Rasch measures of form constancy of letters and numbers, and letters in words for young children

Document Type

Book Chapter


Nova Science Publishers


Faculty of Education and Arts


School of Education / Fogarty Learning Centre




This chapter was originally published as: Richmond, J. E., Waugh, R. F., & Konza, D. M. (2010). Rasch measures of form constancy of letters and numbers, and letters in words for young children. In Russell Waugh (Eds.). Specialized Rasch measures applied at the forefront of education (pp. 67-84). Hauppauge, New York: Nova Science Publishers.Original book available here.


English and number literacy are very important topics and the Australian Government runs numeracy and literacy tests, administered through the State Education Departments, for all Year 3 (8 years old), Year 5 (10 years old) and Year 7 (12 years old) students. Results of these tests are reported to schools and parents with a view to ensuring that all children meet certain literacy standards and that children who are ‘falling behind’ are detected early so that remedial work can be given. Rasch measures were then created with the RUMM2020 computer program for visual discrimination regarding Form Constancy of Letters and Numbers (FCL&N) and Letters in Words (LinW). The student sample was N=324 pre-primary and primary students in Perth, Western Australia, aged 4-9 years old. Data on 24 items for FCL&N and 75 items for LinW, where each item was scored in one of two categories (wrong scored zero and correct scored one), were Rasch analysed to create two linear scales. Six of the initial 24 items for FCL&N were deleted due to item misfit statistics, leaving 18 items. Forty-one of the original 75 items for LinW were deleted due to item misfit, leaving 34 items. The final data for FCL&N and LinW were used to create two highly reliable, linear, uni-dimensional scales (Student Separation Indices of 0.94 and 0.97 and Cronbach Alphas of 0.94 and 0.97, respectively) where the items are ordered from easy to hard and the student measures from low to high on the same scale. The two scales showed no statistically significant interaction of student measures on item difficulties along the scale, meaning that there was good agreement about the item difficulties along each scale, and each scale was unidimensional. The item-trait chi-squares are respectively, χ² = 69.69, df=54, p=0.07, and χ² = 117.59, df=102, p=0.14. The fit residual statistics for each of the two scales was reasonable and the targeting was reasonable.