This study investigates the question of test bias to develop an index of the appropriateness of a test to a particular socioeconomic or racial-ethnic group. Bias is defined as an item by race interaction in an analysis-of-variance design. The sample of 172 third graders at two integrated schools in a large California school district, included 26 white students, 20 Blacks, 64 Mexican-Americans, and 37 Orientals. In order to obtain the initial information about item by race interaction, the Stanford Achievement Test, Paragraph Meaning subtest was used. Item regression data for six racial pairings were inspected: Whites/Blacks; Whites/Mexican-Americans; Whites/Orientals; Blacks/Mexican-Americans; Black/Orientals; and Mexican-Americans/Orientals. Various methods of establishing the existence and nature of test bias are discussed, with the conclusion that test bias cannot be conclusively demonstrated in a wholly satisfactory manner. One method was nontheless selected and applied to test items administrated to two field-test schools for the purpose of investigating bias. The results of that small-scale study are discussed, but do not offer compelling reasons for the observed racial ethnic differences. (Author/LS)