We present a statistical study on dense molecular gas tracers of HCN (4-3), HCO+ (4-3) lines and molecular tracers of [C I], and CO observations for a sample of 26 infrared bright star-forming (SF) galaxies. We investigate the dependence of dense gas star formation efficiency traced by HCN (4-3), HCO+ (4-3) (that is L-IR/L-HCN(') (4-3), and LIR/L-HCO+(')(4-3)), and luminosity ratio of L-HCN(')(4-3)/L-HCO+(')(4-3) on [C I]-CO ratios of L-[C (')(I] (1-0))/LCO (1-0), L[C I](2-1)'/L-CO (1-0()') and L-[C I](2-1)(')/L-[C I] (1-0)(') (hereafter R-[CI]) which are sensitive to interstellar medium condi...