The phrase "greatest increase" refers to the highest amount of growth or improvement in a certain situation. It means that out of all the options or possibilities, one has experienced the biggest positive change. Full definition
Moreover, in the 1980s researchers found gains in literacy were associated with greater increases in life expectancy than gains in wealth were. (newscientist.com)
In particular, individuals with greater increases in fat inside the abdominal cavity showed substantial increases in metabolic risk factors including high blood sugar, high triglycerides and low HDL, or good cholesterol. (sciencedaily.com)
There also was a significant gender difference with mothers of boys showing greater increase in depression and anxiety as the level of attachment avoidance increased. (kci.go.kr)