Here's an example of an experiment with a proper control group.
1. Buy 10 brand new footballs and leave them all in the same room of your house for 24 hours.
2. Take them out of the box and number them 1-10. Measure the beginning PSIs of each.
3. Mix them up, randomly select five balls and take them outside in the cold and rain. Make sure they are stored in the same spot outside and not moved or interacted with in any way.
4. Leave them there for two hours and measure the PSI. Immediately go inside and measure the PSI of the five balls inside the house using the same gauge. Log your findings. Repeat after two more hours.
5. Calculate the decreases in the PSIs for both groups.
6. Assume that the differences you found were due to environmental conditions, as you have CONTROLLED for any other differences between the two groups.
Note how these two groups of balls were completely alike in every way before the experiment started. All brand new. All unboxed at the same time. All stored in the same place for a day. Same number of balls in eeach group. In a true experiment, there is just ONE action (e.g., taking the balls outside) done to one group, and no action done to the other; this way, you can be more certain that the action is what caused the differences you saw. We must make the two groups as similar as possible, so that the only material difference between the two is the intervention that you're testing. A true scientist is never absolutely certain of anything, so we must eliminate as much doubt as we can.
What if, instead of keeping the balls in the same room overnight, you split them up and put half in your garage, basement, or attic, or a room with a dehumidifier running, or maybe a kitchen where food was being cooked? Would you be as sure of your results? Maybe your results would be the same as the ones above, but your comfort level would not be nearly as high. There would be more doubt that other factors could have contributed to the differences you saw.
The Patriots footballs, and those of the Colts, were prepared by different people, from different teams, at different times, in different places, and they were prepared using different techniques. They were inflated to different beginning PSIs by different pumps and measured by different gauges. Yes, before kickoff, they were measured by the same referee, but this hardly nullifies any differences that existed between the footballs. After being taken outside to the field, where it was cold and rainy, the balls were stored on different sidelines and were handled and used for game play by different players on different teams for different amounts of time.
At halftime, eleven balls were selected from the Patriots' group, and four for the Colts' group, for retesting. The same official (with an assistant) measured the footballs using the same gauge (as well as another gauge), and it was disovered that the Patriots' balls had lost more PSI than the Colts' had. Exponent, the research firm hired by the NFL to study this data, declared that the Colts' footballs were a "control group". In other words, their opinion was that the two groups were exactly alike in every way, and that if there was a material difference between the PSIs, that it "more probably than not" was due to human tampering.
Based on what you have learned above, was Exponent correct about all factors being equal? Were these two groups similar enough to assume there were no material differences?