Random assignment within groups with a restricting condition

[Mor Zahavi]

I have data on the volume of transactions in markets and the market category.

input market_id market_volume str20 market_category
1 100 "Big"
2 100 "Big"
3 50 "Medium" 
4 50 "Medium" 
5 10 "Small"
6 10 "Small"
end

I wish to divide the markets into 2 groups randomly - Control and Test. However, it is important that:

1. Each category will be roughly equally represented in the control and test groups.

2. The number of transactions in the control and test groups will be roughly the same.

Ideally, the random process would produce something like this:

input market_id market_volume str20 market_category random_assignment
1 100 "Big"    1
2 100 "Big"    0
3 50 "Medium" 1
4 50 "Medium" 0
5 10 "Small" 1
6 10 "Small" 0
end

How do I make this random assignment with the restrictions stated?

[George Ford]

Dividing into groups using a uniform random number doesn't produce nearly equal means between the groups?

[Andrew Musau]

I wish to divide the markets into 2 groups randomly - Control and Test. However, it is important that:

1. Each category will be roughly equally represented in the control and test groups.

2. The number of transactions in the control and test groups will be roughly the same.

\(\text{Random}\; +\; \text{restrictions}\; =\; \text{Non random}\). Consider an exaggerated example:

Item 1: Weight 1: 20
Item 2: Weight 2: 5000
Item 3: Weight 3: 80
Item 4: Weight 4: 100
Item 5: Weight 5: 0

I wish to randomly choose 2 items and I would like their weight to be 100. I pick items 1 and 3 or items 4 and 5. Fine, you may argue that I should toss a coin to choose between these two options. In any case, do random draws and keep those that satisfy your conditions. Then draw randomly among these.

[George Ford]

g u = runiform()
g group1 = u<0.5
g group2 = 1 - group1