The contrary is not established even when households are mentioned, as far as the record of Scripture is concerned. Noah's household consisted of adults—in all, eight souls. The house of Stephanas "devoted themselves to the saints for service." This implies that its members were old enough for this, and so to profess individual acceptance of the Word, thereupon being baptized and so received into the sphere where "one Lord, one faith, one baptism" is owned. Nothing in the record of Acts 16 warrants the supposition that it was otherwise in Lydia's house or that of the jailer.
If we are to consider them as warranting the practice of baptizing believers' households, it seems remarkable that such are not referred to when baptism was administered to the many who believed, as in Acts 2, 8, and 18. Doubtless it was not the general thing then any more than now for entire households to believe, rather indeed the exception. So may not those mentioned— Lydia, the jailer, Crispus, and Stephanas—be brought forward as an evidence of special power in the work, inasmuch as on these occasions not simply individuals were reached, one or two in families, but entire households brought to profess acceptance of the Word?
In any case, it does not seem that from the facts of the history itself, we can definitely establish any other conclusion than that those able to hear and accept the Word preached were subjects of Christian baptism.