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Flexible factorial

In this tutorial we will look at experimental designs with two or more factors (experimental manipulations) at the between-subjects level. The key strength of factorial designs is they allow us to test for interactions between different factors, as well as the individual effects of each factor (main effects). We will do this using a flexible factorial design and the previously introduced dataset.

We will use the contrast corresponding to overall task activation (con_0009.nii) and explore whether there is an interaction between participants’ handedness and the hand used to execute a task response. As you may remember from the data description, we have four groups of participants here: (1) right handed responding with their right hand, (2) right handed responding with their left hand, (3) left handed responding with their right hand, and (4) left handed responding with their left hand. This is referred to as a 2-by-2 design, with factors response hand (left or right) and handedness (left or right).

Specifying the model

  1. Make an empty folder (directory) where you will save your results. Navigate to derivatives/second_level and make a folder for this analysis. Name it something meanigful to you, e.g. factorial_handedness_response_hand_task.
  2. Select Specify 2nd level from the SPM menu.
  3. In the pop-up batch editor window, select your newly created output folder by clicking Directory and navigating to derivatives/second_level/factorial_handedness_response_hand_task in the selection box.
  4. Define your statistical model by selecting Design Flexible factorial.
  5. Now, under Factors specify the factors you want to investigate, (1) Name Handedness, (2) Name Response hand. Leave the remaining options as default.
  6. Now let’s input our data. Under Specify subjects or all scans & factors you’ll have two ways to do this. You can either specify your subjects and factors on at a time or select all the relevant scans for all subjects in one step and manually specify a corresponding factor matrix. We will choose the latter option, Specify subjects or all scans & factors Specify all.
  7. Under Scans we will specify all contrast images corresponding to task activation (con_0009.nii) for all participants. Using the selection window recursively filter for contrast con_0009.nii. To do this, navigate to derivatives/first-level via the left-hand side panel. In the filter box, type in ^con_0009.nii and click the Rec button. You should see 40 volumes selected in the bottom window. Double check that the correct contrast and subjects have been selected. Confirm selection by pressing Done.

  8. Now, we’ll specify our factor matrix, which identifies which scans go with which experimental factors. SPM can model the effects of up to three factors, plus participant effects. Therefore the matrix has a maximum of 4 columns (nscans-by-4). For this example, we have 40 participants and one scan from each participant (^con_0009.nii). Our matrix is as follows: 

    1   1   1
2   1   1
3   1   1
4   1   1
5   1   1
6   1   1
7   1   1
8   1   1
9   1   1
10  1   1
11  1   1
12  1   1
13  1   2
14  1   2
15  1   2
16  1   2
17  1   2
18  1   2
19  1   2
20  1   2
21  1   2
22  1   2
23  1   2
24  2   1
25  2   1
26  2   1
27  2   1
28  2   1
29  2   1
30  2   2
31  2   2
32  2   2
33  2   2
34  2   2
35  2   1
36  2   2
37  2   2
38  2   2
39  2   2
40  2   2

    Let’s break it down.

    The first column indicates which participant each image belongs to. It should contain distinct contiguous integers if you’re including a single scan per participant. If you have multiple scans per participant, make sure that rows corresponding to the same participants in the factor matrix are marked with the same index.

    The following two columns mark the factors and their levels. In our case, we have two factors (handedness and response hand) with two levels each (1=left and 2=right). That’s why we have two columns filled with 1’s and 2’s. The second column indicates which level of the handedness factor each image belongs to, and the third column indicates which level of the response hand factor each image belongs to.

    Copy and paste the matrix above into Factor matrix box and click OK.

  9. We will now choose the regressors that will appear in the design matrix. We will ask SPM to model our interaction - select Main effects & interactions New: Interaction.

  10. Under factor numbers, specify the factors you want to investigate in your interaction. In our case 1 2.

    Top tip

    The first column of your factor matrix (i.e. participant index) is not counted as a factor by SPM, hence why for main effects and interactions we give the second and third columns indices 1 and 2, respectively.

  11. From the drop-down menu panel, select SPM Stats Model estimation.

  12. Navigate to Model estimation in the left-hand panel of the batch window.
  13. Press Select SPM.mat Dependency Factorial design specification: SPM.mat file OK.
  14. From the drop-down menu panel, select SPM Stats Contrast manager.
  15. Within the Contrast manager, click on Select SPM.mat Dependency Model estimation: SPM.mat file OK.
  16. You can now start specifying your contrasts of interest in Contrast sessions. We will specify F-contrasts rather than T-contrasts, to show both positive and negative effects.
  17. Select Contrast sessions New: F-contrast.
  18. Name your contrast, Name Specify... main effect of handedness.
  19. Specify your contrast weight, Weights matrix Specify... 1 1 -1 -1.
  20. Now, do the same for the main effect of response hand - Contrast sessions New: F-contrast. Name Specify... main effect of response hand. Weights matrix Specify... 1 -1 1 -1.
  21. And now do this for the interaction, Contrast sessions New: F-contrast. Name Specify... interaction. Weights matrix Specify... 1 -1 -1 1.
  22. When you’re ready, save your batch and press to run your analysis.

Your design matrix will have four columns corresponding to the elements of the interaction:

  • Left-handed * left response hand
  • Left-handed * right response hand
  • Right-handed * left response hand
  • Right-handed * right response hand

Viewing the results

Let’s inspect the results. Load each contrast image adjusting the thresholds as needed (for a reminder on how to do that, see the one sample t-test tutorial). You will notice that while we observe a main effect of response hand, there are no main effects of handedness or interaction effects that survive multiple comparisons correction.