In neuroimaging, functional magnetic resonance imaging (fMRI) measures the blood-oxygenation-level dependent (BOLD) signal in the brain. The degree of correlation of the BOLD signal in spatially independent regions of the brain defines the functional connectivity of those regions. During a cognitive fMRI task, a psychophysiological interaction (PPI) analysis can be used to examine changes in the functional connectivity during specific contexts defined by the cognitive task. An example of such a task is one that engages the memory system, asking participants to learn pairs of unrelated words (encoding) and recall the second word in a pair when presented with the first word (retrieval). In the present study, we used this type of associative memory task and a generalized PPI (gPPI) analysis to compare changes in hippocampal connectivity in older adults who are carriers of the Alzheimer's disease (AD) genetic risk factor apolipoprotein-E epsilon-4 (APOEε4). Specifically, we show that the functional connectivity of subregions of the hippocampus changes during encoding and retrieval, the two active phases of the associative memory task. Context-dependent changes in functional connectivity of the hippocampus were significantly different in carriers of APOEε4 compared to non-carriers. PPI analyses make it possible to examine changes in functional connectivity, distinct from univariate main effects, and to compare these changes across groups. Thus, a PPI analysis may reveal complex task effects in specific cohorts that traditional univariate methods do not capture. PPI analyses cannot, however, determine directionality or causality between functionally connected regions. Nevertheless, PPI analyses provide powerful means for generating specific hypotheses regarding functional relationships, which can be tested using causal models. As the brain is increasingly described in terms of connectivity and networks, PPI is an important method for analyzing fMRI task data that is in line with the current conception of the human brain.