I quote Keolu's quote....

"The children who won the lottery were awarded “free” (taxpayer-paid) access to pre-kindergarten Head Start services, while the others either did not attend preschool or sought out alternatives to Head Start."

The other children went into OTHER preschool  or were identified to have stimulation at home - home care with an adult. This is the control group. 

Here's what the quote says about the study results...

"For the four-year old group, compared to similarly (CONTROL group) situated children not allowed access to Head Start, access to the program failed to raise the cognitive abilities of participants "

IOW the control group which went to other preschool programs had the same results. This is significant because Headstart and academic programs claim to do better than regular preschool. All this shows that all preschool programs are equally good in the short run.