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Place Markers let you know where in the sequence a particular random number falls (by marking it with a small number immediately to the left).
Examples:
With Place Markers Off, your results will look something like this:
Set #1: 2, 17, 23, 42, 50
Set #2: 5, 3, 42, 18, 20
This is the default layout Research Randomizer uses.
With Place Markers Within, your results will look something like this:
Set #1: p1=2, p2=17, p3=23, p4=42, p5=50
Set #2: p1=5, p2=3, p3=42, p4=18, p5=20
This layout allows you to know instantly that the number 23 is the third number in Set #1, whereas the number 18 is the fourth number in Set #2.
Notice that with this option, the Place Markers begin again at p1 in each set.
With Place Markers Across, your results will look something like this:
Set #1: p1=2, p2=17, p3=23, p4=42, p5=50
Set #2: p6=5, p7=3, p8=42, p9=18, p10=20
This layout allows you to know that 23 is the third number in the sequence, and 18 is the ninth number over both sets. As discussed in the Quick Tutorial, this option is especially helpful for doing random assignment by blocks.