If the value of one of a firm’s ratios is cut in half, can we be sure that the firm’s condition has improved?

No. While a decrease in some ratios indicates improvement (collection period is an example), this is not true for ratios in general. For many ratios, higher is better (for example, inventory turnover). Still other ratios, such as the current ratio, indicate a worsened condition if they go in either direction from an accepted central value.