An experiment on a threshold discrimination task with four response categories was conducted to check the implicit assumptions of a threshold discrimination task with three response categories. Consideration of a task with three response categories, for example, “stronger,”“don't know,” and “weaker,” leads us to anticipate a relation between position parameters and that between the sizes of scale parameters of a model for a task with four response categories, such as, “stronger,”“probably stronger,”“probably weaker,” and “weaker.” That is, position parameters will be equidistant between adjacent categories and the middle scale parameter will be the largest. The results of the experiment on a four‐category task did not support these anticipated relation, and a possibility of biases in the estimation of point of subjective equality (PSE), using a three‐category task is pointed out. As an alternative to a three‐category task, a four‐category task is suggested when more than two categories are required.