Rejoinder to : Who Assumes the Burden of Proof When There's No Neutral Null Hypothesis?

We welcome the chance to respond to Millar and Kruk's (2014) comment primarily because this gives us an opportunity to expand on an issue that we think deserves broader consideration: Where does the burden of proof lie when there is no neutral null hypothesis? Tests of statistical significance continue to rely on the null hypothesis testing premise. Scientists do not reject the null hypothesis unless statistically significant (pVehement debates have erupted among child custody experts and advocates about whether it is potentially harmful or beneficial for very young children to spend frequent overnights away from the residential parent with their nonresident parent, typically overnights spent with a father away from a mother (e.g., Lamb & Kelly, 2001; Sroufe & McIntosh, 2011). To date, arguments have been based largely on interpretations of attachment theory or studies of attachment security in relation to other topics (e.g., child care). With only three, limited prior studies on the specific issue, we conducted a secondary analysis using the Fragile Families data set, which had the advantages of including (a) a representative sample (albeit only of 20 major U.S. cities with a population over 200,000), (b) measures of overnight contact and attachment security (assessments rarely obtained in large-scale demographic studies), and (c) data collected for the purposes other than testing a highly charged issue that might be influenced by experimenter bias. Our own interpretation of attachment theory, research, and clinical experience led us to hypothesize that frequent overnights would, in fact, predict an increased risk for attachment insecurity among infants and toddlers.Consistent with our hypothesis, a statistically significant univariate analysis found that attachment insecurity was highest among infants (birth to age 1) who had frequent overnights with their nonresident parents (43% insecure) compared to infants with some overnights (16% insecure) or day contact only (25% insecure). Of course, families were not randomly assigned to contact groups, so we used multivariate analyses to control for multiple, potentially relevant selection variables (while noting throughout that correlation does not mean causation). In this analysis, the comparison between the frequent- and some-overnights groups remained statistically significant in the predicted direction (frequent overnights were associated with higher rates of attachment insecurity), even though fathers in the frequent-overnights group were rated by mothers as being better fathers and as having a better relationship with the mother.In their critique, Millar and Kruk reiterate some methodological limitations of our research, make two clear misstatements in interpreting statistical results, and repeatedly misrepresent how we presented our findings. Let us address each of these issues. …