Methods have been developed to measure the effectiveness of many roughages, but few evaluations have been conducted with tropical feeds. The objectives of this research were to determine the effectiveness of roughage sources based on bioassay and laboratory methods and identify the biological attributes of the diets that correlate with these methods. Six ruminally cannulated Nellore steers (408 +/- 12 kg of BW) were randomly assigned to a 6 x 6 Latin square design within six diets: negative control diet (NC) with aNDF as 10\% from corn silage (CS); positive control diet (PC) with aNDF as 20\% from CS; and four diets containing 10\% aNDF from CS and 10\% aNDF from each of the following sources: sugarcane (SC), sugarcane bagasse (SCB), soybean hulls (SH), or low oil cottonseed hulls (LOCH). Physical effectiveness factor (pef, related to the physical characteristics of aNDF) and effectiveness factor (ef, related to the ruminal pH) were determined based on a linear model approach that uses a bioassay method in which CS aNDF was assumed to be the standard fiber source. Laboratory methods to estimate pef of roughage sources were based on the proportion of DM of roughage retained on a 1.18-mm sieve pef(>1.18 mm) or retained on the 8.0-mm Penn State Particle Separator screen pef(>8.0 mm). The pef calculated by the bioassay method (total chewing time and ruminal mat resistance) for CS, SCB, and SC were higher values (P < 0.05) compared with SH and LOCH. The pef(rumen mat) of SC and SCB were higher (P < 0.05) than that of CS, SH, and LOCH. The pef(rumen mat) of LOCH was 61\% higher than SH. The ef(rumen pH) of SC and LOCH was higher (P < 0.05) than CS and SH. The pef(chewing, min/d), pef(chewing, min/kg of DM), pef(rumen mat), and ef(rumen pH) positively correlated with rumination time, total chewing time, and ruminal mat resistance (values from transit time in seconds). No correlation was observed (P > 0.05) between pef(>8.0 mm) and rumination time, chewing time, and ruminal pH. The pef calculated using the bioassay method as well as pef (>8.0 mm) were negatively correlated with rumen pH (P > 0.05). The values of the effectiveness of fiber sources obtained in this research can be used as a guideline for nutritionists aiming to replace roughage sources from tropical regions in beef cattle finishing diets. Under our conditions, the pef using the bioassay method or laboratory methods were not adequate in predicting ruminal pH.