Before presenting statistical procedures for testing differences of item parameters, it is important to first provide a general understanding of the different parameter estimation models and their associated parameters. These include the one-, two-, and three-parameter logistic (PL) models. All these models assume a single underling latent trait or ability. All three of these models have an item difficulty parameter denoted "b". For the 1PL and 2PL models, the "b" parameter corresponds to the inflection point on the ability scale, as mentioned above. In the case of the 3PL model, the inflection corresponds to 1 + c/2 where "c" is a lower asymptote (discussed below). Difficulty values, in theory, can range from -∞ to +∞; however in practice they rarely exceed ±3. Higher values are indicative of harder test items. Items exhibiting low "b" parameters are easy test items. Another parameter that is estimated is a discrimination parameter designated "a" . This parameter pertains to an item's ability to discriminate among individuals. The "a" parameter is estimated in the 2PL and 3PL models. In the case of the 1PL model, this parameter is constrained to be equal between groups. In relation to ICCs, the "a" parameter is the slope of the inflection point. As mentioned earlier, the slope is maximal at the inflection point. The "a" parameter, similar to the "b" parameter, can range from -∞ to +∞; however typical values are less than 2. In this case, higher value indicate greater discrimination between individuals. The 3PL model has an additional parameter referred to as a "guessing" or pseudochance parameter and is denoted by "c". This corresponds to a lower asymptote which essentially allows for the possibility of an individual to get a moderate or difficult item correct even if they are low in ability. Values for "c" range between 0 and 1, however typically fall below .3.