PANDA tutorial, for students and coworkers: This is a short and simple introduction on how to analyze saccades. Students will be introduced to reaction times, histograms, selection vectors, and cumulative probability.

After you have followed a Matlab Introduction course (or have read the first chapters of Matlab for Neuroscientists), you may want to try your newly-found MatLab powers at analyzing actual data. The data for this tutorial can be found here. The PANDA toolbox is also required, together with an index m-file. The data for this tutorial is from one subject (BC), from a study on audiovisual integration.

Specifically, this data is obtained from our study on Auditory-Visual Interactions Subserving Goal-Directed Saccades in a Complex Scene. In this study, subjects had to search for a light, a sound or both among a large number of distractor lights and sounds. The task was to respond as rapidly as possible by generating a voluntary rapid eye movement or saccade. We concluded that responses to a synchronously-presented light and sound followed a "best of both worlds" principle: they were as fast as auditory saccades, yet as accurate as visual saccades. What you will be doing in this tutorial, is determining whether subject BC was faster for audiovisual stimuli than for the auditory or visual stimuli, when the sound lagged the light by 100 ms.

First, you need to load the data into the MatLab workspace. For this, you have to go to the directory where you stored the data and type:

cd('C:\DATA'); load('AVsaccade.mat');This action will produce a matrix stored in the MatLab workspace called

>> whos Name Size Bytes Class Attributes sac 412x7 32200 double

In each *row* of the *sac* matrix **all** saccade parameters of **one** particular saccade are stored. Vice versa, each column of the *sac* matrix represents **one** particular parameter for **all** saccades. The saccade parameters of each column can be obtained in MATLAB by typing:

>> index And [[http:www.mbfys.ru.nl/staff/m.vanwanrooij/Downloads/index.m|this m-file]] will display in the command window: Rows Each row contains saccade parameters for a single trial Columns: 1 Trial Number 2 Saccade Latency [ms] 3 Saccade Amplitude [deg] 4 Saccade direction [deg] 5 Saccade Duration [ms] 6 Peak Saccade Velocity [deg/s] 7 Modality (1 - Visual 2 - Auditory -6 dB 3 - Auditory -18 dB 4 - Audiovisual -6dB 5 - Audiovisual -18 dB)

Below, the first ten rows of the sac matrix parameters are listed:

>> sac(1:10,:) ans = 1.0000 224.0000 12.5494 295.7188 48.0000 458.1762 4.0000 4.0000 310.0000 16.2406 46.2253 60.0000 449.6114 5.0000 7.0000 354.0000 14.6940 271.6397 56.0000 431.0925 1.0000 17.0000 484.0000 15.5194 211.1216 60.0000 431.1098 1.0000 18.0000 290.0000 20.8366 196.1716 72.0000 420.6550 3.0000 19.0000 258.0000 12.7184 96.0820 54.0000 389.2359 3.0000 23.0000 358.0000 16.8306 244.8486 62.0000 455.7257 3.0000 24.0000 322.0000 13.7645 290.5611 54.0000 417.3952 3.0000 32.0000 248.0000 19.7672 3.1488 74.0000 422.2016 5.0000 39.0000 306.0000 17.1490 288.7840 60.0000 497.6191 5.0000

To reiterate, saccades are listed in subsequent rows. From the first column (Trial Number according to *index*), you can see that you are missing some trials, as the numbers are not consecutive.

- Is this because the saccades are randomly placed within the matrix causing you to miss some trial numbers in the first ten rows (e.g. if you
sort

the trial numbers, do you find 412unique

consecutive trial numbers from 1 to 412) or are some trials actually absent from the sac matrix? - The second row contains saccade latency, or reaction time (in ms). This is the time it takes to respond with a saccade after the onset of the target. The last (7th) row tells you the modality of the target: 1 means the stimulus was visual, 2 and 3 are auditory stimuli, 4 and 5 are audiovisual targets. This column tells us that of the first ten saccades of the matrix, two were visually-guided, four were aurally-guided, and four were audiovisual. How many visual trials were there in total? And how many were auditory and visual?

Next, you have to determine which modality elicits the fastest responses. What is the mean reaction time for visual, auditory, and audiovisual responses? Make the same figure as plotted above.

- use
hist

to make histograms of the reaction times for each modality (use selection vectors to select for each modality. Use 20-msec wide bins, starting at 0 and ending at 600). - Plot these histograms (probability vs reaction time), use red for visual ('r'), blue for auditory ('b'), and green for audiovisual ('g') responses in a single graph: hold on. Use correct labeling:
xlabel ylabel legend

- Note that on the y-axis probability is plotted, not the number of responses per reaction time bin (as obtained by
*hist*). You have to normalize by the total number of saccades:length size sum

It is more informative to express the reaction time distributions as cumulative percentage probabilities on a probit scale (i.e. inverted gaussian) as a function of the reciprocal reaction time (-1/RT). In this manner, Gaussian distributions will appear as a straight line. Try this out yourself (or have a look here).

And here is an example code that can create the graph as shown above. Try to write this code yourself first! Note the use of:

- sub-functions
- clear labeling of the m-file and the graphics

function webtutorial_sac % WEBTUTORIAL_SAC % % An m-file producing the graph in the Saccade Introduction Tutorial</p> % Main function % First, let us clear data and plots clear all close all clc % Now let's load the data % Make sure that you are in the correct directory! % cd('C:\DATA'); load AVsaccade %% Let's make a historgam % Bins x = 0:20:600; % Probability PV = getprob(sac,1,x); % Visual PA = getprob(sac,2:3,x); % Auditory PAV = getprob(sac,4:5,x); % Audiovisual %% And let's plot these distributions figure(1) plot(x,PV,'r','LineWidth',2); hold on plot(x,PA,'b','LineWidth',2); plot(x,PAV,'g','LineWidth',2); axis square xlabel('Reaction time (ms)'); ylabel('Probability'); xlim([100 500]) legend('Visual','Auditory','Audiovisual'); function P = getprob(sac,mod,x) % Sub-function % P = GETPROB(SAC,MOD,X) % Get reaction time probability distribution P for saccades SAC with % modality MOD, at bins X. sel = ismember(sac(:,7),mod); N = hist(sac(sel,2),x); P = N/sum(N);