# Meaning of "adjusted mean difference" in a study

From a news report:

Khandaker and colleagues found that participants who were exposed to infections, especially in early childhood, were more likely to have lower IQ (adjusted mean difference for infection at birth to age 1 year = –1.61; 95% CI, –1.74 to –1.47) and increased risk for nonaffective psychosis in adulthood (adjusted HR = 1.19; 95% CI, 1.06-1.33).

What is "adjusted mean difference" in plain English? I found that "mean difference" can have two meanings, but either is hard to understand. And what is adjusted in this case? How was it adjusted? And what is "difference"? What was subtracted from what?

I looked up the original publication in JAMA (free full text):

Cox regression was used to calculate the hazard ratio (HR) and 95% confidence interval for NAP (non-affective psychosis) for those exposed to childhood infection compared with those who were unexposed. Linear regression was used to calculate the mean difference in IQ between those exposed to childhood infection compared with unexposed.

Did they first calculate the mean IQ for the group with infections, then the mean IQ for the group without infection, and then subtracted one figure from the other? And finally, they adjusted this difference? Or did they first adjust (I don't know how) each of the two figures, before subtraction?

• "Adjusted" implies they controlled for covariates, so it likely wasn't as simple as subtracting one group estimate from another. Your first clue is the sentence beginning "The Medical Birth Registry and the Population and Housing Census data were used for birth-related and sociodemographic data..." The existence of a section called "Adjustment for Covariates" confirms what I have surmised. More information is available in the "Statistical Analysis" section.
– whuber
Commented Feb 20, 2018 at 5:00
• @whuber - were numerous pairs of figures used in subtraction? Or was it a single subtraction in the end? (I've just read the Statistical Analysis section and understood several words here and there). Were numerous subtractions made, and then a mean calculated for the obtained differences? If yes, how did they pair persons with and without infection? Commented Feb 20, 2018 at 5:10