The measurement of linear accelerator head scatter factors or in-air output factors, Sc, with columnar miniphantoms is refined in this work. Columnar miniphantoms are constructed from water equivalent materials: solid water and M3, and materials with higher mass density and atomic number: copper and lead. The change in the value of Sc from a 4-cm X 4-cm to a 40-cm X 40-cm field is different by 22% +/- 3%, 18% +/- 2%, and 10% +/- 3% for 6, 15, and 23 MV x rays, respectively, when measured with water equivalent or lead miniphantoms of 10 gm/cm2 depth. Based on measurements of transmission factors in solid-water miniphantoms of different depths, it is demonstrated that the beam energy spectra decreases in energy with increased field size. These changes in beam energy spectra alter the transmission and scatter of radiation and buildup of the dose in the miniphantom even if the miniphantom is made of water-equivalent material. These changes underlie the alteration in Sc when measured by miniphantoms fabricated from materials of different atomic number. It is shown that miniphantoms designed with a depth just adequate to stop contamination electrons will minimize these distortions due to transmission and scatter of radiation and buildup of dose in the miniphantom. Use of a miniphantom constructed from water-equivalent material with a depth appropriate for the x-ray energy being measured is the preferred method for determining Sc for dosimetry in water.