  In this paper, the statistical studies on the force-freeness of photosphere
magnetic fields are given. The studies are based on the vector magnetic fields
observed by Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) on board
Hinode. Three parameters ($F_{x}/ F_{p}$, $F_{y}/ F_{p}$, and $F_{z}/ F_{p}$)
are introduced to investigate the force-freeness of active regions photosphere
magnetic field. Various thresholds and reductions of original resolutions are
selected to calculated parameters. As for the resolutions, the reductions of
original resolution data by a factor of 2, 4 and 8 are applied. While for
thresholds, they are calculated from individual active region with the average
of 75/77/57 G for $B_{x}$/$B_{y}$/$B_{z}$ for all original data. When the
resolution are reduced by 2, 4 and 8, the corresponding averages are 72/75/55,
66/68/49 and 57/59/41 G for $B_{x}$/$B_{y}$/$B_{z}$, respectively. It is found
that the forces indicated by $F_{x}/ F_{p}$ and $F_{y}/ F_{p}$ increase as
thresholds/resolutions increase/decrease. While for $F_{z}/ F_{p}$ the trends
become more complex. For low threshold, when the resolution decrease the trends
of $F_{z}/ F_{p}$ are similar as those of $F_{x}/ F_{p}$ and $F_{y}/ F_{p}$,
while for high threshold the trends of $F_{z}/ F_{p}$ are different from those
of $F_{x}/ F_{p}$ and $F_{y}/ F_{p}$. For original resolution, the forces
indicated by $F_{y}/ F_{p}$ increase as thresholds increase, while for others
resolution they decrease as the thresholds increase contrarily.
