factor is time. But condition can also be a within factor, as long as each participant goes through every condition.

The advantages of a within subjects design are:

• It is more economical (less respondents needed)
• It is more powerful (less noise of unmeasured individual differences)
• Possible to investigate changes over time (in longitudinal context)

The data of a repeated measure design is dependent (because the same respondents are used). This means you need to use an analysis technique that takes this into account.

The null hypothesis is that there is no difference between the groups. This is the same in an ANOVA, so why not use that? Because we know how the data was collected and we know the data is dependent on each other.

There is an assumption: the assumption of sphericity. This means that the variances of all difference scores are equal. You can test this with Mauchly’s test for sphericity. But do not only rely on non-significance of the Mauchly test, also ‘eyeball’ your descriptive data to see if the variance is roughly the same, or look at epsilon.

If the Mauchly test is significant, the assumption of sphericity is not met. If you look at Epsilon: 1,000 is perfect sphericity.

The ‘lower bound’ is based on your design. If you have 4 timepoints, the lower-bound will be: 1/(4-1)=.333.

What to do when the assumption is violated? SPSS offers solutions in the ‘tests of within-subjects effects’ table.

--> Greenhouse-Geisser: for bigger violations; epsilon is smaller than .75.

--> Huynh-Feldt: for milder violations; epsilon is .75 or higher.

If there is a very big violation, and you don’t trust it. Look at the Wilks’ Lambda significance in the ‘multivariate tests’ table. Here you don’t have to worry about sphericity (this is the MANOVA approach). The rule of thumb is: if the epsilon is closer to lower bound that to 1, you use this method.

The follow up tests:

• Post-hoc comparisons between different time points (using alpha corrections)
• Testing pre-specified contrasts. For repeated measures designs (especially if the factor is time) these are called linear and quadratic contrasts. You answer the questions:
  
  • Is the contrast measuring the linear effect significantly non-zero?
  • Is the contrast measuring the quadratic effect significantly non-zero?

These contrasts are called polynomial contrasts and are incluced in SPSS.

Mixed design

Designs with at least one between and at least one within factor are formally called mixed designs (but often also repeated measures).

If the within factor only contains two measurements, you do not have to worry about sphericity.

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