We examine how the choice of CT x-ray beam filtration and phantom size influences patient dose (D) to computed tomography dose index (CTDI) conversion factors (i.e. D/CTDI). The ratio of head to body phantom CTDI(w) for a defined scan technique is alpha, and the ratio of organ dose when the body filter is changed to the head filter is beta. CTDI and organ doses were obtained using the ImPACT CT patient dosimetry calculator, and values of alpha and beta were determined for 39 CT scanners. The average value of alpha for the 39 CT scanners covering a 20 year period was 1.99 +/- 0.23, but 30% of scanners had alpha values that differed by more than 10% from the average. For GE, the value of alpha has been approximately constant at approximately 2.0. Both Philips and Siemens show a definite upward trend from values well below 2.0 in the early 1990s to well over 2.0 for their latest models. The data for Toshiba show no overall trend with time with half the data points below 2.0 and the remainder above this value. The average value of beta was 1.09 +/- 0.25. All vendors showed a downward trend in the beta parameter, and where the most recent scanners from each vendor had a beta value close to unity. Our results show that average D/CTDI conversion factors for a body phantom/filter combination are typically double those appropriate for a head phantom/filter combination.