First- and higher-order factor analyses are explained from a conceptual rather than a mathematical perspective. A case is made for performing higher-order factor analysis when factors are theoretically related. Actual scores of 301 children on 24 ability measures are used to demonstrate interpretation of second-order factors using the FORTRAN program SECONDOR. Higher-order factor analysis using interpretation aids such as the Schmid-Leiman (1957) solution allows the researcher to examine a complex world in a parsimonious manner. Seven tables illustrate the discussion. (Contains 11 references.) (Author/SLD)