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Objectives We compared associations between self-reported and HearCheck screening device measures of hearing difficulty with subsequent general and domain-specific cognitive function in a population-based sample of older English adults.Design Observational cohort study.Setting Population-based sample of older adults in wave 7 of the English Longitudinal Study of Ageing (ELSA) in 2014/15 and its Healthy Cognitive Ageing Project (HCAP) in 2018.Participants N=1119 adults aged ≥62 years.Primary outcome measures Factor scores for general cognitive function and domains of memory, language, orientation and executive function were derived from the HCAP neuropsychological test battery (mean of 0 and SD of 1 for each). Hearing difficulty was assessed using a self-reported 5-point Likert-type scale and the HearCheck screening device, which administered a series of six tones in each ear.Results According to the HearCheck device, 48% of participants had a mild or moderate-to-severe hearing difficulty, while 25% self-reported fair or poor hearing. In multivariable-adjusted, population-weighted linear regression models, hearing difficulty identified via HearCheck was associated with worse general cognitive function (β=−0.34 SD units; 95% CI −0.60 to –0.07 for moderate-to-severe hearing difficulty vs good hearing) as well as worse function in domains of memory, language and executive function, each with a dose-response relationship. Self-reported hearing difficulty was not associated with general or domain-specific cognitive function.Conclusions Peripheral hearing ability, as captured by the HearCheck screening device, may have stronger relevance for later-life cognitive outcomes than the broader construct of perceived hearing difficulty in one’s daily environment that is captured by a self-reported measure.