These are methodological criticisms and alternatives in regards to Connellan et al. (2006). For any of this to make sense, you will need to follow this link and read the original paper.
However, to give you the gist of what's going on, Connellan et al., did a study where the experimenter used her own face as stimuli for empathising. This has been criticised by Cordelia Fine and others as poor experimental methodology as her face could have unconsciously moved eliciting more face-looking time from females, while her hand could have unconsciously moved the mobile around to encourage more looking time from males. I address criticisms and methodological alternatives.
With due respect to Ms. Connellan’s physical appearance, all babies show preference for attractive faces over unattractive faces (Langlois, Ritter, Roggman, & Vaughn, 1991). Resulting differences then may simply be that for female infants, Connellan’s face was marginally more attractive than an alien mobile and for male infants, Connellan’s face was marginally less attractive than the alien mobile. In this way, evaluating attractiveness may also be in relation to the position the infant was in when the stimuli were presented: with the infant lying on their back or sat upright in their mother’s lap (Fine, 2010).