Documentation: Added BSc student documentation on an example 2nd-level analyses

Author: JohnAshburner

docs/tutorials/beginners/fmri/second_level_example.md

@@ -0,0 +1,99 @@
+# Second-level analysis example
+The material here is for students doing the **CLNE0068: Research Methods and Data Analysis in Human Neuroscience** course at UCL.
+
+First of all, create a folder to save your results into.
+Then start MATLAB and type
+```matlab
+spm fmri
+```
+
+## Loading participant information
+
+Age and sex of the participants is stored in a spreadsheet.
+You can load this information into MATLAB by typing the following:
+```matlab
+filename = 'S:\FBS_CLNE0068\Data\Faces\Subject_details.xlsx';
+contents = readmatrix(filename,'OutputType','string')
+subjects = contents(:,1);              % Participants
+age      = str2double(contents(:,2));  % Convert text into numbers
+sex      = double(contents(:,3)=="F"); % One denotes female, zero denotes male
+```
+
+This gives `age` and `sex` variables in the MATLAB workspace that can be entered into a design matrix.
+
+
+## Specify 2nd-level
+Press the `Specify 2nd-level` button on the "Menu" window to get a `Factorial design specification` job in the batch editor.
+Modify the design so it looks like the following
+```matlab
+Directory                            [specify the directory you created]
+Design
+ . Multiple regression
+ . . Scans                           [select the 1st-leve contrast images]
+ . . Covariates
+ . . . Covariate
+ . . . . Vector                      [enter the age variable]
+ . . . . Name                        age
+ . . . . Centering                   Overall mean
+ . . . Covariate
+ . . . . Vector                      [enter the sex variable]
+ . . . . Name                        sex
+ . . . . Centering                   Overall mean
+ . . Intercept                       Include Intercept
+Covariates
+Multiple covariates
+Masking
+ . Threshold masking
+ . . None
+ . Implicit mask                     Yes
+ . Explicit mask
+Global calculation
+ . Omit
+Global normalisation
+ . Overall grand mean scaling
+ . . No
+ . Normalisation                     None
+```
+You can save this as `second_level_spec_job.m` and click the green run button (unless you've forgotten anything) to save the specification.
+
+Once this has finished, you can `Review` the model if you like, and then press the `Estimate` button on the "Menu" window.
+Select the `SPM.mat` file that has just been created and press the green run button.
+Wait a little while until this finished before going on to looking at the results.
+
+
+## 2nd-level Results
+Press the `Results` button on the "Menu" window and select the `SPM.mat` file in order to open the contrast manager.
+there are a few things you could look at from this model.
+Remember that the columns of the design matrix correspond with:
+
+1. `mean` - a column of ones to model the mean
+2. `age` - the participants' ages (years)
+3. `sex` - whether or not the participants are female (1=female, 0=male)
+
+
+### Main Effect
+When the aim is to assess whether the average values in the contrast image are greater than zero, we can simply assess the first beta image, which encodes the mean.
+The t contrast vector to do this is
+```matlab
+1 0 0
+```
+Note that this is an ANCOVA model because effects of age and sex are covaried out.
+
+### Any age effect
+Age is encoded by the second column of the design matrix.
+To see both positive and negative age effects, we would need a two-tailed t test.
+This can be achieved using an F contrast of
+```matlab
+0 1 0
+```
+With data from only 16 participants and three columns in theh design matrix, the statistical analyses have only 13 degrees of freedom.
+It may therefore not be very sensitive to age-related effects.
+
+### Any age or sex effect
+Now we are intersted in any variance explained by the second and third columns of the design matrix.
+This can be done using the following F contrast:
+```matlab
+0 1 0
+0 0 1
+```
+

docs/tutorials/beginners/index.md

@@ -32,5 +32,6 @@
 
     * [fMRI Overview](fmri/index.md)
     * [fMRI Preprocessing](fmri/preprocessing.md)
-    * [fMRI First Level](fmri/first_level.md)
+    * [fMRI First-level](fmri/first_level.md)
+    * [fMRI Second-level Example](fmri/second_level_example.md)
 

mkdocs.yml

@@ -84,9 +84,10 @@ nav:
           - 'Statistical Tests':          'tutorials/beginners/linear_model.md'
           - 'Haemodynamic Modelling':     'tutorials/beginners/haemodynamic_modelling.md'
         - 'fMRI analysis':
-            - 'Overview': 'tutorials/beginners/fmri/index.md'
+            - 'Overview':      'tutorials/beginners/fmri/index.md'
             - 'Preprocessing': 'tutorials/beginners/fmri/preprocessing.md'
-            - 'First-level': 'tutorials/beginners/fmri/first_level.md'
+            - 'First-level':   'tutorials/beginners/fmri/first_level.md'
+            - 'Second-level':  'tutorials/beginners/fmri/second_level_example.md'
       - 'fMRI':
         - 'tutorials/fmri/index.md'
         - 'Block design fMRI':