SAN FRANCISCO — Software company Carrier IQ and a host of cellphone manufacturers fought to convince a federal judge on Wednesday that a massive privacy class action should be knocked into arbitration.

The companies argue that plaintiffs’ claims must be ejected from federal court because they signed contracts containing arbitration clauses when they bought their phones. But plaintiffs counter that the contract is irrelevant because it was struck between consumers and their carriers, which are not defendants in the case. They claim the installation of Carrier IQ’s tracking software, which logged keystrokes and other data, violated their privacy.