Immediately therefore I sent to thee; and thou hast well done that thou art come. Now therefore are we all here present before God, to hear all things that are commanded thee of God.
While Peter yet spake these words, the Holy Ghost fell on all them which heard the Word.
And he commanded them to be baptized in the Name of the Lord. Then prayed they him to tarry certain days.
And he took them the same hour of the night, and washed their stripes; and was baptized, he and all his, straightway.
And Crispus, the chief ruler of the synagogue, believed on the Lord with all his house; and many of the Corinthians hearing believed, and were baptized.
I thank God that I baptized none of you, but Crispus and Gaius;
Lest any should say that I had baptized in mine own name.
And I baptized also the household of Stephanas: besides, I know not whether I baptized any other.
-I Corinthians 1:14-16
In every case, Scripture clearly emphasizes that not only the believing adult, but also the adult's entire household, was baptized. "And a certain woman named Lydia, a seller of purple, of the city of Thyatira, which worshipped God, heard us: whose heart the Lord opened, that she attended unto the things which were spoken of Paul. And when she was baptized, and her household, she besought us, saying, If ye have judged me to be faithful to the Lord, come into my house, and abide there. And she constrained us"
When a new form of administration of God's covenant and church was introduced in the Old Testament, such as circumcision with Abraham, we read that the believing adult was first circumcised and then his family (or household) with him, "In the selfsame day was Abraham circumcised, and Ishmael his son. And all the men of his home, born in the house, and bought with money of the stranger, were circumcised with him" (Genesis 17:26-27).
When the New Testament form of administration was introduced we find the very same procedure. First, believing adults were baptized, but in every case where the baptized had a family and the family was present, the entire family (or household) was also baptized. When John the Baptist ushered in the ecclesiastical form of God's covenant and church (treating Jew and Gentile alike and proclaiming that all need cleansing baptism) he began by baptizing adults. When the apostles observed the beginning of God's worldwide covenant administration, they began by baptizing adults. When the church began its mission outreach to new areas, they began by preaching the Word, and when adults believed and confessed their belief, they were baptized.
Therefore the Reformed view does not disagree with that of the Baptist when considering the establishment of a new form of administration of God's covenant or the preaching of the gospel in a new area. God commands that when a new gospel beginning is made in a new mission area, in a new family, or with a new hearer (one outside of God's covenant and church), then adults must first hear, believe, and confess their belief before they may be baptized. This is clearly taught in Jesus' great mission command to His church, "And He said unto them, Go ye into all the world, and preach the gospel to every creature. He that believeth and is baptized shall be saved; but he that believeth not, shall be damned"