tools for experimental design:

Command: randomizer, selectitems

The randomizer is a tool for generating pseudorandomized sequences, often required in EEG and MEG experimental design, that relies on a large number of trials for event-related averaging. Most often, the sequence must not be predictable by the subject, to avoid expectancy effects. Non-predictable condition sequences have equal transition probabilities from one condition to any other, and the randomizer-program helps you create such sequencies, by creating a large number of these sequencies and selecting the best for your experiment. Sequence vectors are displayed and saved in Presentation-Control-Language format to be used with Presentation Software.

First, enter the number of factors of your experimental design and hit return - the active factor popupmenu then contains as many entries, one for each factor. For instance, consider a 3 X 2 - design with the following number of trials per cell

First, select faktor1 as active and enter the number of gradations. Hit return and note the change of the entry for the active factor: faktor1 with 2 gradations becomes faktor1_2. Then enter the number of  trials for each gradation as vector (e.g. 90 90), and hit return. Note again the change of the factor entries in the popupmenu: faktor1_23 becomes faktor1_2*90 90.Then select the second factor as active and enter 3 gradations and 60 60 60 as Trialvector (faktor2_3*60 60 60). The total number of trials must be equal for all factors and is displayed as signal length on the bottom of the randomizer window.
The resulting sequence for this setup will be a vector of 180 numbers, with 30 ones, 30 twos, 30 threes, 30 fours, 30 fives and 30 sixes in random order.

You can select a number of further restrictions concerning the order of the condition numbers in the sequence:
The repititions-box allows you to enter a maximum number of allowed repetitions of the same condition in the sequence: entering  a 3 will result in a sequence where the same condition is allowed to occur at maximum 3 times in a row. Use  -1 to specify no limits on repitions and deactivate the radiobutton or enter 0 to exclude any repition.
The exclusion-box allows you to specify condition number, that are not allowed to be adjacent to each other. For instance entering 1 4 will result in a squence, where each 4 is preceded and followed by any number but a 1, and each 1 is preceded or followed by any number but a 4.
The factor exclusion-radiobuttonallows you to avoid repetitions of a factor gradation: if activated the sequence will not contain adjacent condition numbers, that share a gradation of the same factor.
The optimize transition probabilites-radiobutton decides how the sequence is generated: if inactive, only one sequence is generated and displayed. For this sequence, the repitition and exclusion limits are taken into account, but no further optimization is performed. If active however, the generated sequence is optimized for equal transition probabilites within the limitations imposed by the repitition and exclusion parameters. This is done by generating a large number of sequences to obtain an estimation for the expected transition probability matrix of a randomly generated sequence. Each sequence is then scored by calculating the "distance" (as sum of elementwise absolute differences) from this expected transition probability matrix, and a low distancefrom the expected matrix will indicate a well balanced sequence. The distances are displayed as a frequency histogram and will often be normally distributed.

Click on the left part of the histogram to specify a maximum allowed distance. The next sequence that will score below this threshold is selected and displayed.

The result if saved by default to a textfile. A sample output is shown below:

Randomizer:

Reihe mit 180 Elementen bestehend aus 6 verschiedenen Zahlen:
(mit beliebiger Wiederholung)

Übergangswahrscheinlichkeiten:

7    2    5    7    5    4   
6    6    4    4    5    5   
6    5    5    3    5    6   
2    8    6    5    5    4   
5    6    5    5    3    6   
3    3    5    6    7    5