Having trouble locating working definitions of this phrase online and wondered if any statisticians were aboot the hoose.

After defining the ‘group’ and the ‘control group’, I am also wondering about the means and methodology of actually making comparisons (between the two groups) - obviously they would tend to be numeric, but . . . but . . . then I fall off the cliff.

Is there a regular group of functions or equations that I might access ?

That’s too generic a phrase to answer the question you’re asking.

Control groups come from scientific research. If you want, for example, to find out if such-and-such a medication reduced your risk of diabetes, you’d get a group of people taking the meds, and a group of people not taking the meds (the control group, against which you measure the drug’s efficacy), monitor them for a certain period, see who got diabetes, and compare the rates of the two groups.

The quantitative nature of the comparison and the specific statistical tools used will be guided by what exactly is being measured.

In statistics, you have two alternate hypotheses, and you’re evaluating which is more likely to be true. Usually one hypotheses is “nothing special here”, and the other is “somethings up”. You take measurements. You run these numbers through statistical formulas, which tell you how likely you are to see the measurements you saw. This is often expressed as a p-value. For example, a p-value of 0.01 means that if the “nothing special here” hypothesis is true, you’d see measurements like you saw only 1% of the time. That seems pretty unlikely, so you figure that’s not true, and that there is indeed “somethings up.” (5% is the standard scientific threshold.)

Control groups are one aspect of good experimental design. If you’re examing the effect of a new drug (for example), you want to design the experiment so that instead of just saying “somethings up”, you can say “the drug caused this effect”. But you can only say that if you rule out all the other things that could lead to the effect. A control group is a separate set of patients who are like your experimental group in every way, except the actual drug. The more alike they are, the more valid the experiment. For instance, you shouldn’t pick one group that starts off healthier than the other, you should assign them to groups randomly. You don’t want one group to know they are taking the drug and the other doesn’t, maybe that knowledge itself will change the outcome. The doctors and measurers shouldn’t know either. This is called double-blinding.

Having a well-designed control group allows you to say that any differences between the two groups outcomes are due solely to whatever it is that’s different between them (hopefully the thing you’re interested in).

Finally, the equations. For simple comparisons of averages, the t-test is what you’re looking for. For multiple groups, you want the ANOVA test. Googling those will get you the formulas, and they are also built into lots of software (Excel has siimple t-tests). It can get complicated. Feel free to post more details of how your experiment is designed, and SDMB can help.

Bonus knowledge - Fun Statistical History Factoid!: The first scientific experiment to use control groups was measuring the effects of various treatments on scurvy victims. The use of a control group led to the conclusion that fruits and vegetables helped. This knowledge spread through the English navy, and soon their sailors were known as “limeys” for all the limes they were eating.

In drug versus no drug experiments, the control group wouldn’t be given no drug because researchers have to compare against the placebo effect as well. At least one control group would need to be administered something that looks or feels like the drug. These may be sugar pills or saline injections for instance.

The statistics part of the question really requires you to take a course in statistics. It is rather involved. However, the end result is that you end with with a probability that any differences between the groups are “statistically significant”. That doesn’t mean that the differences are in the direction you thought that they would be in nor that the effects are all that large. It just tells you the probability that any effects you find are not due to chance.

Thanks all three of you, I appreciate your responses. I now know where I am. Fwiw I’ve heard the phrase used often but in indirect contexts, and just wanted check whether I could make use of the methodology – I’ll muse over that for a few days and let it settle in.

muttrox - Thank you in particular for your respose, and thanks even more for this suggestion.

I don’t know if you can help with this, but it’s today’s issue; I have a range of numbers the lower end of which is 25 and the upper is 95.

What I’m fiddling with today is how to convert 60.5 (within the range 25:95) into a percent.

If it helps any, I have Excel and have just installed SPSS but, regarding the latter, I don’t yet know if I’m walking or on horseback.

I don’t know how to answer your question about the range without knowing more about what those numbers represent and the whole picture. If you’re talking about people’s height, then it seems about average, if you’re talking about survival time in weeks from a stage IV gliablastoma, then it would iimply something very different, if you’re talking about sales prices of 2-room condos in East Point Georgia, it means something different yet.

The context of the numbers is important. People who “lie with statistics” do it by fooling around with the context until they get what they want.

I have a lot of numbers that fall within the range 25.0 to 95.0 i.e. no numbers within my set are greater than 95 and no numbers are less than 25.

Now say one of the numbers within my set is 60.0
What I’d like to do - in order to work more easily with the data - is to convert 60.0 into a percentage figure where 25 = 0% and 95 = 100%
60.0 is actually easy to convert as it lays mid point (between 25 and 95) and converts to 50%.

Ah, sure. The range is 70 (90-25). Take any number, and subtract 25 from it (to align everything at zero). Then divide that by 70 (the range) to get the percent. So 60.5 goes to 35.5 (60.5-25) goes to 50.7% (35.5 / 70).